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pmsco-public/pmsco/edac/edac_all.cpp
matthias muntwiler acea809e4e update public distribution 
based on internal repository c9a2ac8 2019-01-03 16:04:57 +0100
tagged rev-master-2.0.0
2019-01-31 15:45:02 +01:00

15225 lines
711 KiB
C++
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#ifdef jga_edac
#else
#define jga_edac 1
#ifdef jga_jga
#else
#define jga_jga 1
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <math.h>
#define numero double
numero
pi = 3.141592653589793238462643,
au_eV = 27.2113834,
a0_au = 0.529177208,
nm = 10/a0_au,
c_au = 137.03599976;
#define infinite 1.0e20
#define infinity 1.0e20
#define infinite_int 10000
#define infinitesimal 1.0e-20
int verbose=0;
int relativistic_flag=1;
void relativistic_on (void) {c_au = 137.03599976; relativistic_flag=1;}
void relativistic_off(void) {c_au = 137035.99976; relativistic_flag=0;}
typedef enum {electrones, fotones, sonido} particle_type_def;
particle_type_def particle_type=fotones;
FILE *foutput=stdout;
#define fact_max 100
#define fact2_max 200
double *fact,
*fact2,
*ffact,
*ffact2;
int fact_initialized=0,
ffact_initialized=0;
double factorial(int n)
{
double p=1;
if(n<0) {printf("fact: negative number"); return 1;}
while(n) p*=n--;
return p;
}
int init_fact(void)
{
if(fact_initialized) return 0;
int n;
fact = new double [fact_max+1]; fact_initialized=1;
fact2 = new double [fact2_max+1];
fact[0]=fact2[0]=1;
for(n=1; n<=fact_max; n++) {fact[n]=n*fact[n-1]; fact2[n]=sqrt(fact[n]);}
for(n=fact_max+1; n<=fact2_max; n++) fact2[n]=sqrt(n)*fact2[n-1];
return 0;
}
int init_ffact(void)
{
if(ffact_initialized) return 0;
int n; init_fact();
ffact = new double [fact2_max+1]; ffact_initialized=1;
ffact2 = new double [fact2_max+1];
ffact[0]=ffact2[0]=ffact[1]=1; ffact2[1]=sqrt(pi);
for(n=2; n<=fact2_max; n++) {
ffact[n]=n*ffact[n-2];
if(n%2==0) ffact2[n]=fact[n/2-1];
else ffact2[n]=(n-2)*(ffact2[n-2]/2);
}
return 0;
}
numero combination(int n, int k)
{
if(fact_initialized) return (fact[n] /(fact[k] *fact[n-k] ));
else return (factorial(n)/(factorial(k)*factorial(n-k)));
}
numero sqr(numero a) {return a*a;}
int sqr(int i) {return i*i;}
numero ABS(numero a) {return (a<0)?-a:a;}
int ABS(int i) {return (i<0)?-i:i;}
numero SIGN(numero a) {return (a<0)?-1:((a>0)?1:0);}
int SIGN(int i) {return (i<0)?-1:((i>0)?1:0);}
int sign_1l(int l) {if(l%2) return -1; return 1;}
numero *copy(numero *x, int n)
{
numero *val; val=new numero [n];
int i;
for(i=0; i<n; i++) val[i]=x[i];
return val;
}
int *copy(int *x, int n)
{
int *val; val=new int [n];
int i;
for(i=0; i<n; i++) val[i]=x[i];
return val;
}
void cartesian_to_spherical_mu(numero x, numero y, numero z,
numero &d, numero &cth, numero &fi)
{
d=sqrt(x*x+y*y+z*z);
cth=z/d;
if(!x&&!y) fi=0; else fi=atan2(y,x);
}
void cartesian_to_spherical(numero x, numero y, numero z,
numero &d, numero &th, numero &fi)
{
cartesian_to_spherical_mu(x,y,z, d,th,fi);
if(th>1) th=0; else if(th<-1) th=pi;
th=acos(th);
}
void normalize_angles(numero &th, numero &fi)
{
while(th>pi) th-=2*pi; while(th<-pi) th+=2*pi;
if(th<0) {th=-th; fi=pi+fi;}
while(fi>pi) fi-=2*pi; while(fi<=-pi) fi+=2*pi;
}
int strcmpC(char *str1, char *str2)
{
return strcmp(str1,str2);
}
char read_command[80];
void read_name(FILE *f, char *command)
{
fscanf(f,"%s",command); char c; int i;
if(strlen(command)>1)
if(command[0]=='/' && command[1]=='*') {
c=1;
do {
fscanf(f,"%s",command); i=strlen(command);
if(i>1) if(command[i-2]=='*') if(command[i-1]=='/') c=0;
} while(c);
read_name(f, command);
} else
if(command[0]=='/' && command[1]=='/') {
do fscanf(f,"%c",&c); while(c!='\n');
read_name(f,command);
} }
numero read_numero(char *command)
{
if(!strcmpC(command,"infinite")) return infinity;
if(!strcmpC(command,"infinity")) return infinity;
if(!strcmpC(command,"zero")) return 0;
return atof(command);
}
int read_int(char *command)
{
if(!strcmpC(command,"infinite")) return 3*infinite_int;
if(!strcmpC(command,"infinity")) return 3*infinite_int;
if(!strcmpC(command,"all")) return 2*infinite_int;
if(!strcmpC(command,"zero")) return 0;
if(!strcmpC(command,"off")) return 0;
if(!strcmpC(command,"on")) return 1;
return atoi(command);
}
numero read_numero(FILE *f)
{
read_name(f,read_command);
return read_numero(read_command);
}
int read_int(FILE *f)
{
read_name(f,read_command);
return read_int(read_command);
}
numero read_numero(void) {return read_numero(stdout);}
int read_int(void) {return read_int(stdout);}
char ftostr_data[50];
char *ftostr(double x, int d)
{
if(d>0) if(x-floor(x)==0) return ftostr(x,0);
char *val,*v; val=ftostr_data; v=val;
double dec=1e20, eps=1e-12;
int i=0, j;
if(x<0) {val[i]='-'; i++; x=ABS(x);}
while(floor(x/dec+eps)==0 && dec>1) dec=dec/10;
while(dec>=1) {
j=((int) floor(x/dec+eps));
x=x-j*dec; val[i]='0'+j; i++; dec=dec/10;
}
if(ABS(x)>eps) {
val[i]='.'; i++;
while(d) {
j=int(floor(x/dec+eps)); x=x-j*dec;
if(d==1 && j<9) if(x/dec>=0.5) j++;
val[i]='0'+j; i++; dec=dec/10;
d--;
} }
val[i]='\0';
return v;
}
void on_warning(FILE *fout, char *where, char *com1, numero x, char *com2)
{fprintf(fout,"*** warning in '%s': %s %g %s\n",where,com1,x,com2);}
void on_error(FILE *fout, char *where, char *com1, numero x, char *com2)
{fprintf(fout,"*** error in '%s': %s %g %s\n",where,com1,x,com2); exit(1);}
void on_warning(FILE *fout, char *where, char *com1, char *com2)
{fprintf(fout,"*** warning in '%s': %s %s\n",where,com1,com2);}
void on_error(FILE *fout, char *where, char *com1, char *com2)
{fprintf(fout,"*** error in '%s': %s %s\n",where,com1,com2); exit(1);}
void on_warning(FILE *fout, char *where, char *com)
{fprintf(fout,"*** warning in '%s': %s\n",where,com);}
void on_error(FILE *fout, char *where, char *com)
{fprintf(fout,"*** error in '%s': %s\n",where,com); exit(1);}
void on_warning(char *where, char *com1, numero x, char *com2)
{on_warning(foutput, where,com1,x,com2);}
void on_error(char *where, char *com1, numero x, char *com2)
{on_error(foutput, where,com1,x,com2);}
void on_warning(char *where, char *com1, char *com2)
{on_warning(foutput, where,com1,com2);}
void on_error(char *where, char *com1, char *com2)
{on_error(foutput, where,com1,com2);}
void on_warning(char *where, char *com) {on_warning(foutput, where,com);}
void on_error(char *where, char *com) {on_error(foutput, where,com);}
#endif
#ifdef jga_constants
#else
#define jga_constants 1
numero
c_mks = 2.99792458e+8,
e_mks = 1.60217646e-19,
hbar_mks= 1.0545716e-34,
kb_mks = 1.3806503e-23,
kb_au = 3.1668151e-06,
G_mks = 6.673e-11,
s_mks = 5.6704e-8,
Na = 6.022142e+23,
au_m = 0.529177208e-10,
au_kg = 9.1093819e-31,
au_s = 2.4188843e-17,
au_v = 2.18769125e+6,
amu_au = 1822.88848,
mp_au = 1836.15267,
mn_au = 1838.711873,
g_electron=-2.0023193043737,
ee = 2.718281828459045235360287,
g_Euler = 0.577215664901532860606512;
#endif
#ifdef jga_files
#else
#define jga_files 1
FILE *open_file(FILE *fout, char *name, char *mode)
{
FILE *ff; ff=NULL;
if(!strcmpC(name,"inline")) return stdin;
if(!strcmpC(name,"terminal")) return stdout;
if(strcmpC(name,"none"))
if((ff=fopen(name,mode))==NULL)
on_error(fout, "open_file", "cannot open file", name);
return ff;
}
FILE *open_file(char *name, char *mode)
{return open_file(foutput,name,mode);}
void close_file(FILE *ff)
{if(ff!=NULL && ff!=stdout && ff!=stdin) fclose(ff);}
void skip(FILE *fin, int ls)
{
int i; char c;
for(i=0; i<ls; i++) do fscanf(fin,"%c",&c); while(c!='\n' && !feof(fin));
}
int number_of_columns(int ls, char *name)
{
FILE *fin;
int nc=0;
char c;
fin=open_file(name,"r");
skip(fin,ls);
if(!feof(fin)) {
do fscanf(fin,"%c",&c); while(c==' '||c=='\t'||c=='\n');
do {nc++; do fscanf(fin,"%c",&c); while(c!=' '&&c!='\t'&&c!='\n');
if(c!='\n') do fscanf(fin,"%c",&c); while(c==' '||c=='\t');
} while(c!='\n');
}
close_file(fin);
return nc;
}
int number_of_words(int ls, char *name)
{
FILE *fin;
char palabra[80];
int nw=-1;
fin=open_file(name,"r");
skip(fin,ls);
if(!feof(fin)) do {fscanf(fin,"%s",palabra); nw++;} while(!feof(fin));
close_file(fin);
return nw;
}
int number_of_rows(int ls, char *name)
{
int nc=number_of_columns(ls,name);
int nw=number_of_words(ls,name);
if(nw%nc!=0) on_warning("number_of_rows", "unstructured file");
return nw/nc;
}
int number_of_chars(int ls, char *name)
{
FILE *fin;
int nc=0;
char c;
fin=open_file(name,"r");
skip(fin,ls);
if(!feof(fin)) do {fscanf(fin,"%c",&c); nc++;} while(!feof(fin));
close_file(fin);
return nc;
}
int number_of_columns(char *name) {return number_of_columns(0,name);}
int number_of_words (char *name) {return number_of_words (0,name);}
int number_of_rows (char *name) {return number_of_rows (0,name);}
int number_of_chars (char *name) {return number_of_chars (0,name);}
void limit_values(int ls, char *name, int &nc,
numero *vmin, numero *vmax, numero *vave)
{
FILE *fin;
int nr=number_of_rows(ls,name); nc=number_of_columns(ls,name);
int i,j;
float v;
for(j=0; j<nc; j++) {vmin[j]=infinity; vmax[j]=-infinity; vave[j]=0;}
fin=open_file(name,"r");
skip(fin,ls);
for(i=0; i<nr; i++)
for(j=0; j<nc; j++) {
fscanf(fin,"%f",&v); vave[j]+=v;
if(v>vmax[j]) vmax[j]=v;
if(v<vmin[j]) vmin[j]=v;
}
close_file(fin);
for(j=0; j<nc; j++) vave[j]=vave[j]/nr;
}
#endif
#ifdef jga_time
#else
#define jga_time 1
#define time_seconds 0.000001
numero time_initial=clock(),
time_partial=0,
time_total=0;
void time_update(void)
{
numero time_temp=clock();
time_partial+=time_temp-time_initial;
time_initial=time_temp;
}
void time_print(FILE *fout)
{
time_update(); time_total+=time_partial;
fprintf(fout, "--- Time: total=%4.2f sec, partial= %4.2f sec.\n",
time_total*time_seconds,
time_partial*time_seconds);
time_partial=0;
}
void time_print(void) {time_print(foutput);}
#endif
#ifdef jga_cg
#else
#define jga_cg 1
double Clebsch_Gordan(int a, int b, int c, int alpha, int beta, int gamma)
{
double delabc,term1,term2=0,term3; int nu=0;
init_fact();
if(alpha + beta != gamma || a<0 || b<0 || c<0 ||
ABS(alpha)>a || ABS(beta)>b || ABS(gamma)>c ||
c<ABS(a-b) || a+b<c) return 0;
delabc = ((fact2[a+b-c]/fact2[a+b+c+1]) * fact2[a+c-b]) * fact2[b+c-a];
term1 = sqrt((2*c+1))*fact2[a+alpha]*fact2[a-alpha]*fact2[b+beta];
term1 *= fact2[b-beta]*fact2[c+gamma]*fact2[c-gamma];
while((nu <= (a-alpha)) && (nu <= (b+beta)) && (nu <= (a+b-c))) {
if((c-b+alpha+nu >= 0) && (c-a-beta+nu >= 0)) {
term3 = ((((((term1/fact[a-alpha-nu])/fact[c-b+alpha+nu])
/fact[b+beta -nu])/fact[c-a-beta +nu])
/fact[nu])/fact[a+b-c-nu]);
term2 += (((nu<0?-nu:nu)&1)?-term3:term3);
}
nu++;
}
return delabc*term2;
}
double Clebsch_Gordan(int a, int b, int c, int alpha, int beta)
{return Clebsch_Gordan(a,b,c,alpha,beta,alpha+beta);}
double Gaunt(int a, int b, int c, int alpha, int beta)
{
int gamma=alpha+beta;
if(a<0 || b<0 || c<0 ||
ABS(alpha)>a || ABS(beta)>b || ABS(gamma)>c ||
c<ABS(a-b) || a+b<c) return 0;
return sqrt((2*a+1)*(2*b+1)/(4*pi*(2*c+1)))
*Clebsch_Gordan(a,b,c,0,0,0)
*Clebsch_Gordan(a,b,c,alpha,beta,gamma);
}
double Gaunt(int a, int b, int c, int alpha, int beta, int gamma)
{
if(alpha + beta != gamma) return 0;
return Gaunt(a,b,c,alpha,beta);
}
double CGspin1_2(int j1, int j3, int m2, int m3)
{
if(j1<0 || j3<0 || m3>j3 || m3<-j3 || m3-m2>j1 || m3-m2<-j1) return 0;
if(j3==j1+1) if(m2==1) return sqrt((j1+m3+1.0)/(2*j1+2.0)); else
if(m2==-1) return sqrt((j1-m3+1.0)/(2*j1+2.0));
if(j3==j1-1) if(m2==1) return -sqrt((j1-m3+1.0)/(2*j1+2.0)); else
if(m2==-1) return sqrt((j1+m3+1.0)/(2*j1+2.0));
return 0;
}
double CGspin1(int j1, int j3, int m2, int m3)
{
if(j3==j1+2) if(m2==2) return sqrt( (j1+m3)*(j1+m3+2.0)
/((2*j1+2.0)*(2*j1+4.0))); else
if(m2==0) return sqrt( (j1-m3+2.0)*(j1+m3+2.0)
/((2*j1+2.0)*(j1+2.0))); else
if(m2==-2) return sqrt( (j1-m3)*(j1-m3+2.0)
/((2*j1+2.0)*(2*j1+4.0)));
if(j3==j1) if(m2==2) return -sqrt( (j1+m3)*(j1-m3+2.0)
/( 2*j1*(j1+2.0))); else
if(m2==0) return m3/sqrt(j1*(j1+2.0)); else
if(m2==-2) return sqrt( (j1-m3)*(j1+m3+2.0)
/( 2*j1*(j1+2.0)));
if(j3==j1-2) if(m2==2) return sqrt( (j1-m3)*(j1-m3+2.0)
/( 2*j1*(2*j1+2.0))); else
if(m2==0) return -sqrt( (j1-m3)*(j1+m3)
/( j1*(2*j1+2.0))); else
if(m2==-2) return sqrt( (j1+m3+2.0)*(j1+m3)
/( 2*j1*(2*j1+2.0)));
return 0;
}
int k_lj(int l, int j) {if(j==2*l+1) return -l-1; return l;}
void lj_k(int &l, int &j, int k)
{
if(k<0) {l=-k-1; j=2*l+1;} else {l=k; j=2*l-1;}
}
double Gaunt_spin(int k1, int k2, int mj1, int mj2, int i)
{
int j1,l1,j2,l2;
lj_k(l1,j1,k1); lj_k(l2,j2,k2); if(l1!=l2) return 0; l1=2*l1;
if(ABS(mj1)>j1 || ABS(mj2)>j2) return 0;
if(i==-1) if(mj1!=mj2-2) return 0;
else return CGspin1_2(l1,j1,-1,mj1)
* CGspin1_2(l1,j2, 1,mj2) / sqrt(2);
if(i== 0) if(mj1!=mj2 ) return 0;
else return ( CGspin1_2(l1,j1, 1,mj1)
* CGspin1_2(l1,j2, 1,mj1)
- CGspin1_2(l1,j1,-1,mj1)
* CGspin1_2(l1,j2,-1,mj1) )/2;
if(i== 1) if(mj1!=mj2+2) return 0;
else return CGspin1_2(l1,j1, 1,mj1)
* CGspin1_2(l1,j2,-1,mj2) / sqrt(2);
return 0;
}
#endif
#ifdef jga_complex
#else
#define jga_complex 1
class complex {
friend complex operator+(numero x, const complex &v);
friend complex operator+(const complex &u, numero x);
friend complex operator+(const complex &u, const complex &v);
friend complex operator-(const complex &v);
friend complex operator-(numero x, const complex &v);
friend complex operator-(const complex &u, numero x);
friend complex operator-(const complex &u, const complex &v);
friend complex operator*(numero x, const complex &v);
friend complex operator*(const complex &u, numero x);
friend complex operator*(const complex &u, const complex &v);
friend complex operator/(numero x, const complex &v);
friend complex operator/(const complex &u, numero x);
friend complex operator/(const complex &u, const complex &v);
friend numero real(const complex &v);
friend numero imag(const complex &v);
friend numero mod(const complex &v);
friend numero mod2(const complex &v);
friend complex conj(const complex &v);
friend complex exp(const complex &v);
friend complex pow(const complex &v, int m);
friend complex pow(const complex &a, numero x);
friend complex sqrt(const complex &v);
friend complex sqr(const complex &v);
friend complex log(const complex &v);
friend complex llog(const complex &v);
friend complex sin(const complex &v);
friend complex cos(const complex &v);
friend complex atan(const complex &v);
friend complex sinh(const complex &v);
friend complex cosh(const complex &v);
friend complex euler(numero a, numero b);
friend numero arg(complex a);
public:
numero &real(void);
numero &imag(void);
complex(void) {}
complex(numero re);
complex(int re);
complex(numero re, numero im);
complex(const complex &v);
complex &operator=(numero x);
complex &operator=(int x);
complex &operator=(const complex &v);
complex &operator+=(numero x);
complex &operator+=(const complex &v);
complex &operator-=(numero x);
complex &operator-=(const complex &v);
private:
numero re, im;
};
inline numero &complex::real(void)
{return re;}
inline numero &complex::imag(void)
{return im;}
inline complex::complex(numero r)
{re=r; im=0.0;}
inline complex::complex(int r)
{re=r; im=0.0;}
inline complex::complex(numero r, numero i)
{re=r; im=i;}
inline complex::complex(const complex &v)
{re=v.re; im=v.im;}
inline complex &complex::operator=(numero x)
{re=x; im=0.0; return *this;}
inline complex &complex::operator=(int x)
{re=x; im=0.0; return *this;}
inline complex &complex::operator=(const complex &v)
{re=v.re; im=v.im; return *this;}
inline complex &complex::operator+=(numero x)
{re+=x; return *this;}
inline complex &complex::operator+=(const complex &v)
{re+=v.re; im+=v.im; return *this;}
inline complex &complex::operator-=(numero x)
{re-=x; return *this;}
inline complex &complex::operator-=(const complex &v)
{re-=v.re; im-=v.im; return *this;}
inline complex operator+(numero x, const complex &v)
{return complex(x+v.re,v.im);}
inline complex operator+(const complex &u, numero x)
{return complex(u.re+x,u.im);}
inline complex operator+(const complex &u, const complex &v)
{return complex(u.re+v.re,u.im+v.im);}
inline complex operator-(const complex &v)
{return complex(-v.re,-v.im);}
inline complex operator-(numero x, const complex &v)
{return complex(x-v.re,-v.im);}
inline complex operator-(const complex &u, numero x)
{return complex(u.re-x,u.im);}
inline complex operator-(const complex &u, const complex &v)
{return complex(u.re-v.re,u.im-v.im);}
inline complex operator*(numero x, const complex &v)
{return complex(x*v.re,x*v.im);}
inline complex operator*(const complex &u, numero x)
{return complex(u.re*x,u.im*x);}
inline complex operator*(const complex &u, const complex &v)
{return complex(u.re*v.re-u.im*v.im,u.re*v.im+u.im*v.re);}
inline complex operator/(numero x, const complex &v)
{numero m=v.re*v.re+v.im*v.im;
return complex(x*v.re/m,-x*v.im/m);}
inline complex operator/(const complex &u, numero x)
{return complex(u.re/x,u.im/x);}
inline complex operator/(const complex &u, const complex &v)
{numero m=v.re*v.re+v.im*v.im;
return complex((u.re*v.re+u.im*v.im)/m,(u.im*v.re-u.re*v.im)/m);}
inline numero real(const complex &v)
{return v.re;}
inline numero imag(const complex &v)
{return v.im;}
inline numero mod(const complex &v)
{return sqrt(v.re*v.re+v.im*v.im);}
inline numero mod2(const complex &v)
{return v.re*v.re+v.im*v.im;}
inline complex conj(const complex &v)
{return complex(v.re,-v.im);}
inline complex exp(const complex &v)
{return exp(v.re)*complex(cos(v.im),sin(v.im));}
inline complex sqr(const complex &v)
{return complex(v.re*v.re-v.im*v.im, 2*(v.re*v.im));}
inline complex euler(numero a, numero b)
{return complex(a*cos(b), a*sin(b));}
inline complex sin(const complex &v)
{return complex(sin(v.re)*cosh(v.im), cos(v.re)*sinh(v.im));}
inline complex cos(const complex &v)
{return complex(cos(v.re)*cosh(v.im),-sin(v.re)*sinh(v.im));}
inline complex sinh(const complex &v)
{return (exp(v)-exp(-v))/2;}
inline complex cosh(const complex &v)
{return (exp(v)+exp(-v))/2;}
complex pow(const complex &v, int m)
{
if(m<0) return pow(1/v,-m);
if(m==0) return complex(1,0);
if(m==1) return v;
if(m==2) return v*v;
if(m%2) return v*sqr(pow(v,m/2));
return sqr(pow(v,m/2));
}
complex pow(const complex &a, numero x)
{
if(x<0) return pow(1/a,-x);
if(x==0) return complex(1,0);
return euler(pow(mod(a),x),x*arg(a));
}
complex sqrt(const complex &v)
{
if(!v.im) if(v.re<0) return complex(0,sqrt(-v.re));
else return complex(sqrt(v.re), 0);
numero a;
if(v.re>0) {
a=sqrt((v.re+sqrt(v.re*v.re+v.im*v.im))/2);
return complex(a,v.im/(2*a));
} else {
a=sqrt((-v.re+sqrt(v.re*v.re+v.im*v.im))/2);
if(v.im>=0) return complex(v.im/(2*a),a);
else return complex(-v.im/(2*a),-a);
} }
numero arg(complex a)
{
if(!a.re && !a.im) return 0;
return atan2(a.im,a.re);
}
complex log(const complex &v)
{
complex b=0;
if(!v.re && !v.im) printf(" Error: log(0)\n");
numero va=mod(v);
if(va<1e-20) return llog(v);
b.re=log(va);
if(!v.re) if(v.im>0) b.im=pi/2; else b.im=-pi/2;
else {
b.im=atan(fabs(v.im/v.re));
if(v.im<0 && v.re>0) b.im=-b.im; else
if(v.im<0 && v.re<0) b.im= b.im + pi; else
if(v.im>0 && v.re<0) b.im=-b.im + pi;
while(b.im>pi) b.im-=2*pi;
while(b.im<-pi) b.im+=2*pi;
}
return b;
}
complex llog(const complex &v)
{
numero magnitude=fabs(v.re)+fabs(v.im);
complex b=0, w=v/magnitude;
if(!v.re && !v.im) printf(" Error: llog(0)\n");
b.re=log(mod(w))+log(magnitude);
if(!v.re) if(v.im>0) b.im=pi/2; else b.im=-pi/2;
else {
b.im=atan(fabs(v.im/v.re));
if(v.im<0 && v.re>0) b.im=-b.im; else
if(v.im<0 && v.re<0) b.im= b.im + pi; else
if(v.im>0 && v.re<0) b.im=-b.im + pi;
while(b.im>pi) b.im-=2*pi;
while(b.im<-pi) b.im+=2*pi;
}
return b;
}
complex atan(const complex &v)
{
exit(0);
return complex(cos(v.re)*cosh(v.im),-sin(v.re)*sinh(v.im));
}
complex i_c(0,1);
complex i_l(int l)
{
l=l%4; if(l<0) l+=4;
if(l==0) return complex( 1, 0);
if(l==1) return complex( 0, 1);
if(l==2) return complex(-1, 0);
if(l==3) return complex( 0,-1);
return 0;
}
complex *copy(complex *x, int n)
{
complex *val; val=new complex [n];
int i;
for(i=0; i<n; i++) val[i]=x[i];
return val;
}
#endif
#ifdef jga_qfint
#else
#define jga_qfint 1
numero *qfint_xv, *qfint_wv;
int qfint_mmax=0;
int qfint_init(int mmax)
{
if(mmax<=qfint_mmax) return 0;
numero pi2=2*pi, theta;
int i,j,m;
if(qfint_mmax>0) {delete [] qfint_xv; delete [] qfint_wv;}
qfint_xv=new numero [mmax+2];
qfint_wv=new numero [mmax+2];
j=1; m=4; qfint_mmax=mmax;
do {
for(i=1; i<m; i++) if(i%2 || m==4) {
theta = i * (pi2 / m);
qfint_xv [j]= i/((numero) m) - sin (theta) / pi2;
qfint_wv [j]= 1 - cos (theta);
j++;
}
m=2*m;
} while (m<=mmax || m<=8);
return 0;
}
numero qfint(numero a, numero b, numero func(numero x), numero err, int mmax)
{
numero esm,sigmam; int i,j,m;
numero eta, e;
if(mmax>qfint_mmax) qfint_init(mmax);
if(a==b) return 0;
m=4; j=1; esm=0;
do {
sigmam=0;
for(i=1; i<m; i++) if(i%2 || m==4) {
eta=(b-a)*qfint_xv[j]+a;
sigmam+=qfint_wv[j]*func(eta);
j++;
}
sigmam=2*(b-a)/m*sigmam;
e =(esm-sigmam)/2; if(e<0) e=-e;
esm =0.5*(esm+sigmam);
m=2*m;
} while ((e>err && m<=mmax) || m<=8);
return esm;
}
#ifdef jga_complex
complex qfint(numero a, numero b, complex func(numero x), numero err, int mmax)
{
complex esm,sigmam; int i,j,m;
numero eta, e;
if(mmax>qfint_mmax) qfint_init(mmax);
if(a==b) return 0;
m=4; j=1; esm=0;
do {
sigmam=0;
for(i=1; i<m; i++) if(i%2 || m==4) {
eta=(b-a)*qfint_xv[j]+a;
sigmam+=qfint_wv[j]*func(eta);
j++;
}
sigmam=2*(b-a)/m*sigmam;
e =mod(esm-sigmam)/2;
esm =0.5*(esm+sigmam);
m=2*m;
} while ((e>err && m<=mmax) || m<=8);
return esm;
}
#endif
#endif
#ifndef jga_bessel
#define jga_bessel 1
numero chebev(numero a, numero b, numero c[], int m, numero x)
{
numero d=0,dd=0,sv,y,y2; int j;
if((x-a)*(x-b)>0) on_warning("chebev", "x not in range");
y=(2*x-a-b)/(b-a); y2=2*y;
for(j=m; j>=1; j--) {sv=d; d=y2*d-dd+c[j]; dd=sv;}
return y*d-dd+c[0]/2;
}
void beschb (numero x, numero &g1, numero &g2, numero &gamp, numero &gamm)
{
numero xx,c1[7],c2[8];
c1[0] = -1.142022680371172; c1[1] = 0.006516511267076;
c1[2] = 0.000308709017308; c1[3] = -3.470626964e-6;
c1[4] = 6.943764e-9; c1[5] = 3.678e-11;
c1[6] = -1.36e-13;
c2[0] = 1.843740587300906; c2[1] = -0.076852840844786;
c2[2] = 0.001271927136655; c2[3] = -4.971736704e-6;
c2[4] = -3.3126120e-8; c2[5] = 2.42310e-10;
c2[6] = -1.7e-13; c2[7] = -1.0e-15;
xx=8*x*x-1;
g1=chebev(-1,1,c1,6,xx); g2=chebev(-1,1,c2,7,xx);
gamp=g2-x*g1; gamm=g2+x*g1;
}
int besselJY(numero xnu, numero x, numero &rj, numero &ry,
numero &rjp, numero &ryp)
{
int i,isign=1,l,nl, maxit=100000, salir;
numero xmin=2.0, eps=1.0e-10, fpmin=1.0e-30,
a,b,br,bi,c,cr,ci,d=0,del,del1,den,di,dlr,dli,
dr,e,f,fct,fct2,fct3,ff,gam,gam1,gam2,gammi,gampl,h,
p,pimu,pimu2,q,r,rjl,rjl1,rjmu,rjp1,rjpl,rjtemp,ry1,
rymu,rymup,rytemp,sum,sum1,temp,w,x2,xi,xi2,xmu,xmu2;
if(x<=0) on_error("besselJY", "wrong argument x =", x, "");
if(xnu<0) on_error("besselJY", "wrong order n =", xnu, "");
if(x<xmin) nl=int(xnu+0.5);
else {nl=int(xnu-x+1.5); nl=0>nl?0:nl;}
xmu=xnu-nl; xmu2=xmu*xmu; xi=1/x; xi2=2*xi; w=xi2/pi; h=xnu*xi;
if(h<fpmin) h=fpmin; c=h; b=xi2*xnu;
for(i=1, salir=1; i<=maxit && salir; i++) {
b+=xi2; d=b-d; if(fabs(d)<fpmin) d=fpmin;
c=b-1/c; if(fabs(c)<fpmin) c=fpmin;
d=1/d; del=c*d; h=del*h; if(d<0) isign=-isign;
if(fabs(del-1)<eps) salir=0; else salir=1;
}
if(salir) on_warning("besselJY", "x too large");
rjl1=rjl=isign*fpmin; rjp1=rjpl=h*rjl; fct=xnu*xi;
for(l=nl; l; l--) {rjtemp=fct*rjl+rjpl;
fct-=xi; rjpl=fct*rjtemp-rjl; rjl=rjtemp;}
if(rjl==0.0) rjl=eps;
f=rjpl/rjl;
if(x<xmin) {
x2=x/2; pimu=pi*xmu;
if(fabs(pimu)<eps) fct=1; else fct=pimu/sin(pimu);
d=-log(x2); e=xmu*d;
if(fabs(e)<eps) fct2=1; else fct2=sinh(e)/e;
beschb(xmu,gam1,gam2,gampl,gammi);
ff=2/pi*fct*(gam1*cosh(e)+gam2*fct2*d);
e=exp(e); p=e/(gampl*pi);
q=1/(e*pi*gammi);
pimu2=pimu/2;
if(fabs(pimu2)<eps) fct3=1; else fct3=sin(pimu2)/pimu2;
r=pi*pimu2*fct3*fct3;
c=1; d=-x2*x2; sum=ff+r*q; sum1=p;
for(i=1, salir=1; i<=maxit && salir; i++) {
ff=(i*ff+p+q)/(i*i-xmu2); c*=d/i;
p/=(i-xmu); q/=(i+xmu); del=c*(ff+r*q);
sum+=del; del1=c*p-i*del;
sum1+=del1;
if(fabs(del)<(1+fabs(sum))*eps) salir=0; else salir=1;
}
if(salir) on_warning("besselJY", "series failed to converge");
rymu=-sum; ry1=-sum1*xi2; rymup=xmu*xi*rymu-ry1;
rjmu=w/(rymup-f*rymu);
} else {
a=0.25-xmu2; p=-xi/2; q=1; br=2*x; bi=2;
fct=a*xi/(p*p+q*q); cr=br+q*fct; ci=bi+p*fct;
den=br*br+bi*bi; dr=br/den; di=-bi/den; dlr=cr*dr-ci*di;
dli=cr*di+ci*dr; temp=p*dlr-q*dli; q=p*dli+q*dlr;
p=temp;
for(i=2, salir=1; i<=maxit && salir; i++) {
a+=2*(i-1); bi+=2; dr=a*dr+br; di=a*di+bi;
if(fabs(dr)+fabs(di)<fpmin) dr=fpmin;
fct=a/(cr*cr+ci*ci); cr=br+cr*fct; ci=bi-ci*fct;
if(fabs(cr)+fabs(ci)<fpmin) cr=fpmin;
den=dr*dr+di*di; dr=dr/den; di=-di/den;
dlr=cr*dr-ci*di; dli=cr*di+ci*dr; temp=p*dlr-q*dli;
q=p*dli+q*dlr; p=temp;
if(fabs(dlr-1)+fabs(dli)<eps) salir=0; else salir=1;
}
if(salir) on_warning("besselJY", "cf2 failed");
gam=(p-f)/q;
rjmu=sqrt(w/((p-f)*gam+q));
if(rjl<0) rjmu=-rjmu;
rymu=rjmu*gam;
rymup=rymu*(p+q/gam);
ry1=xmu*xi*rymu-rymup;
}
fct=rjmu/rjl;
rj=rjl1*fct;
rjp=rjp1*fct;
for(i=1; i<=nl; i++) {
rytemp=(xmu+i)*xi2*ry1-rymu;
rymu=ry1; ry1=rytemp;
}
ry=rymu; ryp=xnu*xi*rymu-ry1;
return 0;
}
void besselIK(numero xnu, numero x, numero &ri, numero &rk, numero &rip,
numero &rkp)
{
int maxit=100000;
int i,l,nl;
numero xmin=2.0, eps=1.0e-10, fpmin=1.0e-30,
a,a1,b,c,d,del,del1,delh,dels,e,f,fact,fact2,ff,gam1,gam2,
gammi,gampl,h,p,pimu,q,q1,q2,qnew,ril,ril1,rimu,rip1,ripl,
ritemp,rk1,rkmu,rkmup,rktemp,s,sum,sum1,x2,xi,xi2,xmu,xmu2;
if(x<=0) on_error("besselIK", "wrong argument x =", x, "");
if(xnu<0) on_error("besselIK", "wrong order n =", xnu, "");
nl=(int)(xnu+0.5);
xmu=xnu-nl;
xmu2=xmu*xmu;
xi=1.0/x;
xi2=2.0*xi;
h=xnu*xi;
if (h < fpmin) h=fpmin;
b=xi2*xnu;
d=0.0;
c=h;
for (i=1;i<=maxit;i++) {
b += xi2;
d=1.0/(b+d);
c=b+1.0/c;
del=c*d;
h=del*h;
if (fabs(del-1.0) < eps) break;
}
if (i > maxit) on_warning("besselIK", "x too large: try asymptotic expan.");
ril=fpmin;
ripl=h*ril;
ril1=ril;
rip1=ripl;
fact=xnu*xi;
for (l=nl;l>=1;l--) {
ritemp=fact*ril+ripl;
fact -= xi;
ripl=fact*ritemp+ril;
ril=ritemp;
}
f=ripl/ril;
if (x < xmin) {
x2=0.5*x;
pimu=pi*xmu;
fact = (fabs(pimu) < eps ? 1.0 : pimu/sin(pimu));
d = -log(x2);
e=xmu*d;
fact2 = (fabs(e) < eps ? 1.0 : sinh(e)/e);
beschb(xmu,gam1,gam2,gampl,gammi);
ff=fact*(gam1*cosh(e)+gam2*fact2*d);
sum=ff;
e=exp(e);
p=0.5*e/gampl;
q=0.5/(e*gammi);
c=1.0;
d=x2*x2;
sum1=p;
for (i=1;i<=maxit;i++) {
ff=(i*ff+p+q)/(i*i-xmu2);
c *= (d/i);
p /= (i-xmu);
q /= (i+xmu);
del=c*ff;
sum += del;
del1=c*(p-i*ff);
sum1 += del1;
if (fabs(del) < fabs(sum)*eps) break;
}
if (i > maxit) on_warning("besselIK", "series failed to converge");
rkmu=sum;
rk1=sum1*xi2;
} else {
b=2.0*(1.0+x);
d=1.0/b;
h=delh=d;
q1=0.0;
q2=1.0;
a1=0.25-xmu2;
q=c=a1;
a = -a1;
s=1.0+q*delh;
for (i=2;i<=maxit;i++) {
a -= 2*(i-1);
c = -a*c/i;
qnew=(q1-b*q2)/a;
q1=q2;
q2=qnew;
q += c*qnew;
b += 2.0;
d=1.0/(b+a*d);
delh=(b*d-1.0)*delh;
h += delh;
dels=q*delh;
s += dels;
if (fabs(dels/s) < eps) break;
}
if (i > maxit) on_warning("besselIK", "cf2 failed");
h=a1*h;
rkmu=sqrt(pi/(2.0*x))*exp(-x)/s;
rk1=rkmu*(xmu+x+0.5-h)*xi;
}
rkmup=xmu*xi*rkmu-rk1;
rimu=xi/(f*rkmu-rkmup);
ri=(rimu*ril1)/ril;
rip=(rimu*rip1)/ril;
for (i=1;i<=nl;i++) {
rktemp=(xmu+i)*xi2*rk1+rkmu;
rkmu=rk1;
rk1=rktemp;
}
rk=rkmu;
rkp=xnu*xi*rkmu-rk1;
}
numero besselJ0(numero x)
{
numero ax,xx,z,y,ans1,ans2;
if(x==0) return 1;
if(x<8 && x>-8) {
y = sqr(x);
ans1 = 57568490574.0+y*(-13362590354.0+y*(651619640.7
+y*(-11214424.18+y*(77392.33017+y*(-184.9052456)))));
ans2 = 57568490411.0+y*(1029532985.0+y*(9494680.718
+y*(59272.64853+y*(267.8532712+y*1.0))));
return ans1/ans2;
}
ax=x<0?-x:x; z = 8.0/ax; y = sqr(z); xx = ax-0.785398164;
ans1 = 1.0+y*(-0.1098628627e-2+y*(0.2734510407e-4
+y*(-0.2073370639e-5+y*0.2093887211e-6)));
ans2 = -0.1562499995e-1+y*(0.1430488765e-3
+y*(-0.6911147651e-5+y*(0.7621095161e-6
-y*0.934945152e-7)));
return sqrt(0.636619772/ax)*(cos(xx)*ans1-z*sin(xx)*ans2);
}
numero besselJ1(numero x)
{
numero ax,xx,z,y,ans1,ans2;
if (x==0) return 0;
if (x<8 && x>-8) {
y = sqr(x);
ans1 = x*(72362614232.0+y*(-7895059235.0+y*(242396853.1
+y*(-2972611.439+y*(15704.48260+y*(-30.16036606))))));
ans2 = 144725228442.0+y*(2300535178.0+y*(18583304.74
+y*(99447.43394+y*(376.9991397+y*1.0))));
return ans1/ans2;
}
ax = x<0?-x:x; z = 8.0/ax; y = sqr(z); xx = ax-2.356194491;
ans1 = 1.0+y*(0.183105e-2+y*(-0.3516396496e-4
+y*(0.2457520174e-5+y*(-0.240337019e-6))));
ans2 = 0.04687499995+y*(-0.2002690873e-3
+y*(0.8449199096e-5+y*(-0.88228987e-6+y*0.105787412e-6)));
return sqrt(0.636619772/ax)*(cos(xx)*ans1
-z*sin(xx)*ans2)*(x>0?1:-1);
}
numero besselJJ(int n, numero x)
{
if(n<0) if(n%2) return -besselJJ(-n,x); else return besselJJ(-n,x);
if(ABS(x)<1e-12) if(n==0) return 1; else return 0;
numero J,Y,Jp,Yp; besselJY(n,x,J,Y,Jp,Yp);
return J;
}
numero besselYY(int n, numero x)
{
if(n<0) if(n%2) return -besselJJ(-n,x); else return besselJJ(-n,x);
if(ABS(x)<1e-12) if(n==0) return 1; else return 0;
numero J,Y,Jp,Yp; besselJY(n,x,J,Y,Jp,Yp);
return Y;
}
numero besselJp(int n, numero x)
{
if(n<0) if(n%2) return -besselJp(-n,x); else return besselJp(-n,x);
if(ABS(x)<1e-12) if(n==1) return 0.5; else
if(n==-1) return -0.5; else return 0;
numero J,Y,Jp,Yp; besselJY(n,x,J,Y,Jp,Yp);
return Jp;
}
numero besselJ(int n, numero x)
{
int iacc=40, j,jsum,m;
numero bigno=1.0e10, bigni=1.0e-10,
bj,bjm,bjp,sum,tox,ans=0;
if(ABS(x)<1e-12) if(n==0) return 1; else return 0;
if(n==0) return besselJ0(x);
if(n==1) return besselJ1(x);
if(n<0) if(n%2) return -besselJ(-n,x); else return besselJ(-n,x);
tox = 2.0/x;
if(x>n) {
bjm=besselJ0(x);
bj=besselJ1(x);
for(j=1; j<n; j++) {
bjp=j*tox*bj-bjm;
bjm=bj;
bj=bjp;
}
return bj;
}
m= 2*((n+ int(floor(sqrt(1.0*(iacc*n)))) ) / 2);
jsum=0; sum=bjp=0; bj=1;
for(j=m; j>=1; j--) {
bjm=j*tox*bj-bjp;
bjp=bj;
bj=bjm;
if(bj>bigno || bj<-bigno) {
bj=bj*bigni;
bjp=bjp*bigni;
ans=ans*bigni;
sum=sum*bigni;
}
if(jsum) sum = sum+bj;
jsum = 1-jsum;
if(j==n) ans=bjp;
}
sum = 2.0*sum-bj;
return ans/sum;
}
void besseljy(int l, numero x, numero &j, numero &y)
{
numero jp,yp;
numero factor=sqrt(pi/(2*x));
besselJY(l+0.5,x,j,y,jp,yp);
j*=factor; y*=factor;
}
numero besselj(int l, numero x)
{
if(ABS(x)<1e-10) if(l==0) return 1.0; else
if(l==1) return x/3; else
if(l==2) return x*x/15; else return 0;
numero jl,yl;
besseljy(l,x,jl,yl);
return jl;
}
numero bessely(int l, numero x)
{
numero jl,yl;
besseljy(l,x,jl,yl);
return yl;
}
void besseljyp(int l, numero x, numero &jp, numero &yp)
{
numero j,y;
numero factor=sqrt(pi/(2*x));
besselJY(l+0.5,x,j,y,jp,yp);
jp=factor*(jp-j/(2*x)); yp=factor*(yp-y/(2*x));
}
numero besselI0(numero x)
{
numero ax,y;
if(-3.75<x && x<3.75) {
y=x/3.75; y=y*y;
return 1.0+y*(3.5156229+y*(3.0899424+y*(1.2067492+y*
(0.2659732+y*(0.360768e-1+y*0.45813e-2)))));
} else {
ax=(x<0)?-x:x; y=3.75/ax;
return (exp(ax)/sqrt(ax))*(0.39894228+y*(0.1328592e-1
+y*(0.225319e-2+y*(-0.157565e-2+y*(0.916281e-2
+y*(-0.2057706e-1+y*(0.2635537e-1+y*(-0.1647633e-1
+y*0.392377e-2))))))));
}
}
numero besselI1(numero x)
{
numero ax,y,ans;
if(-3.75<x && x<3.75) {
y=x/3.75; y=y*y;
return x*(0.5+y*(0.87890594+y*(0.51498869+y*(0.15084934
+y*(0.2658733e-1+y*(0.301532e-2+y*0.32411e-3))))));
} else {
ax=(x<0)?-x:x; y=3.75/ax;
ans=0.2282967e-1+y*(-0.2895312e-1+y*(0.1787654e-1-y*0.420059e-2));
ans=0.39894228+y*(-0.3988024e-1+y*(-0.362018e-2
+y*(0.163801e-2+y*(-0.1031555e-1+y*ans))));
return (exp(ax)/sqrt(ax))*ans;
}
}
numero besselK0(numero x)
{
numero y;
if(x<=2) {
y=x*x/4;
return -log(x/2.0)*besselI0(x)+(-0.57721566+y*(0.42278420
+y*(0.23069756+y*(0.3488590e-1+y*(0.262698e-2
+y*(0.10750e-3+y*0.74e-5))))));
} else {
y=2/x;
return (exp(-x)/sqrt(x))*(1.25331414+y*(-0.7832358e-1
+y*(0.2189568e-1+y*(-0.1062446e-1+y*(0.587872e-2
+y*(-0.251540e-2+y*0.53208e-3))))));
}
}
numero besselK1(numero x)
{
numero y;
if(x<=2) {
y=x*x/4;
return log(x/2.0)*besselI1(x)+(1.0/x)*(1.0+y*(0.15443144
+y*(-0.67278579+y*(-0.18156897+y*(-0.1919402e-1
+y*(-0.110404e-2+y*(-0.4686e-4)))))));
} else {
y=2/x;
return (exp(-x)/sqrt(x))*(1.25331414+y*(0.23498619
+y*(-0.3655620e-1+y*(0.1504268e-1+y*(-0.780353e-2
+y*(0.325614e-2+y*(-0.68245e-3)))))));
}
}
numero besselI(int n, numero x)
{
if(ABS(x)<1e-20) if(n==0) return 1.0; else return 0.0;
int iacc=40, j,m;
numero bigno=1.0e10,
bigni=1.0e-10,
bi=1, bim, bip=0, tox=2/x, ans=0;
if(n==0) return besselI0(x);
if(n==1) return besselI1(x);
if(n<0) n=-n;
m=2*(n+int(floor(sqrt(iacc*n))));
for(j=m; j>=1; j--) {
bim=bip+j*tox*bi; bip=bi; bi=bim;
if(bi<-bigno || bigno<bi) {
ans=ans*bigni;
bi=bi*bigni;
bip=bip*bigni;
}
if(j==n) ans=bip;
}
return ans*besselI0(x)/bi;
}
numero besselK(int n, numero x)
{
numero tox,bkp,bkm,bk;
int j;
if(n==0) return besselK0(x);
if(n==1) return besselK1(x);
if(n<0) n=-n;
tox=2/x;
bkm=besselK0(x);
bk=besselK1(x);
for(j=1; j<n; j++) {
bkp=bkm+j*tox*bk; bkm=bk; bk=bkp;
}
return bk;
}
numero besselIp(int n, numero x)
{
if(n==0) return besselI(1,x);
return (besselI(n-1,x)+besselI(n+1,x))/2;
}
numero besselKp(int n, numero x)
{
if(n==0) return -besselK(1,x);
return -(besselK(n-1,x)+besselK(n+1,x))/2;
}
#ifdef jga_complex
int besselIKexp_flag=1;
complex besselI0(complex x)
{
complex y,eax,deax; if(real(x)<0) on_error("besselI0", "real(x)<0");
if(besselIKexp_flag) {eax=exp(x); deax=1;} else {eax=1; deax=exp(-x);}
if(mod(x)<3.75) {
y=x/3.75; y=y*y;
return (1.0+y*(3.5156229+y*(3.0899424+y*(1.2067492
+y*(0.2659732+y*(0.360768e-1+y*0.45813e-2))))))*deax;
} else {
y=3.75/x;
return (eax/sqrt(x))*(0.39894228+y*(0.1328592e-1
+y*(0.225319e-2+y*(-0.157565e-2+y*(0.916281e-2
+y*(-0.2057706e-1+y*(0.2635537e-1+y*(-0.1647633e-1
+y*0.392377e-2))))))));
} }
complex besselI1(complex x)
{
complex y,ans,eax,deax; if(real(x)<0) on_error("besselI1", "real(x)<0");
if(besselIKexp_flag) {eax=exp(x); deax=1;} else {eax=1; deax=exp(-x);}
if(mod(x)<3.75) {
y=x/3.75; y=y*y;
return (x*(0.5+y*(0.87890594+y*(0.51498869+y*(0.15084934
+y*(0.2658733e-1+y*(0.301532e-2+y*0.32411e-3)))))))*deax;
} else {
y=3.75/x;
ans=0.2282967e-1+y*(-0.2895312e-1+y*(0.1787654e-1-y*0.420059e-2));
ans=0.39894228+y*(-0.3988024e-1+y*(-0.362018e-2
+y*(0.163801e-2+y*(-0.1031555e-1+y*ans))));
return (eax/sqrt(x))*ans;
} }
complex besselK0(complex x)
{
complex y,eax,deax;
if(besselIKexp_flag) {eax=exp(-x); deax=1;} else {eax=1; deax=exp(x);}
if(mod(x)<=2) {
y=x*x/4;
return (-log(x/2.0)*besselI0(x)*deax+(-0.57721566+y*(0.42278420
+y*(0.23069756+y*(0.3488590e-1+y*(0.262698e-2
+y*(0.10750e-3+y*0.74e-5)))))))*deax;
} else {
y=2/x;
return eax/sqrt(x)*(1.25331414+y*(-0.7832358e-1
+y*(0.2189568e-1+y*(-0.1062446e-1+y*(0.587872e-2
+y*(-0.251540e-2+y*0.53208e-3))))));
} }
complex besselK1(complex x)
{
complex y,eax,deax;
if(besselIKexp_flag) {eax=exp(-x); deax=1;} else {eax=1; deax=exp(x);}
if(mod(x)<=2) {
y=x*x/4;
return (log(x/2.0)*besselI1(x)*deax+(1.0/x)*(1.0+y*(0.15443144
+y*(-0.67278579+y*(-0.18156897+y*(-0.1919402e-1
+y*(-0.110404e-2+y*(-0.4686e-4))))))))*deax;
} else {
y=2/x;
return eax/sqrt(x)*(1.25331414+y*(0.23498619
+y*(-0.3655620e-1+y*(0.1504268e-1+y*(-0.780353e-2
+y*(0.325614e-2+y*(-0.68245e-3)))))));
} }
complex besselI(int n, complex x)
{
if(mod(x)<1e-20) if(n==0) return 1.0; else return 0.0;
int iacc=40, j,m;
numero bigno=1.0e10, bigni=1.0e-10;
complex bi(1,0), bim, bip(0,0), tox, ans=0; tox=2/x;
if(n<0) n=-n;
if(n==0) return besselI0(x);
if(n==1) return besselI1(x);
m=2*(n+int(floor(sqrt(iacc*n))));
for(j=m; j>=1; j--) {
bim=bip+j*tox*bi; bip=bi; bi=bim;
if(bigno<mod(bi)) {
ans=ans*bigni;
bi=bi*bigni;
bip=bip*bigni;
}
if(j==n) ans=bip;
}
return ans*besselI0(x)/bi;
}
complex besselK(int n, complex x)
{
complex tox,bkp,bkm,bk;
int j;
if(n<0) n=-n;
if(n==0) return besselK0(x);
if(n==1) return besselK1(x);
tox=2/x;
bkm=besselK0(x);
bk=besselK1(x);
for(j=1; j<n; j++) {
bkp=bkm+j*tox*bk; bkm=bk; bk=bkp;
}
return bk;
}
complex besselIp(int n, complex x)
{
if(n==0) return besselI(1,x);
return (besselI(n-1,x)+besselI(n+1,x))/2;
}
complex besselKp(int n, complex x)
{
if(n==0) return -besselK(1,x);
return -(besselK(n-1,x)+besselK(n+1,x))/2;
}
complex besselh(int l, numero x)
{
numero jl,yl;
besseljy(l,x,jl,yl);
return i_c*jl-yl;
}
complex besselhp(int l, numero x)
{
numero j,y,jp,yp;
numero factor=sqrt(pi/(2*x));
besselJY(l+0.5,x,j,y,jp,yp);
return factor*((i_c*jp-yp)-(i_c*j-y)/(2*x));
}
complex bessely(int l, complex z)
{
if(l==0) return -cos(z)/z;
if(l==1) return -(cos(z)/z+sin(z))/z;
int n;
complex yl_2, yl_1=bessely(0,z), yl=bessely(1,z);
for(n=2; n<=l; n++) {yl_2=yl_1; yl_1=yl; yl=(n+n-1)/z*yl_1-yl_2;}
return yl;
}
complex besselyp(int l, complex z)
{
if(l==0) return -bessely(1,z);
else return bessely(l-1,z)-((l+1)/z)*bessely(l,z);
}
complex besselilh(int l, complex z)
{
complex val=1, fct=1, fct1=i_c/(2*z);
int s;
init_fact();
for(s=1; s<=l; s++) {
fct=fct*fct1/s;
val=val+fct*fact[l+s]/fact[l-s];
}
return exp(i_c*z)/z * val;
}
complex besselilhp(int l, complex z)
{
if(l>0) return i_c*besselilh(l-1,z)-(l+1)/z*besselilh(l,z);
return i_c*besselilh(l+1,z)+ l/z*besselilh(l,z);
}
#ifdef jga_qfint
complex besselj_int_z;
int besselj_int_l;
complex besselj_int(numero th)
{
return cos(besselj_int_z*cos(th)) * pow(sin(th),2*besselj_int_l+1.0);
}
complex besselj(int l, complex z)
{
if(l==0) if(!real(z) && !imag(z)) return complex(1,0);
else return sin(z)/z;
if(l==1) if(!real(z) && !imag(z)) return complex(0,0);
else return (sin(z)/z-cos(z))/z;
complex coef(1,0); int i;
besselj_int_z=z;
besselj_int_l=l;
for(i=1; i<=l; i++) coef=coef*z/(2*i);
return coef * qfint(0,pi/2,besselj_int,0.00001,2048);
}
complex besseljp(int l, complex z)
{
if(l==0) return -besselj(1,z);
else return besselj(l-1,z)-((l+1)/z)*besselj(l,z);
}
complex besselh(int l, complex z)
{
if(ABS(imag(z))<infinitesimal) return besselh(l, real(z));
return i_c*besselj(l,z) -bessely(l,z);
}
complex besselhp (int l, complex z)
{
if(ABS(imag(z))<infinitesimal) return besselhp(l, real(z));
return i_c*besseljp(l,z)-besselyp(l,z);
}
complex besselh1 (int l, complex z) {return besselj(l,z) +i_c*bessely(l,z);}
complex besselh1p(int l, complex z) {return besseljp(l,z)+i_c*besselyp(l,z);}
complex besselh2 (int l, complex z) {return besselj(l,z) -i_c*bessely(l,z);}
complex besselh2p(int l, complex z) {return besseljp(l,z)-i_c*besselyp(l,z);}
void besseljh(int l, numero x, numero &j, numero &jp, complex &h, complex &hp)
{
numero y,yp, x2=2*x;
numero factor=sqrt(pi/x2);
besselJY(l+0.5,x,j,y,jp,yp);
j=factor*j; y=factor*y; h=i_c*j-y;
jp=factor*jp-j/x2; yp=factor*yp-y/x2; hp=i_c*jp-yp;
}
void besseljh(int l, complex z, complex &j, complex &jp,
complex &h, complex &hp)
{
complex y,yp, hh,hhp, b=complex(0,imag(z));
numero rj,rjp,rjj,rjjp, x=real(z);
if(ABS(imag(z))<1e-2*ABS(real(z)) && ABS(imag(z))<1e-2) {
besseljh(l, real(z), rj, rjp, h, hp);
besseljh(l+1, real(z), rjj,rjjp,hh,hhp);
j=rj+b*rjp; h=h+b*hp;
jp=rjp+b*(l/x*(rjp-rj/x)-rjjp);
hp= hp+b*(l/x*( hp- h/x)- hhp);
} else {
on_warning("besseljh", "complex z");
j=besselj(l,z); jp=besseljp(l,z);
y=bessely(l,z); yp=besselyp(l,z);
h=i_c*j-y; hp=i_c*jp-yp;
} }
#endif
#endif
#endif
#ifdef jga_spline
#else
#define jga_spline 1
class spline {
public:
numero *x, *y, *y2, a,b;
int n, interpol;
spline(void) {n=0;}
void alloc(int na, int type_interpol);
void alloc(int na) {alloc(na,0);}
void put(int na, numero xa, numero ya) {x[na]=xa; y[na]=ya;}
void add(int na, numero xa, numero ya) {x[na]+=xa; y[na]+=ya;}
void prod(numero v) {int i; for(i=0; i<n; i++) y[i]=y[i]*v;}
int init(numero yp0, numero ypn_1);
void init(void) {if(n>1) init(infinity,infinity);}
void init(numero *xx, numero *yy, int nn);
void init(numero *xx, numero *yy, int nn, int type_interpol);
numero integ(numero aa, numero bb, int l);
numero integ(numero aa, numero bb) {return integ(aa,bb,0);}
numero val(numero xx);
numero der(numero xx);
void free(void);
void find(numero xx, int &ii, int &jj);
numero integ(int k, numero aa, numero bb, int l);
numero dpow(numero aa, numero bb, int l);
};
void spline::free(void)
{
if(n>0) {delete [] x; delete [] y;}
if(n>=4 && interpol==0) delete [] y2;
n=0;
}
void spline::alloc(int na, int type_interpol)
{
free(); n=na; interpol=type_interpol;
if(n>0) {
x=new numero [n]; y=new numero [n];
for(na=0; na<n; na++) {x[na]=0; y[na]=0;}
}
if(n>=4 && interpol==0) y2=new numero [n];
}
int spline::init(numero yp0, numero ypn_1)
{
int i,k; numero p,qn,sig,un; numero *u;
if(n==0) return 0;
if(n==1) {y[0]=yp0; return 0;}
a=x[0]; b=x[n-1];
if(interpol) return 0;
u=new numero [n];
if(yp0>0.99*infinity) y2[0]=u[0]=0;
else { y2[0]=-0.5;
u[0]=3/(x[1]-x[0])*((y[1]-y[0])/(x[1]-x[0])-yp0);}
for(i=1; i<n-1; i++) {
sig=(x[i]-x[i-1])/(x[i+1]-x[i-1]);
p=sig*y2[i-1]+2;
y2[i]=(sig-1)/p;
u[i]=(y[i+1]-y[i])/(x[i+1]-x[i])
-(y[i]-y[i-1])/(x[i]-x[i-1]);
u[i]=(6*u[i]/(x[i+1]-x[i-1])-sig*u[i-1])/p;
}
if(ypn_1>0.99*infinity) qn=un=0;
else {qn=0.5;
un=3.0/(x[n-1]-x[n-2])*(ypn_1-(y[n-1]-y[n-2])/(x[n-1]-x[n-2]));}
y2[n-1]=(un-qn*u[n-2])/(qn*y2[n-2]+1);
for(k=n-2; k>=0; k--) y2[k]=y2[k]*y2[k+1]+u[k];
delete [] u; return 0;
}
numero spline::val(numero xx)
{
if(n==0) return 0;
if(n==1) return y[0];
if(n<4 && interpol==0) on_error("spline::val", "less than 4 points");
int klo,khi; numero h,bb,aa;
find(xx, klo,khi);
h=x[khi]-x[klo];
if(h==0) on_error("spline::val", "vanishing spacing");
if(interpol) return y[klo] + (y[khi]-y[klo])*(xx-x[klo])/h;
aa=(x[khi]-xx)/h;
bb=(xx-x[klo])/h;
return aa*y[klo]+bb*y[khi]+((aa*aa*aa-aa)*y2[klo]
+(bb*bb*bb-bb)*y2[khi])*h*h/6;
}
numero spline::der(numero xx)
{
if(n<=1) return 0;
if(n<4 && interpol==0) on_error("spline::der", "less than 4 points");
int klo,khi; numero h,bb,aa,ap,bp;
find(xx, klo,khi);
h=x[khi]-x[klo];
if(h==0) on_error("spline::der", "vanishing spacing");
if(interpol) return (y[khi]-y[klo])/h;
aa=(x[khi]-xx)/h; ap=-1/h;
bb=(xx-x[klo])/h; bp= 1/h;
return ap*y[klo]+bp*y[khi]+
((3*aa*aa*ap-ap)*y2[klo]+(3*bb*bb*bp-bp)*y2[khi])*h*h/6;
}
void spline::init(numero *xx, numero *yy, int nn, int type_interpol)
{
free(); n=nn; interpol=type_interpol;
if(type_interpol==0) y2=new numero [n];
x=copy(xx,n); y=copy(yy,n);
init();
}
void spline::init(numero *xx, numero *yy, int nn) {init(xx,yy,nn,0);}
void spline::find(numero xx, int &klo, int &khi)
{
int s,k;
if(x[0]>x[n-1]) s=0; else s=1;
klo=0; khi=n-1;
while(khi-klo>1) {
k=(khi+klo)/2;
if((x[k]>xx&&s)||(x[k]<xx&&s==0)) khi=k; else klo=k;
} }
numero spline::dpow(numero aa, numero bb, int l)
{
if(l!=-1) return (pow(bb,l+1.0)-pow(aa,l+1.0))/(l+1);
else return log(bb/aa);
}
numero spline::integ(int k, numero aa, numero bb, int l)
{
numero x0=x[k], x1=x[k+1];
numero h=x1-x0;
numero I0=dpow(aa,bb,l);
numero I1=dpow(aa,bb,l+1);
if(interpol) return y[k]*I0+(y[k+1]-y[k])*(I1-x[k]*I0)/h;
numero I2=dpow(aa,bb,l+2);
numero I3=dpow(aa,bb,l+3);
numero h3=h*h*h;
numero A1=(x1*I0-I1)/h;
numero B1=(I1-x0*I0)/h;
numero A3=((( I0*x1-3*I1)*x1+3*I2)*x1-I3)/h3;
numero B3=(((-I0*x0+3*I1)*x0-3*I2)*x0+I3)/h3;
return A1*y[k]+B1*y[k+1]+((A3-A1)*y2[k]+(B3-B1)*y2[k+1])*h*h/6;
}
numero spline::integ(numero aa, numero bb, int l)
{
if(n==0) return 0;
if(n==1) return y[0]*dpow(aa,bb,l);
if(n<4 && interpol==0) on_error("spline::integ", "less than 4 points");
int i, kalo,kahi,kblo,kbhi; find(aa,kalo,kahi); find(bb,kblo,kbhi);
numero val=integ(kalo,aa,x[kahi],l);
for(i=kahi; i<kblo; i++) val+=integ(i,x[i],x[i+1],l);
return val+integ(kblo,x[kblo],bb,l);
}
#ifdef jga_complex
class splinec {
public:
numero *x, a,b;
complex *y, *y2;
int n, interpol;
splinec(void) {n=0;}
void alloc(int na, int type_interpol);
void alloc(int na) {alloc(na,0);}
void put(int na, numero xa, complex ya) {x[na]=xa; y[na]=ya;}
void add(int na, numero xa, complex ya) {x[na]+=xa; y[na]+=ya;}
void prod(complex v) {int i; for(i=0; i<n; i++) y[i]=y[i]*v;}
int init(complex yp0, complex ypn_1);
void init(void) {if(n>1) init(infinity,infinity);}
void init(numero *xx, complex *yy, int nn);
complex val(numero xx);
complex der(numero xx);
void free(void);
};
void splinec::free(void)
{
if(n>0) {delete [] x; delete [] y;}
if(n>=4 && interpol==0) delete [] y2;
n=0;
}
void splinec::alloc(int na, int type_interpol)
{
free(); n=na; interpol=type_interpol;
if(n>0) {
x= new numero [n]; y= new complex [n];
for(na=0; na<n; na++) {x[na]=0; y[na]=0;}
}
if(n>=4 && interpol==0) y2=new complex [n];
}
int splinec::init(complex yp0, complex ypn_1)
{
int i,k; complex p,qn,sig,un; complex *u;
if(n==0) return 0;
if(n==1) {y[0]=yp0; return 0;}
a=x[0]; b=x[n-1];
if(interpol) return 0;
u=new complex [n];
if(real(yp0)>0.99*infinity) y2[0]=u[0]=0;
else { y2[0]=-0.5;
u[0]=3/(x[1]-x[0])*((y[1]-y[0])/(x[1]-x[0])-yp0);}
for(i=1; i<n-1; i++) {
sig=(x[i]-x[i-1])/(x[i+1]-x[i-1]);
p=sig*y2[i-1]+2;
y2[i]=(sig-1)/p;
u[i]=(y[i+1]-y[i])/(x[i+1]-x[i])
-(y[i]-y[i-1])/(x[i]-x[i-1]);
u[i]=(6*u[i]/(x[i+1]-x[i-1])-sig*u[i-1])/p;
}
if(real(ypn_1)>0.99*infinity) qn=un=0;
else {qn=0.5;
un=3.0/(x[n-1]-x[n-2])*(ypn_1-(y[n-1]-y[n-2])/(x[n-1]-x[n-2]));}
y2[n-1]=(un-qn*u[n-2])/(qn*y2[n-2]+1);
for(k=n-2; k>=0; k--) y2[k]=y2[k]*y2[k+1]+u[k];
delete [] u; return 0;
}
complex splinec::val(numero xx)
{
if(n==0) return 0;
if(n==1) return y[0];
if(n<4 && interpol==0) on_error("splinec::val", "less than 4 points");
int klo,khi,k,s; numero h,bb,aa;
if(x[0]>x[n-1]) s=0; else s=1;
klo=0; khi=n-1;
while(khi-klo>1) {
k=(khi+klo)/2;
if((x[k]>xx&&s)||(x[k]<xx&&s==0)) khi=k; else klo=k;
}
h=x[khi]-x[klo];
if(h==0) on_error("splinec::val", "vanishing spacing");
if(interpol) return y[klo] + (y[khi]-y[klo])*(xx-x[klo])/h;
aa=(x[khi]-xx)/h;
bb=(xx-x[klo])/h;
return aa*y[klo]+bb*y[khi]+((aa*aa*aa-aa)*y2[klo]
+(bb*bb*bb-bb)*y2[khi])*h*h/6;
}
complex splinec::der(numero xx)
{
if(n<=1) return 0;
if(n<4 && interpol==0) on_error("splinec::der", "less than 4 points");
int klo,khi,k,s; numero h,bb,aa,ap,bp;
if(x[0]>x[n-1]) s=0; else s=1;
klo=0; khi=n-1;
while(khi-klo>1) {
k=(khi+klo)/2;
if((x[k]>xx&&s)||(x[k]<xx&&s==0)) khi=k; else klo=k;
}
h=x[khi]-x[klo];
if(h==0) on_error("splinec::der", "vanishing spacing");
if(interpol) return (y[khi]-y[klo])/h;
aa=(x[khi]-xx)/h; ap=-1/h;
bb=(xx-x[klo])/h; bp= 1/h;
return ap*y[klo]+bp*y[khi]+
((3*aa*aa*ap-ap)*y2[klo]+(3*bb*bb*bp-bp)*y2[khi])*h*h/6;
}
void splinec::init(numero *xx, complex *yy, int nn)
{
free(); n=nn; interpol=0;
x=copy(xx,n); y=copy(yy,n); y2=new complex [n];
init();
}
#endif
#endif
#ifdef jga_legendre
#else
#define jga_legendre 1
numero legendre(int l, int m, numero x)
{
if(m<0 || m>l || x<-1 || 1<x) {
printf(" Error: Bad argument in legendre: l=%1d m=%1d x=%f\n",l,m,x);
return 0;
}
int i,ll;
numero pmm=1, somx2, fct=1, pmmp1, pll;
if(m>0) {
somx2=sqrt((1-x)*(1+x));
for(i=1; i<=m; i++, fct+=2) pmm=pmm*fct*somx2;
}
if(l==m) return pmm;
pmmp1=x*(2*m+1)*pmm;
if(l>m+1) for(ll=m+2; ll<=l; ll++) {
pll=(x*(2*ll-1)*pmmp1-(ll+m-1)*pmm)/(ll-m);
pmm=pmmp1; pmmp1=pll;
}
return pmmp1;
}
#ifdef jga_complex
complex legendre(int l, int m, complex x)
{
if(m<0 || m>l) {
printf(" Error: Bad argument in legendre: l=%1d m=%1d\n",l,m);
return complex(0,0);
}
int i,ll;
complex pmm=1, somx2, fct=1, pmmp1, pll;
if(m>0) {
somx2=sqrt((1-x)*(1+x));
for(i=1; i<=m; i++, fct+=2) pmm=pmm*fct*somx2;
}
if(l==m) return pmm;
pmmp1=x*(2*m+1)*pmm;
if(l>m+1) for(ll=m+2; ll<=l; ll++) {
pll=(x*(2*ll-1)*pmmp1-(ll+m-1)*pmm)/(ll-m);
pmm=pmmp1; pmmp1=pll;
}
return pmmp1;
}
#endif
#endif
#ifdef jga_Ylm
#else
#define jga_Ylm 1
numero Ylma(int l, int m)
{
numero a; int mm=ABS(m);
a=sqrt((l+l+1)*fact[l-mm]/(4*pi*fact[l+mm]));
if(m>0) if(m%2) return -a;
return a;
}
numero Ylmmu0(int l, int m, numero cth)
{return legendre(l,ABS(m),cth) * Ylma(l,m);}
numero Ylm0(int l, int m, numero th)
{
while(th> pi) th-=2*pi;
while(th<-pi) th+=2*pi;
return Ylmmu0(l,m,cos(th));
}
complex Ylmmu(int l, int m, numero cth, numero fi)
{return Ylmmu0(l,m,cth) * euler(1,m*fi);}
complex Ylm(int l, int m, numero th, numero fi)
{return Ylm0(l,m,th) * euler(1,m*fi);}
complex Ylmmu(int l, int m, complex cth, numero fi)
{return legendre(l,ABS(m),cth) * Ylma(l,m) * euler(1,m*fi);}
#endif
#ifdef jga_matrix
#else
#define jga_matrix 1
class matrix {
public:
int n,m,nm, sel;
complex *p;
matrix(void) {n=m=nm=sel=0;}
void free(void) {if(nm) {delete [] p;} n=m=nm=0;}
matrix(int i, int j) {nm=0; alloc(i,j);}
matrix(int i) {nm=0; alloc(i,1);}
matrix(const matrix &A);
~matrix(void) {free();}
void alloc(int i, int j);
void alloc(int i) {alloc(i,1);}
void alloc_diagonal(int i) {alloc(i,1); sel=1;}
void a(int i, int j, complex x) {p[i*m+j]=x;}
void a(int i, int j, numero x) {p[i*m+j]=x;}
void a(int i, complex x) {p[i]=x;}
void a(int i, numero x) {p[i]=x;}
void add(int i, int j, complex x) {p[i*m+j]+=x;}
void add(int i, int j, numero x) {p[i*m+j]+=x;}
void add(int i, complex x) {p[i]+=x;}
void add(int i, numero x) {p[i]+=x;}
void set_column(int j, matrix &B);
void set_row(int i, matrix &B);
complex a(int i, int j);
complex a(int i) {if(i>-1 && i<nm) return p[i]; else return complex(0,0);}
matrix &operator=(complex x);
matrix &operator=(numero x);
matrix &operator=(const matrix &A);
matrix &operator++(void);
matrix &operator--(void);
complex inv(void);
complex gaussj(const matrix &Mb, int n, int m, int opt);
complex gaussj(const matrix &Mb, int n, int m)
{return gaussj(Mb,n,m,0);}
void print(numero val);
void print(void) {print(0);}
friend matrix transpose(matrix A);
friend matrix conj(matrix A);
friend matrix operator+(complex x, matrix A);
friend matrix operator+(numero x, matrix A) {return complex(x,0)+A;};
friend matrix operator+(matrix A, complex x) {return x+A;}
friend matrix operator+(matrix A, numero x) {return x+A;}
friend matrix operator+(matrix A, const matrix &B);
friend matrix operator%(matrix A, matrix B);
friend matrix operator-(matrix A);
friend matrix operator-(complex x, matrix A);
friend matrix operator-(numero x, matrix A) {return complex(x,0)-A;};
friend matrix operator-(matrix A, complex x) {return (-x)+A;}
friend matrix operator-(matrix A, numero x) {return (-x)+A;}
friend matrix operator-(matrix A, const matrix &B);
friend matrix operator*(complex x, matrix A);
friend matrix operator*(numero x, matrix A);
friend matrix operator*(matrix A, complex x) {return x*A;}
friend matrix operator*(matrix A, numero x) {return x*A;}
friend matrix operator*(const matrix &A, const matrix &B);
friend matrix operator*(numero *r, matrix A);
friend matrix operator*(const matrix &A, numero *r) {return r*A;}
friend matrix operator%(numero *r, matrix A);
friend matrix operator%(matrix A, numero *r);
friend complex prod(matrix A, matrix B);
friend matrix operator/(complex x, matrix A) {return x*(--A);}
friend matrix operator/(numero x, matrix A) {return x*(--A);}
friend matrix operator/(matrix A, complex x) {return (1/x)*A;}
friend matrix operator/(matrix A, numero x) {return (1/x)*A;}
friend matrix operator/(matrix A, matrix B) {return A*(--B);}
friend complex trace(const matrix &A);
friend complex sum(const matrix &A);
friend numero mod2(const matrix &A);
friend numero mod(const matrix &A) {return sqrt(mod2(A));}
friend int dim(const matrix &A) {return A.nm;}
friend complex det(const matrix &A);
friend complex lndet(const matrix &A);
friend int dimn(const matrix &A) {return A.n;}
friend int dimm(const matrix &A) {return A.m;}
friend matrix neg_off_diag(matrix A);
};
matrix::matrix(const matrix &A)
{
int ij;
nm=0; if(A.nm) alloc(A.n,A.m); sel=A.sel;
for(ij=0; ij<nm; ij++) p[ij]=A.p[ij];
}
complex matrix::a(int i, int j)
{
if(i>-1 && i<n) {
if(sel==1) if(i==j) return p[i];
if(sel==0) if (j>-1 && j<m) return p[i*m+j];
}
return 0;
}
void matrix::alloc(int i, int j)
{
if(nm) delete [] p; n=i; m=j; nm=i*j; sel=0;
if(nm) {p=new complex [nm]; for(i=0; i<nm; i++) p[i]=0;}
}
void matrix::set_column(int j, matrix &B)
{
if((B.n!=1 && B.m!=1) || B.nm!=n)
on_error("matrix::set_column", "incompatible dimensions");
int i;
complex *q,*r; q=p+j; r=B.p;
for(i=0; i<n; i++, q+=m, r++) *q=*r;
}
void matrix::set_row(int i, matrix &B)
{
if((B.n!=1 && B.m!=1) || B.nm!=m)
on_error("matrix::set_row", "incompatible dimensions");
int j;
complex *q,*r; q=p+i*m; r=B.p;
for(j=0; j<m; j++, q++, r++) *q=*r;
}
matrix operator+(complex x, matrix A)
{
int i,j,ij;
if(A.sel==0) {
if(A.n!=A.m) on_error("matrix","A is not square in x+A");
for(i=ij=0; i<A.n; i++) for(j=0; j<A.m; j++,ij++) if(i==j) A.p[ij]+=x;
} else
if(A.sel==1) for(i=0; i<A.n; i++) A.p[i]+=x;
return A;
}
matrix operator+(matrix A, const matrix &B)
{
int i,j,ij;
if(A.sel==0 && B.sel==0) {
if(A.n!=B.n || A.m!=B.m) on_error("matrix","diff. dimensions in A+B (1)");
for(ij=0; ij<A.nm; ij++) A.p[ij]+=B.p[ij];
} else
if(A.sel==0 && B.sel==1) {
if(A.n!=B.n || A.m!=B.n) on_error("matrix","diff. dimension in A+B (2)");
for(i=ij=0; i<A.n; i++) for(j=0; j<A.m; j++,ij++)
if(i==j) A.p[ij]+=B.p[i];
} else
if(A.sel==1 && B.sel==1) {
if(A.n!=B.n) on_error("matrix","different dimension in A+B (3)");
for(i=0; i<A.n; i++) A.p[i]+=B.p[i];
} else
if(A.sel==1 && B.sel==0) return B+A;
return A;
}
matrix operator-(matrix A)
{
int ij;
for(ij=0; ij<A.nm; ij++) A.p[ij]=-A.p[ij];
return A;
}
matrix operator-(complex x, matrix A)
{
int i,j,ij;
if(A.sel==0) {
if(A.n!=A.m) on_error("matrix","A is not square in x-A");
for(i=ij=0; i<A.n; i++) for(j=0; j<A.m; j++,ij++)
if(i==j) A.p[ij]=x-A.p[ij]; else A.p[ij]=-A.p[ij];
} else
if(A.sel==1) for(i=0; i<A.n; i++) A.p[i]=x-A.p[i];
return A;
}
matrix operator-(matrix A, const matrix &B)
{
int i,j,ij;
if(A.sel==0 && B.sel==0) {
if(A.n!=B.n || A.m!=B.m) on_error("matrix","diff. dimensions in A-B (1)");
for(ij=0; ij<A.nm; ij++) A.p[ij]-=B.p[ij];
} else
if(A.sel==0 && B.sel==1) {
if(A.n!=B.n || A.m!=B.n) on_error("matrix","diff. dimension in A-B (2)");
for(i=ij=0; i<A.n; i++) for(j=0; j<A.m; j++,ij++)
if(i==j) A.p[ij]-=B.p[i];
} else
if(A.sel==1 && B.sel==1) {
if(A.n!=B.n) on_error("matrix","different dimension in A-B (3)");
for(i=0; i<A.n; i++) A.p[i]-=B.p[i];
} else
if(A.sel==1 && B.sel==0) return -(B-A);
return A;
}
matrix operator*(complex x, matrix A)
{
int ij;
for(ij=0; ij<A.nm; ij++) A.p[ij]=x*A.p[ij];
return A;
}
matrix operator*(numero x, matrix A)
{
int ij;
for(ij=0; ij<A.nm; ij++) A.p[ij]=x*A.p[ij];
return A;
}
matrix operator*(const matrix &A, const matrix &B)
{
int i,j,k,ij; complex val; matrix C;
complex *Cp,*Ap0,*Ap,*Bp,*Bp0;
if(A.sel==0 && B.sel==0) {
if(A.m!=B.n) on_error("matrix","incompatible dimensions in A*B");
C.alloc(A.n,B.m);
for(i=0, Cp=C.p, Ap0=A.p; i<A.n; i++, Ap0+=A.m)
for(j=0, Bp0=B.p; j<B.m; j++, Cp++, Bp0++) {
for(k=0, val=0, Ap=Ap0, Bp=Bp0; k<A.m; k++, Ap++, Bp+=B.m)
val+=(*Ap)*(*Bp);
*Cp=val;
} } else
if(A.sel==0 && B.sel==1) {
if(A.m!=B.n) on_error("matrix","incompatible dimensions in A*B");
C.alloc(A.n,A.m);
for(i=ij=0; i<A.n; i++) for(j=0; j<A.m; j++,ij++) C.p[ij]=A.p[ij]*B.p[j];
} else
if(A.sel==1 && B.sel==0) {
if(A.n!=B.n) on_error("matrix","incompatible dimensions in A*B");
C.alloc(B.n,B.m);
for(i=ij=0; i<B.n; i++) for(j=0; j<B.m; j++,ij++) C.p[ij]=A.p[i]*B.p[ij];
} else
if(A.sel==1 && B.sel==1) {
if(A.n!=B.n) on_error("matrix","incompatible dimensions in A*B");
C.alloc_diagonal(A.n);
for(i=0; i<A.n; i++) C.p[i]=A.p[i]*B.p[i];
}
return C;
}
matrix transpose(matrix A)
{
if(A.sel==1) return A;
matrix C(A.m,A.n);
int i,j,ij;
for(ij=0; ij<A.nm; ij++) {
j=ij%A.m; i=ij/A.m;
C.p[j*C.m+i]=A.p[ij];
}
return C;
}
matrix conj(matrix A)
{
matrix C(A.m,A.n);
int i,j,ij;
if(A.sel==0)
for(ij=0; ij<A.nm; ij++) {
j=ij%A.m; i=ij/A.m;
C.p[j*C.m+i]=conj(A.p[ij]);
}
else if(A.sel==1) for(ij=0; ij<A.nm; ij++) C.p[ij]=conj(A.p[ij]);
return C;
}
matrix neg_off_diag(matrix A)
{
matrix C(A.m,A.n);
int i,j,ij,l=A.m/2;
if(A.m!=A.n) on_error("matrix::neg_off_diag", "n!=m");
if(A.m%2) on_error("matrix::neg_off_diag", "odd dimension");
for(i=ij=0; i<A.n; i++) for(j=0; j<A.m; j++,ij++)
if((i<l && j>=l) || (i>=l && j<l)) C.p[ij]=-A.p[ij];
else C.p[ij]= A.p[ij];
return C;
}
matrix &matrix::operator++(void)
{
int i,j,ij;
if(sel==0)
for(ij=0; ij<nm; ij++) {
j=ij%m; i=ij/m;
p[j*m+i]=conj(p[ij]);
}
else if(sel==1) for(ij=0; ij<nm; ij++) p[ij]=conj(p[ij]);
return *this;
}
matrix &matrix::operator--(void)
{
int ij; if(sel==1) {for(ij=0; ij<nm; ij++) p[ij]=1/p[ij]; return *this;}
matrix B;
gaussj(B,n,0);
return *this;
}
complex matrix::inv(void)
{
int ij;
complex val;
if(sel==1) {
val=0;
for(ij=0; ij<nm; ij++) {val+=log(p[ij]); p[ij]=1/p[ij];}
return val;
}
matrix B;
return gaussj(B,n,0);
}
matrix &matrix::operator=(const matrix &A)
{
int ij;
if(A.nm) alloc(A.n,A.m); sel=A.sel;
for(ij=0; ij<nm; ij++) p[ij]=A.p[ij];
return *this;
}
matrix &matrix::operator=(complex x)
{
int i,j,ij;
if(sel==0)
for(i=ij=0; i<n; i++) for(j=0; j<m; j++,ij++)
if(i==j) p[ij]=x; else p[ij]=0;
else if(sel==1) for(i=0; i<n; i++) p[i]=x;
return *this;
}
matrix &matrix::operator=(numero x)
{
int i,j,ij;
if(sel==0)
for(i=ij=0; i<n; i++) for(j=0; j<m; j++,ij++)
if(i==j) p[ij]=x; else p[ij]=0;
else if(sel==1) for(i=0; i<n; i++) p[i]=x;
return *this;
}
matrix operator%(matrix A, matrix B)
{
int i,j,ij;
if(A.sel==1 || B.sel==1) on_error("matrix","% not allowed with diag. mat.");
if(A.nm==B.nm)
for(ij=0; ij<A.nm; ij++) A.p[ij]=A.p[ij]*B.p[ij]; else
if(A.nm==B.n) {
for(i=ij=0; i<B.n; i++)
for(j=0; j<B.m; j++,ij++) B.p[ij]=A.p[i]*B.p[ij];
return B;
} else
if(A.m==B.nm) {
for(i=ij=0; i<A.n; i++)
for(j=0; j<A.m; j++,ij++) A.p[ij]=A.p[ij]*B.p[j];
} else
on_error("matrix","incompatible dimensions in A%B");
return A;
}
matrix operator*(numero *r, matrix A)
{
int ij; complex *p; p=A.p;
for(ij=0; ij<A.nm; ij++, r++, p++) *p=(*r)*(*p);
return A;
}
matrix operator%(matrix A, numero *r)
{
complex *p; p=A.p;
numero *rr;
int i,j;
for(i=0; i<A.n; i++) {
rr=r;
for(j=0; j<A.m; j++,p++,rr++) *p=(*rr)*(*p);
}
return A;
}
matrix operator%(numero *r, matrix A)
{
complex *p; p=A.p;
int i,j;
for(i=0; i<A.n; i++, r++)
for(j=0; j<A.m; j++,p++) *p=(*r)*(*p);
return A;
}
complex prod(matrix A, matrix B)
{
complex val=0;
int i;
if(A.m!=1 || B.m!=1 || A.n!=B.n) on_error("matrix","A*B is not a scalar");
for(i=0; i<A.n; i++) val+=conj(A.p[i])*B.p[i];
return val;
}
complex trace(const matrix &A)
{
if(A.n!=A.m) on_error("matrix","A is not square in trace(A)");
int ij; complex x(0,0);
for(ij=0; ij<A.nm; ij+=A.n) x+=A.p[ij];
return x;
}
complex sum(const matrix &A)
{
if(A.m!=1) on_error("matrix","A is not (mx1) in sum(A)");
int i; complex x=0;
for(i=0; i<A.n; i++) x+=A.p[i];
return x;
}
numero mod2(const matrix &A)
{
int ij; numero x=0;
for(ij=0; ij<A.nm; ij++) x+=mod2(A.p[ij]);
return x;
}
complex det(const matrix &A) {return exp(lndet(A));}
complex lndet(const matrix &A)
{
matrix B,C; C=A;
return C.gaussj(B,C.n,0,1);
}
void matrix::print(numero val)
{
int ij;
for(ij=0; ij<nm; ij++) if(mod(p[ij])>=val) printf("%3d %3d %15g %15g\n",
ij/m, ij%m, real(p[ij]), imag(p[ij]));
}
complex matrix::gaussj(const matrix &Mb, int nn, int mm, int opt)
{
if(n!=m || n<nn) on_error("matrix","A not square in gaussj(A)");
if(mm) if(m!=Mb.n || Mb.m<mm)
on_error("matrix","incompatible dimensions in gaussj");
int i,icol,irow,j,k,l,ll, *indxc,*indxr,*ipiv,*iA,*iB;
numero big,val;
complex dum,pivinv, *pirow,*picol,*pp,*ppp,*pa,*pb,*ppb, det=0;
ipiv=new int [nn]; indxc=new int [nn]; indxr=new int [nn];
iA=new int [nn]; iB=new int [nn];
for(i=0; i<nn; i++) {ipiv[i]=0; iA[i]=i*m; iB[i]=i*Mb.m;}
for(i=0; i<nn; i++) {
big=0;
for(j=0,pp=p; j<nn; j++,pp+=m) {
if(ipiv[j]!=1)
for(k=0,ppp=pp; k<nn; k++,ppp++) {
if(!ipiv[k]) {
val=mod(*ppp);
if(val>=big) {
big=val;
irow=j;
icol=k;
} } else if(ipiv[k]>1)
on_error("matrix","1) singular matrix in gaussj");
} }
ipiv[icol]=ipiv[icol]+1;
if(irow!=icol) {
det=det+complex(0,pi);
pirow=p+iA[irow]; picol=p+iA[icol];
for(l=0; l<nn; l++,pirow++,picol++) {
dum=*pirow; *pirow=*picol; *picol=dum;
}
if(mm) {
pirow=Mb.p+iB[irow]; picol=Mb.p+iB[icol];
for(l=0; l<mm; l++,pirow++,picol++) {
dum=*pirow; *pirow=*picol; *picol=dum;
} } }
indxr[i]=irow;
indxc[i]=icol; pp=p+iA[icol]+icol;
if(real(*pp)==0 && imag(*pp)==0) {
if(opt) return -infinity;
else on_error("matrix","2) singular matrix in gaussj");
}
det=det+log(*pp);
pivinv=1/(*pp);
*pp=1;
for(l=0, pp=p+iA[icol]; l<nn; l++,pp++) *pp=(*pp)*pivinv;
if(mm) for(l=0, pp=Mb.p+iB[icol]; l<mm; l++,pp++) *pp=(*pp)*pivinv;
for(ll=0,pp=p,ppb=Mb.p; ll<nn; ll++,pp+=m,ppb+=mm) if(ll!=icol) {
dum=*(pp+icol);
*(pp+icol)=0; pa=p+iA[icol]; pb=Mb.p+iB[icol];
for(l=0,ppp=pp; l<nn; l++,ppp++,pa++) *ppp=*ppp-(*pa)*dum;
if(mm) for(l=0,ppp=ppb; l<mm; l++,ppp++,pb++) *ppp=*ppp-(*pb)*dum;
}
}
for(l=nn-1; l>=0; l--) if(indxr[l]!=indxc[l])
for(k=0,pp=p+indxr[l],ppp=p+indxc[l]; k<nn; k++,pp+=m,ppp+=m) {
dum=*pp; *pp=*ppp; *ppp=dum;
}
delete [] ipiv; delete [] indxc; delete [] indxr;
delete [] iA; delete [] iB;
val=imag(det); val-=int(val/(2*pi))*2*pi;
while(val<-2*pi) val+=2*pi; while(val>2*pi) val-=2*pi;
return complex(real(det), val);
}
void escribe_matrix(matrix &a)
{
int i,j,ij;
for(i=ij=0; i<a.n; i++)
for(j=0; j<a.m; j++, ij++) {
printf(" (%2d:%2d) %14.6g", i, j, mod(a.a(i,j)));
if((ij+1)%3==0) printf("\n");
}
printf("\n");
}
#endif
#ifdef jga_recurs
#else
#define jga_recurs 1
class recurs {
private:
complex bb(int p);
complex Ij(int j, int p, int q);
complex *I, *a, *b;
int *iI, *ib, n, n2, nn,
init_flag;
public:
int init(int n_, complex *mu);
void free(void);
complex eval(complex E, int n_, int termination);
complex eval(numero E, int n_, int termination);
complex eval(complex E, int n_, complex *mu, int termination);
complex eval(numero E, int n_, complex *mu, int termination);
recurs(void) {init_flag=0;}
};
complex recurs::bb(int p)
{
if(p<1) return 0;
if(!ib[p]) {
b[p]=sqrt(Ij(2,p-1,p-1)-sqr(Ij(1,p-1,p-1))-sqr(bb(p-1)));
ib[p]=1;
}
return b[p];
}
complex recurs::Ij(int j, int p, int q)
{
if(p<0 || q<0) return 0;
int k=j*n2+p*n+q; complex bb_;
if(!iI[k]) {
if(p>0) bb_=bb(p); else bb_=bb(q);
if(ABS(real(bb_))<infinitesimal &&
ABS(imag(bb_))<infinitesimal) I[k]=0; else
if(p>0) I[k]=( Ij(j+1,p-1,q)
-Ij(1,p-1,p-1)*Ij(j,p-1,q)
-bb(p-1)*Ij(j,p-2,q) )/bb_;
else I[k]=( Ij(j+1,p,q-1)
-Ij(1,q-1,q-1)*Ij(j,p,q-1)
-bb(q-1)*Ij(j,p,q-2) )/bb_;
iI[k]=1;
}
return I[k];
}
int recurs::init(int n_, complex *mu)
{
if(n_>=1)
if(mod(mu[0])<1e-10*mod(mu[1]) || mod(mu[0])<1e-10) {
mu++;
init(n_-1,mu);
return 0;
}
free(); init_flag=1; nn=n_;
if(nn<1) {
n=0;
b=new complex [1+1000]; b[0]=mu[0];
return 0;
}
n =(nn-1)/2 + 1;
n2=sqr(n);
int i,n3=(2*n+1)*n2+n2+n;
a=new complex [n+2];
b=new complex [n+2];
ib=new int [n+2];
I=new complex [n3];
iI=new int [n3];
for(i=0; i<n; i++) ib[i]=0;
for(i=0; i<n3; i++) iI[i]=0;
for(i=0; i<=nn; i++) {
I[i*n2]=mu[i]/mu[0];
iI[i*n2]=1;
}
for(i=0; i<n; i++) a[i]=Ij(1,i,i);
for(i=1; i<n; i++) b[i]=bb(i);
for(i=1; i<n; i++) b[i]=sqr(b[i]);
b[0]=mu[0];
delete [] I; delete [] iI; delete [] ib;
return 0;
}
void recurs::free(void)
{
if(init_flag) {if(n>0) delete [] a; delete [] b;}
}
complex recurs::eval(complex E, int n_, int termination)
{
if(n_>nn) n_=nn;
int nt=(n_-1)/2 + 1;
if(n_==0) return b[0]/E;
complex t;
int i;
if(!termination || nt==1) t=0;
else t=(E-a[nt-1]-sqrt(sqr(E-a[nt-1]) - 4*b[nt-1]))/2.0;
for(i=nt-1; i>=0; i--) t=b[i]/(E-a[i]-t);
return t;
}
complex recurs::eval(complex E, int n_, complex *mu, int termination)
{
complex val;
init(n_,mu);
val=eval(E,n_,termination);
free();
return val;
}
complex recurs::eval(numero E, int n_, int termination)
{return eval(complex(E,0),n_,termination);}
complex recurs::eval(numero E, int n_, complex *mu, int termination)
{return eval(complex(E,0),n_,mu,termination);}
#endif
#ifdef jga_light
#else
#define jga_light 1
void light_polarization_mu(numero th, numero fi, numero al, numero del,
complex *eps)
{
numero cal=cos(al), cth=cos(th), sal=sin(al), sth=sin(th);
eps[0]=( cal*cth + i_c*sal*exp(i_c*del))*exp( i_c*fi)/sqrt(2);
eps[1]= -cal*sth;
eps[2]=(-cal*cth + i_c*sal*exp(i_c*del))*exp(-i_c*fi)/sqrt(2);
}
void light_polarization_xyz(complex *eps,
complex &ex, complex &ey, complex &ez)
{
ex= -(eps[2]-eps[0])/sqrt(2);
ey=-i_c*(eps[2]+eps[0])/sqrt(2);
ez= eps[1];
}
void light_polarization_xyz(numero th, numero fi, numero al, numero del,
complex *EE)
{
complex eps[3], ex,ey,ez;
light_polarization_mu(th,fi,al,del, eps);
light_polarization_xyz(eps, ex, ey, ez);
EE[0]=ex; EE[1]=ey; EE[2]=ez;
}
void light_E_field(numero th, numero fi, numero alpha, numero delta,
complex &ex, complex &ey, complex &ez)
{
ex= cos(alpha)*cos(th)*cos(fi)-sin(alpha)*sin(fi)*exp(i_c*delta);
ey= cos(alpha)*cos(th)*sin(fi)+sin(alpha)*cos(fi)*exp(i_c*delta);
ez=-cos(alpha)*sin(th);
}
void light_A_potential(complex w,
numero th, numero fi, numero alpha, numero delta,
complex &ax, complex &ay, complex &az)
{
complex ik=i_c*w/c_au;
light_E_field(th,fi,alpha,delta,ax,ay,az);
ax=ax/ik; ay=ay/ik; az=az/ik;
}
#endif
#ifndef jga_Salvat
#define jga_Salvat 1
class Salvat {
public:
numero *r, *rr, *P, *Q;
int ngp, nmax, ndim;
spline PP,QQ;
numero phase_last, E_last, kk_last;
int k_last;
void vint(numero *R_, numero *RV_, int np);
void vint(numero *r_in, numero *V_in, int n_in, int atZ);
void dbound(numero &E, numero err, int N, int K);
void dfree(numero E, numero &PHASE, int k);
void printwf(FILE *fout);
void free(void);
void wf(numero r_, numero &f, numero &g);
void phases(numero *r_in, numero *V_in, int n_in,
int atZ,
numero Ei, numero Ef, int nE,
int rel, int lmax, numero *ph);
void phases(numero *r_in, numero *V_in, int n_in,
int atZ, numero E,
int rel, int lmax, numero *ph)
{phases(r_in, V_in, n_in, atZ, E,E,1, rel, lmax, ph);}
numero eps;
Salvat(void) {eps=1.0e-15; ndim=0;}
numero *RV, *VA, *VB, *VC, *VD;
numero *Y, *A, *B, *C, *D;
int NZMAX, NSTEP,NCHS, NSUM;
numero RV0, RV1, RV2, RV3;
numero PPI,QQI,PF,QF,RA,RB,RLN;
numero P0,Q0,P1,Q1,CA[61],CB[61],R0,R1;
numero vacuum(int l, numero kr, numero ps)
{return besselj(l,kr)*cos(ps) - bessely(l,kr)*sin(ps);}
int DOUTW(numero E, int K, int NR, int &NCERO, int IOTP);
void DINW(numero E, int K, int IOTP);
void DIR(numero E, numero AK);
int DIR0(numero E, numero AK);
void SPLINE(numero *X, numero *Y, numero S1, numero SN, int &N);
numero INTEG(numero *X, numero XL, numero XU, int N);
int FINDI(numero *X, numero XC, int N);
numero DMAX1(numero a, numero b) {if(a>b) return a; else return b;}
numero DMIN1(numero a, numero b) {if(a<b) return a; else return b;}
numero DMAX1(numero a, numero b, numero c, numero d)
{return DMAX1(DMAX1(a,b),DMAX1(c,d));}
};
void Salvat::free(void) {
if(ndim) {
delete [] r; delete [] rr; delete [] P; delete [] Q;
delete [] RV; delete [] VA; delete [] VB; delete [] VC; delete [] VD;
delete [] Y; delete [] A; delete [] B; delete [] C; delete [] D;
}
PP.free(); QQ.free(); ndim=0;
}
void Salvat::vint(numero *R_, numero *RV_, int np)
{
free(); ndim=np+1;
r=new numero [ndim]; rr=new numero [ndim];
P=new numero [ndim]; Q=new numero [ndim];
RV=new numero [ndim]; VA=new numero [ndim]; VB=new numero [ndim];
VC=new numero [ndim]; VD=new numero [ndim];
Y=new numero [ndim]; A=new numero [ndim]; B=new numero [ndim];
C=new numero [ndim]; D=new numero [ndim];
int IO=0,I=0,K=0,J;
gt1: I++; K++;
P[K]=R_[I-1]; Q[K]=RV_[I-1];
if(I==np) goto gt2;
if(R_[I-1]<R_[I]-1.0e-12) goto gt1;
gt2: SPLINE(P,Q,0,0,K);
K--;
for(J=1; J<=K; J++) {
IO++;
rr[IO-1]=r[IO]=P[J];
RV[IO]=Q[J];
VA[IO]=A[J]; VB[IO]=B[J];
VC[IO]=C[J]; VD[IO]=D[J];
}
if(I<np) {K=0; goto gt1;}
ngp=IO+1;
rr[ngp-1]=r[ngp]=P[K+1];
RV[ngp]=Q[K+1];
}
void Salvat::wf(numero r_, numero &f, numero &g)
{
if(ndim==0) on_error("Salvat::wf(r,f,g)","no wf is not available");
numero kr;
int l,lp;
if(r_<=PP.b) {f=PP.val(r_); g=QQ.val(r_);} else
if(E_last>0) {
kr=kk_last*r_;
if(k_last<0) l=-k_last-1; else l=k_last;
if(k_last<0) lp=l+1; else lp=l-1;
f = r_ * vacuum(l,kr,phase_last);
g = -r_ * vacuum(lp,kr,phase_last) * E_last/(kk_last*c_au);
} else on_error("Salvat::wf(r,f,g)","r out of range for bound state");
}
void Salvat::dbound(numero &E, numero err, int N, int K)
{
numero FL1,ESUP,EMIN,EMAX,EKIN,PO,QO,FACT,RLAST,SUM,DE,EP,EO;
int NR,ICMIN,ICMAX,L,I,J,IOTP,NCERO;
k_last=K; phase_last=0;
if(N<1||K==0||K<-N||K>N-1)
on_error("Salvat::dbound","n or k out of range");
if(K<0) L=-K-1; else L=K;
NR=N-L-1;
err=ABS(err);
if(E>-0.1) E=-0.1;
FL1=0.5*L*(L+1);
EMIN=1;
for(I=2; I<=ngp; I++) EMIN=DMIN1(EMIN,(RV[I]+FL1/r[I])/r[I]);
if(EMIN>=0)
on_error("Salvat::dbound", "error 1: EMIN>0: use denser grid");
ESUP=(RV[ngp]+FL1/r[ngp])/r[ngp];
if(ESUP>0) ESUP=0;
if(EMIN<-c_au*c_au) EMIN=-c_au*c_au;
if(E>ESUP || E<EMIN) E=0.5*(ESUP+EMIN);
EMAX=ESUP;
ICMIN=0;
ICMAX=0;
gt2: if(E>-1.0e-16)
on_error("Salvat::dbound", "error 2: bound state does not exist");
for(J=2; J<=ngp; J++) {
IOTP=ngp+2-J;
EKIN=E-(RV[IOTP]+FL1/r[IOTP])/r[IOTP];
if(EKIN>0) goto gt4;
}
gt4: IOTP++;
if(IOTP>ngp-1) on_error("Salvat::dbound", "error 3: use denser grid");
DOUTW(E,K,NR,NCERO,IOTP);
if(NZMAX>1 && NCERO<=NR)
on_error("Salvat::dbound", "error 4: use denser grid");
if(NCERO>NR) {
if(ICMIN==0) EMIN=EMIN-(EMAX-E);
EMAX=E;
ICMAX=1;
E=0.5*(EMIN+E);
if(EMAX-EMIN<err*ABS(EMIN))
on_error("Salvat::dbound", "error 5: E out of range");
goto gt2;
}
if(NCERO<NR) {
ICMIN=1;
EMIN=E;
E=0.5*(E+EMAX);
if(EMAX-EMIN<err*ABS(EMIN))
on_error("Salvat::dbound", "error 5: E out of range");
goto gt2;
}
PO=P[IOTP];
QO=Q[IOTP];
DINW(E,K,IOTP);
FACT=PO/P[IOTP];
for(I=IOTP; I<=ngp; I++) {
P[I]=P[I]*FACT;
Q[I]=Q[I]*FACT;
}
QQI=Q[IOTP];
for(I=1; I<=nmax; I++) Y[I]=sqr(P[I])+sqr(Q[I]);
RLAST=r[nmax];
SPLINE(r,Y,0,0,nmax);
SUM=INTEG(r,0,RLAST,nmax);
if(SUM<1.0e-15) SUM=1;
DE=c_au*PO*(QQI-QO)/SUM;
EP=E+DE;
if(DE<0) {ICMAX=1; EMAX=E;}
if(DE>0) {ICMIN=1; EMIN=E;}
if(ICMIN==0 && EP<EMIN) {
EMIN=1.1*EMIN;
if(EP<EMIN) EP=0.5*(E+EMIN);
}
if(ICMIN==1 && EP<EMIN) EP=0.5*(E+EMIN);
if(ICMAX==1 && EP>EMAX) EP=0.5*(E+EMAX);
if(EP>ESUP) EP=0.5*(ESUP+E);
if(EP>ESUP && ABS(E-ESUP)<err*ABS(ESUP))
on_error("Salvat::dbound", "error 5: E out of range");
EO=E;
E=EP;
if(DMIN1(ABS(DE),ABS(E-EO))>ABS(E*err)) goto gt2;
FACT=1/sqrt(SUM);
PP.alloc(nmax); QQ.alloc(nmax);
for(I=0; I<nmax; I++) {
P[I]=P[I+1]*FACT; Q[I]=-Q[I+1]*FACT;
PP.put(I,rr[I],P[I]); QQ.put(I,rr[I],Q[I]);
}
PP.init(); QQ.init();
for(I=nmax; I<ndim; I++) P[I]=Q[I]=0;
if(ABS(P[ngp])>1.0e-3*ABS(P[IOTP]))
on_error("Salvat::dbound", "error 3: use larger radii");
E_last=E;
}
void Salvat::dfree(numero E, numero &PHASE, int K)
{
int L,I,IL,NCERO;
numero FL1,T,RF,PF_,QF_,RK,BJL,BJLP,BNL,BNLP,TT,VF,PPF,RATIO,FACT;
if(K==0) on_error("Salvat::dfree", "K=0"); k_last=K;
if(E<=0) on_error("Salvat::dfree", "E<0"); E_last=E;
if(K<0) L=-K-1; else L=K;
FL1=0.5*L*(L+1);
T=1.0e-6*r[ngp]*ABS(E-FL1/(r[ngp]*r[ngp]));
if(ABS(RV[ngp])>T)
on_error("Salvat::dfree", "error 7: extend grid to larger radii");
nmax=ngp;
for(I=4; I<=ngp; I++) {
IL=nmax-1;
T=1-10*r[IL]*ABS(E-FL1/(r[IL]*r[IL]));
if(ABS(RV[IL])>T) goto gt2;
nmax=IL;
}
gt2:
DOUTW(E,K,1,NCERO,nmax);
RF=r[nmax];
PF_=P[nmax];
QF_=Q[nmax];
RK=sqrt(E*(E+2*sqr(c_au)))/c_au;
T=RK*RF;
BJL=besselj(L,T); BNL=bessely(L,T);
besseljyp(L,T,BJLP,BNLP);
IL=nmax-1;
VF=VA[IL]/RF+VB[IL]+RF*(VC[IL]+RF*VD[IL]);
PPF=-K*PF_/RF-(E-VF+2*sqr(c_au))*QF_/c_au;
RATIO=PPF/PF_-1/RF;
PHASE=atan2(RK*BJLP-RATIO*BJL,RK*BNLP-RATIO*BNL);
TT=ABS(PHASE);
if(TT>0.5*pi) PHASE=PHASE*(1-pi/TT);
kk_last=sqrt(E*(E+2*c_au*c_au))/c_au;
FACT=r[nmax]*vacuum(L,kk_last*r[nmax],PHASE)/P[nmax];
PP.alloc(nmax); QQ.alloc(nmax);
for(I=0; I<nmax; I++) {
P[I]=P[I+1]*FACT; Q[I]=-Q[I+1]*FACT;
PP.put(I,rr[I],P[I]); QQ.put(I,rr[I],Q[I]);
}
PP.init(); QQ.init();
for(I=nmax; I<ndim; I++) P[I]=Q[I]=0;
phase_last=PHASE;
}
int Salvat::DOUTW(numero E, int K, int NR, int &NCERO, int IOTP)
{
numero AK,FACT;
int N1,I,J;
NCERO=0;
NZMAX=0;
AK=K;
N1=IOTP-1;
P[1]=0;
Q[1]=0;
for(I=1; I<=N1; I++) {
RA=r[I];
RB=r[I+1];
RV0=VA[I];
RV1=VB[I];
RV2=VC[I];
RV3=VD[I];
PPI=P[I];
QQI=Q[I];
DIR(E,AK);
NCERO=NCERO+NCHS;
if(NCHS>NZMAX) NZMAX=NCHS;
if(NCERO>NR && E<0) return 1;
P[I+1]=PF;
Q[I+1]=QF;
if(I>1 && RLN>0) {
FACT=exp(-RLN);
for(J=1; J<=I; J++) {
P[J]=P[J]*FACT;
Q[J]=Q[J]*FACT;
} } }
return 1;
}
void Salvat::DINW(numero E, int K, int IOTP)
{
numero AK,AL,RN,RVN,RVNP,CMU,CRAT,FACT, TRINF=5625.0;
int L,N,N1,I,J,I1,M;
if(K<0) L=-K-1; else L=K;
AK=K;
AL=L;
N=ngp;
FACT=(E+2*c_au*c_au)/(c_au*c_au);
gt1: N1=N-1;
RN=r[N];
RVN=VA[N1]+RN*(VB[N1]+RN*(VC[N1]+RN*VD[N1]));
RVNP=VB[N1]+RN*(2*VC[N1]+RN*3*VD[N1]);
CMU=FACT*RN*(RVN-E*RN)+AL*(AL+1);
if(CMU<=0) on_error("Salvat::DINW", "error 6: RV[ngp]<<0 or E>0");
if(CMU<TRINF || N==IOTP+1) {
CRAT=(0.5-sqrt(CMU))/RN-0.25*FACT*(RVN+RN*RVNP-2*RN*E)/CMU;
P[N]=1;
Q[N]=-c_au*(CRAT+AK/RN)/(E+2*c_au*c_au);
nmax=N;
} else {
P[N]=0;
Q[N]=0;
N--;
goto gt1;
}
N1=N-IOTP;
for(J=1; J<=N1; J++) {
I=N-J;
I1=I+1;
RA=r[I1];
RB=r[I];
RV0=VA[I];
RV1=VB[I];
RV2=VC[I];
RV3=VD[I];
PPI=P[I1];
QQI=Q[I1];
DIR(E,AK);
P[I]=PF;
Q[I]=QF;
if(RLN>0) {
FACT=exp(-RLN);
for(M=I1; M<=N; M++) {
P[M]=P[M]*FACT;
Q[M]=Q[M]*FACT;
} } } }
void Salvat::DIR(numero E, numero AK)
{
numero H, DIRECT,TST;
int K,IOUT;
NCHS=0;
RLN=0;
H=RB-RA;
if(H<0) DIRECT=-1; else DIRECT=1;
K=-2;
NSTEP=0;
R1=RA;
P1=PPI;
Q1=QQI;
gtD1: R0=R1;
P0=P1;
Q0=Q1;
gtD2: IOUT=0;
R1=R0+H;
if(DIRECT*(RB-R1)<DIRECT*0.1*H) {
R1=RB;
H=RB-R0;
IOUT=1;
}
DIR0(E,AK);
K++;
if(NSUM>15) goto gtD3;
if(K<0) goto gtD4;
H+=H;
K=0;
goto gtD4;
gtD3: if(NSUM<60) goto gtD4;
H=0.5*H;
K=-4;
goto gtD2;
gtD4: NSTEP++;
TST=ABS(P1);
if(TST>100) {
RLN=RLN+log(TST);
P1=P1/TST;
Q1=Q1/TST;
}
if(P0*P1<0 && R0>0) NCHS++;
if(IOUT==0) goto gtD1;
PF=P1;
QF=Q1;
}
int Salvat::DIR0(numero E, numero AK)
{
int ISIG,I,K;
numero H,H2,RVE,U0,U1,U2,U3,UT,UQ,UH,S,CAI,CBI,DS,QP1,PP1,TST,T1A,
T1B,T1,T2,DS1,RHO,UB;
numero OVER=1.0e15;
ISIG=1;
if(AK>0) ISIG=-1;
H=R1-R0;
H2=H*H;
RVE=RV1-E;
if(R0>1.0e-10) goto gt07;
U0=RV0/c_au;
U1=RVE*R1/c_au;
U2=RV2*R1*R1/c_au;
U3=RV3*R1*R1*R1/c_au;
UT=U0+U1+U2+U3;
UQ=UT-2*c_au*R1;
UH=U1-2*c_au*R1;
if(ABS(U0)<1.0e-10) goto gt02;
S=sqrt(AK*AK-U0*U0);
DS=S+S;
CA[1]=1;
CB[1]=(S+AK)/U0;
CAI=U1*CA[1];
CBI=UH*CB[1];
CA[2]=(U0*CAI+(S+1-AK)*CBI)/(DS+1);
CB[2]=(-(S+1+AK)*CAI+U0*CBI)/(DS+1);
CAI=U1*CA[2]+U2*CA[1];
CBI=UH*CB[2]+U2*CB[1];
CA[3]=(U0*CAI+(S+2-AK)*CBI)/(2*(DS+2));
CB[3]=(-(S+2+AK)*CAI+U0*CBI)/(2*(DS+2));
P1=CA[1]+CA[2]+CA[3];
PP1=S*CA[1]+(S+1)*CA[2]+(S+2)*CA[3];
Q1=CB[1]+CB[2]+CB[3];
QP1=S*CB[1]+(S+1)*CB[2]+(S+2)*CB[3];
for(I=4; I<=60; I++) {
K=I-1;
CAI=U1*CA[K]+U2*CA[I-2]+U3*CA[I-3];
CBI=UH*CB[K]+U2*CB[I-2]+U3*CB[I-3];
CA[I]=(U0*CAI+(S+K-AK)*CBI)/(K*(DS+K));
CB[I]=(-(S+K+AK)*CAI+U0*CBI)/(K*(DS+K));
P1=P1+CA[I];
PP1=PP1+(S+K)*CA[I];
Q1=Q1+CB[I];
QP1=QP1+(S+K)*CB[I];
TST=DMAX1(ABS(P1),ABS(Q1),ABS(PP1),ABS(QP1));
if(TST>OVER) {NSUM=100; return 1;}
T1A=ABS(R1*PP1+H*(AK*P1-UQ*Q1));
T1B=ABS(R1*QP1-H*(AK*Q1-UT*P1));
T1=DMAX1(T1A,T1B);
T2=DMAX1(ABS(CA[I]),ABS(CB[I]));
TST=eps*DMAX1(ABS(P1),ABS(Q1));
if(T1<TST && T2<TST) goto gt06;
}
goto gt06;
gt02: if(ISIG<0) goto gt04;
S=ABS(AK);
DS1=S+S+1;
CA[1]=1;
CB[1]=-U1*CA[1]/DS1;
CA[2]=0;
CB[2]=-U2*CA[1]/(DS1+1);
CA[3]=UH*CB[1]/2;
CB[3]=-(U1*CA[3]+U3*CA[1])/(DS1+2);
CA[4]=(UH*CB[2]+U2*CB[1])/3;
CB[4]=-(U1*CA[4]+U2*CA[3])/(DS1+3);
P1=CA[1]+CA[2]+CA[3]+CA[4];
PP1=S*CA[1]+(S+1)*CA[2]+(S+2)*CA[3]+(S+3)*CA[4];
Q1=CB[1]+CB[2]+CB[3]+CB[4];
QP1=(S+1)*CB[1]+(S+2)*CB[2]+(S+3)*CB[3];
for(I=5; I<=60; I++) {
K=I-1;
CA[I]=(UH*CB[I-2]+U2*CB[I-3]+U3*CB[I-4])/K;
CB[I]=-(U1*CA[I]+U2*CA[K]+U3*CA[I-2])/(DS1+K);
P1=P1+CA[I];
PP1=PP1+(S+K)*CA[I];
Q1=Q1+CB[I];
QP1=QP1+(S+I)*CB[I];
TST=DMAX1(ABS(P1),ABS(Q1),ABS(PP1),ABS(QP1));
if(TST>OVER) {NSUM=100; return 1;}
T1A=ABS(R1*PP1+H*(AK*P1-UQ*Q1));
T1B=ABS(R1*QP1-H*(AK*Q1-UT*P1));
T1=DMAX1(T1A,T1B);
T2=DMAX1(ABS(CA[I]),ABS(CB[I]));
TST=eps*DMAX1(ABS(P1),ABS(Q1));
if(T1<TST && T2<TST) goto gt06;
}
goto gt06;
gt04: S=ABS(AK)+1;
DS1=S+ABS(AK);
CB[1]=1;
CA[1]=UH*CB[1]/DS1;
CB[2]=0;
CA[2]=U2*CB[1]/(DS1+1);
CB[3]=-U1*CA[1]/2;
CA[3]=(UH*CB[3]+U3*CB[1])/(DS1+2);
CB[4]=-(U1*CA[2]+U2*CA[1])/3;
CA[4]=(UH*CB[4]+U2*CB[3])/(DS1+3);
P1=CA[1]+CA[2]+CA[3]+CA[4];
PP1=S*CA[1]+(S+1)*CA[2]+(S+2)*CA[3]+(S+3)*CA[4];
Q1=CB[1]+CB[2]+CB[3]+CB[4];
QP1=(S-1)*CB[1]+S*CB[2]+(S+1)*CB[3];
for(I=5; I<=60; I++) {
K=I-1;
CB[I]=-(U1*CA[I-2]+U2*CA[I-3]+U3*CA[I-4])/K;
CA[I]=(UH*CB[I]+U2*CB[K]+U3*CB[I-2])/(DS1+K);
P1=P1+CA[I];
PP1=PP1+(S+K)*CA[I];
Q1=Q1+CB[I];
QP1=QP1+(S+K-1)*CB[I];
TST=DMAX1(ABS(P1),ABS(Q1),ABS(PP1),ABS(QP1));
if(TST>OVER) {NSUM=100; return 1;}
T1A=ABS(R1*PP1+H*(AK*P1-UQ*Q1));
T1B=ABS(R1*QP1-H*(AK*Q1-UT*P1));
T1=DMAX1(T1A,T1B);
T2=DMAX1(ABS(CA[I]),ABS(CB[I]));
TST=eps*DMAX1(ABS(P1),ABS(Q1));
if(T1<TST && T2<TST) goto gt06;
}
gt06: NSUM=K+1;
Q1=Q1/P1;
P1=1;
return 1;
gt07:
RHO=H/R0;
U0=(RV0+R0*(RVE+R0*(RV2+R0*RV3)))/c_au;
U1=(RVE+R0*(2*RV2+R0*3*RV3))*H/c_au;
U2=(RV2+R0*3*RV3)*H2/c_au;
U3=RV3*H*H2/c_au;
UB=U0-2*c_au*R0;
UH=U1-2*c_au*H;
UT=U0+U1+U2+U3;
UQ=UT-2*c_au*R1;
CA[1]=P0;
CB[1]=Q0;
CA[2]=RHO*(-AK*CA[1]+UB*CB[1]);
CB[2]=-RHO*(U0*CA[1]-AK*CB[1]);
CA[3]=RHO*(-(1+AK)*CA[2]+UB*CB[2]+UH*CB[1])/2;
CB[3]=-RHO*(U0*CA[2]+(1-AK)*CB[2]+U1*CA[1])/2;
CAI=-(2+AK)*CA[3]+UB*CB[3]+UH*CB[2]+U2*CB[1];
CBI=U0*CA[3]+(2-AK)*CB[3]+U1*CA[2]+U2*CA[1];
CA[4]=RHO*CAI/3;
CB[4]=-RHO*CBI/3;
P1=CA[1]+CA[2]+CA[3]+CA[4];
PP1=CA[2]+2*CA[3]+3*CA[4];
Q1=CB[1]+CB[2]+CB[3]+CB[4];
QP1=CB[2]+2*CB[3]+3*CB[4];
for(I=5; I<=60; I++) {
K=I-1;
CAI=-(K-1+AK)*CA[K]+UB*CB[K]+UH*CB[I-2]+U2*CB[I-3]+U3*CB[I-4];
CBI= U0*CA[K]+(K-1-AK)*CB[K]+U1*CA[I-2]+U2*CA[I-3]+U3*CA[I-4];
CA[I]=RHO*CAI/K;
CB[I]=-RHO*CBI/K;
P1=P1+CA[I];
PP1=PP1+K*CA[I];
Q1=Q1+CB[I];
QP1=QP1+K*CB[I];
TST=DMAX1(ABS(P1),ABS(Q1),ABS(PP1),ABS(QP1));
if(TST>OVER) {NSUM=100; return 1;}
T1A=ABS(R1*PP1+H*(AK*P1-UQ*Q1));
T1B=ABS(R1*QP1-H*(AK*Q1-UT*P1));
T1=DMAX1(T1A,T1B);
T2=DMAX1(ABS(CA[I]),ABS(CB[I]));
TST=eps*DMAX1(ABS(P1),ABS(Q1));
if(T1<TST && T2<TST) goto gt010;
}
gt010: NSUM=K+1;
return 1;
}
void Salvat::SPLINE(numero *X, numero *Y_, numero S1, numero SN, int &N)
{
int N1=N-1;
int N2=N-2;
int I,K;
numero H,HI,R,SI,SI1;
if(N<4) on_error("Salvat::SPLINE", "less than 4 points");
for(I=1; I<=N1; I++) {
if(X[I+1]-X[I]<1.0e-10)
on_error("Salvat::SPLINE", "X is not in increasing order");
A[I]=X[I+1]-X[I];
D[I]=(Y_[I+1]-Y_[I])/A[I];
}
for(I=1; I<=N2; I++) {
B[I]=2.0*(A[I]+A[I+1]);
K=N1-I+1;
D[K]=6.0*(D[K]-D[K-1]);
}
D[2]=D[2]-A[1]*S1;
D[N1]=D[N1]-A[N1]*SN;
for(I=2; I<=N2; I++) {
R=A[I]/B[I-1];
B[I]=B[I]-R*A[I];
D[I+1]=D[I+1]-R*D[I];
}
D[N1]=D[N1]/B[N2];
for(I=2; I<=N2; I++) {
K=N1-I+1;
D[K]=(D[K]-A[K]*D[K+1])/B[K-1];
}
D[N]=SN;
SI1=S1;
for(I=1; I<=N1; I++) {
SI=SI1;
SI1=D[I+1];
H=A[I];
HI=1/H;
A[I]= HI/6*(SI*sqr(X[I+1])*X[I+1]-SI1*sqr(X[I])*X[I])
+HI*(Y_[I]*X[I+1]-Y_[I+1]*X[I])
+H/6*(SI1*X[I]-SI*X[I+1]);
B[I]= HI/2*(SI1*sqr(X[I])-SI*sqr(X[I+1]))
+HI*(Y_[I+1]-Y_[I])+(H/6)*(SI-SI1);
C[I]= HI/2*(SI*X[I+1]-SI1*X[I]);
D[I]= HI/6*(SI1-SI);
} }
numero Salvat::INTEG(numero *X, numero XL, numero XU, int N)
{
numero SUM, SIGN, X1,X2, SUMP;
int IL,IU,I;
SIGN=1;
if(XU<XL) {
SUM=XL;
XL=XU;
XU=SUM;
SIGN=-1;
}
if(XL<X[1] || XU>X[N])
on_error("Salvat::INTEG", "integral limits out of range");
SUM=0;
IL=FINDI(X,XL,N);
IU=FINDI(X,XU,N);
if(IL==IU) {
X1=XL;
X2=XU;
SUM= X2*(A[IL]+X2*((B[IL]/2)+X2*((C[IL]/3)+X2*D[IL]/4)))
-X1*(A[IL]+X1*((B[IL]/2)+X1*((C[IL]/3)+X1*D[IL]/4)));
} else {
X1=XL;
X2=X[IL+1];
SUM= X2*(A[IL]+X2*((B[IL]/2)+X2*((C[IL]/3)+X2*D[IL]/4)))
-X1*(A[IL]+X1*((B[IL]/2)+X1*((C[IL]/3)+X1*D[IL]/4)));
IL=IL+1;
for(I=IL; I<=IU; I++) {
X1=X[I];
X2=X[I+1];
if(I==IU) X2=XU;
SUMP= X2*(A[I]+X2*((B[I]/2)+X2*((C[I]/3)+X2*D[I]/4)))
-X1*(A[I]+X1*((B[I]/2)+X1*((C[I]/3)+X1*D[I]/4)));
SUM=SUM+SUMP;
} }
return SIGN*SUM;
}
int Salvat::FINDI(numero *X, numero XC, int N)
{
int I=1, I1=N, IT;
if(XC>X[N]) return I=N-1;
if(XC<X[1]) return I=1;
do {
IT=(I+I1)/2;
if(XC>X[IT]) I=IT;
if(XC<=X[IT]) I1=IT;
} while(I1-I>1);
return I;
}
void Salvat::printwf(FILE *fout)
{
int I;
fprintf(fout, "%d %f %d %f\n", nmax, E_last, k_last, phase_last);
for(I=0; I<nmax; I++)
fprintf(fout, "%12.5f %15.8f %15.8f\n", rr[I], P[I], Q[I]);
}
void Salvat::vint(numero *r_in, numero *V_in, int n_in, int atZ)
{
numero *R_, *RV_;
int i, nn;
nn=n_in+5;
R_=new numero[nn]; RV_=new numero[nn];
R_[0]=0; RV_[0]=-atZ;
for(i=1; i<nn; i++) if(i<=n_in) {
R_[i]=r_in[i-1];
RV_[i]=r_in[i-1]*V_in[i-1];
} else {R_[i]=r_in[n_in-1]+0.001*(i-n_in-1); RV_[i]=0;}
vint(R_,RV_,nn);
delete [] R_; delete [] RV_;
}
void Salvat::phases(numero *r_in, numero *V_in, int n_in,
int atZ,
numero Ei, numero Ef, int nE,
int rel, int lmax, numero *ph)
{
numero E;
int i,l,k;
vint(r_in, V_in, n_in, atZ);
for(i=0; i<nE; i++) {
if(nE==1) E=Ei; else E=Ei+i*(Ef-Ei)/(nE-1);
if(rel) for(k=-lmax-1; k<=lmax; k++) dfree(E,ph[k+lmax+1],k);
else for(l=0; l<=lmax; l++) dfree(E,ph[i*(lmax+1)+l],-l-1);
} }
#endif
#ifdef jga_Poisson
#else
#define jga_Poisson 1
numero Poisson(numero r, spline rho)
{
if(r==0) r=1e-10;
return r*rho.integ(r,rho.b,-1) + rho.integ(1e-10,r);
}
#endif
#ifdef jga_exchange
#else
#define jga_exchange 1
numero Vxc_Barth_Hedin_F(numero z)
{
return (1+z*z*z)*log(1+1/z) + z/2 - z*z -1/3.0;
}
numero Vxc_Barth_Hedin(numero den, numero denup)
{
if(den<1e-10) return 0;
if(denup<0) denup=0;
numero rs=1/pow(4*pi/3*den, 1/3.0);
numero x=denup/den;
numero alpha0=pow(4/(9*pi), 1/3.0);
numero a=1/pow(2.0, 1/3.0);
numero gamma=4*a/(3*(1-a));
numero cF=0.0254, cP=0.0504;
numero rF=75, rP=30;
numero epsilonFc=-cF*Vxc_Barth_Hedin_F(rs/rF);
numero epsilonPc=-cP*Vxc_Barth_Hedin_F(rs/rP);
numero vc=gamma*(epsilonFc-epsilonPc);
numero epsilon0x=3/(2*pi*alpha0);
numero epsilonPx=-epsilon0x/rs;
numero muPx=4*epsilonPx/3;
numero muPc=-cP*log(1+rP/rs);
numero AA=muPx+vc;
numero BB=muPc-vc;
return (AA*pow(2*x, 1/3.0) + BB) / 2;
}
numero Vxc_Slater(numero x)
{
numero alpha=0.6666666666667;
return -1.5*alpha*pow(3*x/pi,1/3.0);
}
#endif
#ifdef jga_elements
#else
#define jga_elements 1
int element_Z=0;
numero element_mass=0;
char element_symbol[3];
void element_properties(int Z_)
{
int Z=Z_;
numero mass=0;
char symbol[3];
switch(Z) {
case 1: strcpy(symbol,"H" ); mass= 1.008; break;
case 2: strcpy(symbol,"He"); mass= 4.003; break;
case 3: strcpy(symbol,"Li"); mass= 6.941; break;
case 4: strcpy(symbol,"Be"); mass= 9.012; break;
case 5: strcpy(symbol,"B" ); mass= 10.811; break;
case 6: strcpy(symbol,"C" ); mass= 12.011; break;
case 7: strcpy(symbol,"N" ); mass= 14.007; break;
case 8: strcpy(symbol,"O" ); mass= 15.999; break;
case 9: strcpy(symbol,"F" ); mass= 18.998; break;
case 10: strcpy(symbol,"Ne"); mass= 20.180; break;
case 11: strcpy(symbol,"Na"); mass= 22.990; break;
case 12: strcpy(symbol,"Mg"); mass= 24.305; break;
case 13: strcpy(symbol,"Al"); mass= 26.982; break;
case 14: strcpy(symbol,"Si"); mass= 28.086; break;
case 15: strcpy(symbol,"P" ); mass= 30.974; break;
case 16: strcpy(symbol,"S" ); mass= 32.066; break;
case 17: strcpy(symbol,"Cl"); mass= 35.453; break;
case 18: strcpy(symbol,"Ar"); mass= 39.948; break;
case 19: strcpy(symbol,"K" ); mass= 39.098; break;
case 20: strcpy(symbol,"Ca"); mass= 40.078; break;
case 21: strcpy(symbol,"Sc"); mass= 44.956; break;
case 22: strcpy(symbol,"Ti"); mass= 47.880; break;
case 23: strcpy(symbol,"V" ); mass= 50.942; break;
case 24: strcpy(symbol,"Cr"); mass= 51.996; break;
case 25: strcpy(symbol,"Mn"); mass= 54.938; break;
case 26: strcpy(symbol,"Fe"); mass= 55.847; break;
case 27: strcpy(symbol,"Co"); mass= 58.933; break;
case 28: strcpy(symbol,"Ni"); mass= 58.693; break;
case 29: strcpy(symbol,"Cu"); mass= 63.546; break;
case 30: strcpy(symbol,"Zn"); mass= 65.390; break;
case 31: strcpy(symbol,"Ga"); mass= 69.723; break;
case 32: strcpy(symbol,"Ge"); mass= 72.610; break;
case 33: strcpy(symbol,"As"); mass= 74.922; break;
case 34: strcpy(symbol,"Se"); mass= 78.960; break;
case 35: strcpy(symbol,"Br"); mass= 79.904; break;
case 36: strcpy(symbol,"Kr"); mass= 83.800; break;
case 37: strcpy(symbol,"Rb"); mass= 85.468; break;
case 38: strcpy(symbol,"Sr"); mass= 87.620; break;
case 39: strcpy(symbol,"Y" ); mass= 88.906; break;
case 40: strcpy(symbol,"Zr"); mass= 91.224; break;
case 41: strcpy(symbol,"Nb"); mass= 92.906; break;
case 42: strcpy(symbol,"Mo"); mass= 95.940; break;
case 43: strcpy(symbol,"Tc"); mass= 97.907; break;
case 44: strcpy(symbol,"Ru"); mass=101.070; break;
case 45: strcpy(symbol,"Rh"); mass=102.906; break;
case 46: strcpy(symbol,"Pd"); mass=106.420; break;
case 47: strcpy(symbol,"Ag"); mass=107.868; break;
case 48: strcpy(symbol,"Cd"); mass=112.411; break;
case 49: strcpy(symbol,"In"); mass=114.818; break;
case 50: strcpy(symbol,"Sn"); mass=118.710; break;
case 51: strcpy(symbol,"Sb"); mass=121.757; break;
case 52: strcpy(symbol,"Te"); mass=127.600; break;
case 53: strcpy(symbol,"I" ); mass=126.904; break;
case 54: strcpy(symbol,"Xe"); mass=131.290; break;
case 55: strcpy(symbol,"Cs"); mass=132.905; break;
case 56: strcpy(symbol,"Ba"); mass=137.327; break;
case 57: strcpy(symbol,"La"); mass=138.906; break;
case 58: strcpy(symbol,"Ce"); mass=140.115; break;
case 59: strcpy(symbol,"Pr"); mass=140.908; break;
case 60: strcpy(symbol,"Nd"); mass=144.240; break;
case 61: strcpy(symbol,"Pm"); mass=144.913; break;
case 62: strcpy(symbol,"Sm"); mass=150.360; break;
case 63: strcpy(symbol,"Eu"); mass=151.965; break;
case 64: strcpy(symbol,"Gd"); mass=157.250; break;
case 65: strcpy(symbol,"Tb"); mass=158.925; break;
case 66: strcpy(symbol,"Dy"); mass=162.500; break;
case 67: strcpy(symbol,"Ho"); mass=164.930; break;
case 68: strcpy(symbol,"Er"); mass=167.260; break;
case 69: strcpy(symbol,"Tm"); mass=168.934; break;
case 70: strcpy(symbol,"Yb"); mass=173.040; break;
case 71: strcpy(symbol,"Lu"); mass=174.967; break;
case 72: strcpy(symbol,"Hf"); mass=178.490; break;
case 73: strcpy(symbol,"Ta"); mass=180.948; break;
case 74: strcpy(symbol,"W" ); mass=183.840; break;
case 75: strcpy(symbol,"Re"); mass=186.207; break;
case 76: strcpy(symbol,"Os"); mass=190.230; break;
case 77: strcpy(symbol,"Ir"); mass=192.220; break;
case 78: strcpy(symbol,"Pt"); mass=195.080; break;
case 79: strcpy(symbol,"Au"); mass=196.967; break;
case 80: strcpy(symbol,"Hg"); mass=200.590; break;
case 81: strcpy(symbol,"Tl"); mass=204.383; break;
case 82: strcpy(symbol,"Pb"); mass=207.200; break;
case 83: strcpy(symbol,"Bi"); mass=208.980; break;
case 84: strcpy(symbol,"Po"); mass=208.982; break;
case 85: strcpy(symbol,"At"); mass=209.987; break;
case 86: strcpy(symbol,"Rn"); mass=222.018; break;
case 87: strcpy(symbol,"Fr"); mass=223.020; break;
case 88: strcpy(symbol,"Ra"); mass=226.025; break;
case 89: strcpy(symbol,"Ac"); mass=227.028; break;
case 90: strcpy(symbol,"Th"); mass=232.038; break;
case 91: strcpy(symbol,"Pa"); mass=231.036; break;
case 92: strcpy(symbol,"U" ); mass=238.029; break;
case 93: strcpy(symbol,"Np"); mass=237.048; break;
case 94: strcpy(symbol,"Pu"); mass=244.064; break;
case 95: strcpy(symbol,"Am"); mass=243.061; break;
case 96: strcpy(symbol,"Cm"); mass=247.070; break;
case 97: strcpy(symbol,"Bk"); mass=247.070; break;
case 98: strcpy(symbol,"Cf"); mass=251.080; break;
case 99: strcpy(symbol,"Es"); mass=252.083; break;
default: strcpy(symbol, "" ); Z=0; break;
}
element_Z=Z;
element_mass=mass;
strcpy(element_symbol, symbol);
}
int element_properties(char *symbol)
{
int Z;
if(!strcmp(symbol,"H" )) Z= 1; else if(!strcmp(symbol,"He")) Z= 2; else
if(!strcmp(symbol,"Li")) Z= 3; else if(!strcmp(symbol,"Be")) Z= 4; else
if(!strcmp(symbol,"B" )) Z= 5; else if(!strcmp(symbol,"C" )) Z= 6; else
if(!strcmp(symbol,"N" )) Z= 7; else if(!strcmp(symbol,"O" )) Z= 8; else
if(!strcmp(symbol,"F" )) Z= 9; else if(!strcmp(symbol,"Ne")) Z=10; else
if(!strcmp(symbol,"Na")) Z=11; else if(!strcmp(symbol,"Mg")) Z=12; else
if(!strcmp(symbol,"Al")) Z=13; else if(!strcmp(symbol,"Si")) Z=14; else
if(!strcmp(symbol,"P" )) Z=15; else if(!strcmp(symbol,"S" )) Z=16; else
if(!strcmp(symbol,"Cl")) Z=17; else if(!strcmp(symbol,"Ar")) Z=18; else
if(!strcmp(symbol,"K" )) Z=19; else if(!strcmp(symbol,"Ca")) Z=20; else
if(!strcmp(symbol,"Sc")) Z=21; else if(!strcmp(symbol,"Ti")) Z=22; else
if(!strcmp(symbol,"V" )) Z=23; else if(!strcmp(symbol,"Cr")) Z=24; else
if(!strcmp(symbol,"Mn")) Z=25; else if(!strcmp(symbol,"Fe")) Z=26; else
if(!strcmp(symbol,"Co")) Z=27; else if(!strcmp(symbol,"Ni")) Z=28; else
if(!strcmp(symbol,"Cu")) Z=29; else if(!strcmp(symbol,"Zn")) Z=30; else
if(!strcmp(symbol,"Ga")) Z=31; else if(!strcmp(symbol,"Ge")) Z=32; else
if(!strcmp(symbol,"As")) Z=33; else if(!strcmp(symbol,"Se")) Z=34; else
if(!strcmp(symbol,"Br")) Z=35; else if(!strcmp(symbol,"Kr")) Z=36; else
if(!strcmp(symbol,"Rb")) Z=37; else if(!strcmp(symbol,"Sr")) Z=38; else
if(!strcmp(symbol,"Y" )) Z=39; else if(!strcmp(symbol,"Zr")) Z=40; else
if(!strcmp(symbol,"Nb")) Z=41; else if(!strcmp(symbol,"Mo")) Z=42; else
if(!strcmp(symbol,"Tc")) Z=43; else if(!strcmp(symbol,"Ru")) Z=44; else
if(!strcmp(symbol,"Rh")) Z=45; else if(!strcmp(symbol,"Pd")) Z=46; else
if(!strcmp(symbol,"Ag")) Z=47; else if(!strcmp(symbol,"Cd")) Z=48; else
if(!strcmp(symbol,"In")) Z=49; else if(!strcmp(symbol,"Sn")) Z=50; else
if(!strcmp(symbol,"Sb")) Z=51; else if(!strcmp(symbol,"Te")) Z=52; else
if(!strcmp(symbol,"I" )) Z=53; else if(!strcmp(symbol,"Xe")) Z=54; else
if(!strcmp(symbol,"Cs")) Z=55; else if(!strcmp(symbol,"Ba")) Z=56; else
if(!strcmp(symbol,"La")) Z=57; else if(!strcmp(symbol,"Ce")) Z=58; else
if(!strcmp(symbol,"Pr")) Z=59; else if(!strcmp(symbol,"Nd")) Z=60; else
if(!strcmp(symbol,"Pm")) Z=61; else if(!strcmp(symbol,"Sm")) Z=62; else
if(!strcmp(symbol,"Eu")) Z=63; else if(!strcmp(symbol,"Gd")) Z=64; else
if(!strcmp(symbol,"Tb")) Z=65; else if(!strcmp(symbol,"Dy")) Z=66; else
if(!strcmp(symbol,"Ho")) Z=67; else if(!strcmp(symbol,"Er")) Z=68; else
if(!strcmp(symbol,"Tm")) Z=69; else if(!strcmp(symbol,"Yb")) Z=70; else
if(!strcmp(symbol,"Lu")) Z=71; else if(!strcmp(symbol,"Hf")) Z=72; else
if(!strcmp(symbol,"Ta")) Z=73; else if(!strcmp(symbol,"W" )) Z=74; else
if(!strcmp(symbol,"Re")) Z=75; else if(!strcmp(symbol,"Os")) Z=76; else
if(!strcmp(symbol,"Ir")) Z=77; else if(!strcmp(symbol,"Pt")) Z=78; else
if(!strcmp(symbol,"Au")) Z=79; else if(!strcmp(symbol,"Hg")) Z=80; else
if(!strcmp(symbol,"Tl")) Z=81; else if(!strcmp(symbol,"Pb")) Z=82; else
if(!strcmp(symbol,"Bi")) Z=83; else if(!strcmp(symbol,"Po")) Z=84; else
if(!strcmp(symbol,"At")) Z=85; else if(!strcmp(symbol,"Rn")) Z=86; else
if(!strcmp(symbol,"Fr")) Z=87; else if(!strcmp(symbol,"Ra")) Z=88; else
if(!strcmp(symbol,"Ac")) Z=89; else if(!strcmp(symbol,"Th")) Z=90; else
if(!strcmp(symbol,"Pa")) Z=91; else if(!strcmp(symbol,"U" )) Z=92; else
if(!strcmp(symbol,"Np")) Z=93; else if(!strcmp(symbol,"Pu")) Z=94; else
if(!strcmp(symbol,"Am")) Z=95; else if(!strcmp(symbol,"Cm")) Z=96; else
if(!strcmp(symbol,"Bk")) Z=97; else if(!strcmp(symbol,"Cf")) Z=98; else
if(!strcmp(symbol,"Es")) Z=99; else Z= 0;
element_properties(Z);
return Z;
}
void element_orbital(int orb, int &n, int &k)
{
switch(orb) {
case 0: k=-1; n=1; break; case 1: k=-1; n=2; break;
case 2: k= 1; n=2; break; case 3: k=-2; n=2; break;
case 4: k=-1; n=3; break; case 5: k= 1; n=3; break;
case 6: k=-2; n=3; break; case 7: k= 2; n=3; break;
case 8: k=-3; n=3; break; case 9: k=-1; n=4; break;
case 10: k= 1; n=4; break; case 11: k=-2; n=4; break;
case 12: k= 2; n=4; break; case 13: k=-3; n=4; break;
case 14: k= 3; n=4; break; case 15: k=-4; n=4; break;
case 16: k=-1; n=5; break; case 17: k= 1; n=5; break;
case 18: k=-2; n=5; break; case 19: k= 2; n=5; break;
case 20: k=-3; n=5; break; case 21: k= 3; n=5; break;
case 22: k=-4; n=5; break; case 23: k=-1; n=6; break;
case 24: k= 1; n=6; break; case 25: k=-2; n=6; break;
case 26: k= 2; n=6; break; case 27: k=-3; n=6; break;
case 28: k=-1; n=7; break; case -1: k= 0; n=0; break;
} }
int element_orbital(char *name, int &n, int &k)
{
int orb=-1, nr=0;
if(!strcmp(name,"1s")) orb= 0; else
if(!strcmp(name,"2s")) orb= 1; else
if(!strcmp(name,"2p1/2")) orb= 2; else
if(!strcmp(name,"2p3/2")) orb= 3; else
if(!strcmp(name,"3s")) orb= 4; else
if(!strcmp(name,"3p1/2")) orb= 5; else
if(!strcmp(name,"3p3/2")) orb= 6; else
if(!strcmp(name,"3d3/2")) orb= 7; else
if(!strcmp(name,"3d5/2")) orb= 8; else
if(!strcmp(name,"4s")) orb= 9; else
if(!strcmp(name,"4p1/2")) orb=10; else
if(!strcmp(name,"4p3/2")) orb=11; else
if(!strcmp(name,"4d3/2")) orb=12; else
if(!strcmp(name,"4d5/2")) orb=13; else
if(!strcmp(name,"4f5/2")) orb=14; else
if(!strcmp(name,"4f7/2")) orb=15; else
if(!strcmp(name,"5s")) orb=16; else
if(!strcmp(name,"5p1/2")) orb=17; else
if(!strcmp(name,"5p3/2")) orb=18; else
if(!strcmp(name,"5d3/2")) orb=19; else
if(!strcmp(name,"5d5/2")) orb=20; else
if(!strcmp(name,"5f5/2")) orb=21; else
if(!strcmp(name,"5f7/2")) orb=22; else
if(!strcmp(name,"6s")) orb=23; else
if(!strcmp(name,"6p1/2")) orb=24; else
if(!strcmp(name,"6p3/2")) orb=25; else
if(!strcmp(name,"6d3/2")) orb=26; else
if(!strcmp(name,"6d5/2")) orb=27; else
if(!strcmp(name,"7s")) orb=28; else
if(!strcmp(name,"2p")) {orb= 2; nr=1;} else
if(!strcmp(name,"3p")) {orb= 5; nr=1;} else
if(!strcmp(name,"3d")) {orb= 7; nr=1;} else
if(!strcmp(name,"4p")) {orb=10; nr=1;} else
if(!strcmp(name,"4d")) {orb=12; nr=1;} else
if(!strcmp(name,"4f")) {orb=14; nr=1;} else
if(!strcmp(name,"5p")) {orb=17; nr=1;} else
if(!strcmp(name,"5d")) {orb=19; nr=1;} else
if(!strcmp(name,"5f")) {orb=21; nr=1;} else
if(!strcmp(name,"6p")) {orb=24; nr=1;} else
if(!strcmp(name,"6d")) {orb=26; nr=1;}
element_orbital(orb,n,k); if(nr) orb=1000;
return orb;
}
int element_orbital(char *name) {int n,k; return element_orbital(name,n,k);}
int element_occ(int Z, int orb)
{
int *a,
a1[29] ={1,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a2[29] ={2,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a3[29] ={2,1,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a4[29] ={2,2,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a5[29] ={2,2,1,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a6[29] ={2,2,2,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a7[29] ={2,2,2,1,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a8[29] ={2,2,2,2,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a9[29] ={2,2,2,3,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a10[29]={2,2,2,4,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a11[29]={2,2,2,4,1, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a12[29]={2,2,2,4,2, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a13[29]={2,2,2,4,2, 1,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a14[29]={2,2,2,4,2, 2,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a15[29]={2,2,2,4,2, 2,1,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a16[29]={2,2,2,4,2, 2,2,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a17[29]={2,2,2,4,2, 2,3,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a18[29]={2,2,2,4,2, 2,4,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a19[29]={2,2,2,4,2, 2,4,0,0,1, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a20[29]={2,2,2,4,2, 2,4,0,0,2, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a21[29]={2,2,2,4,2, 2,4,1,0,2, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a22[29]={2,2,2,4,2, 2,4,2,0,2, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a23[29]={2,2,2,4,2, 2,4,3,0,2, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a24[29]={2,2,2,4,2, 2,4,4,1,1, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a25[29]={2,2,2,4,2, 2,4,4,1,2, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a26[29]={2,2,2,4,2, 2,4,4,2,2, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a27[29]={2,2,2,4,2, 2,4,4,3,2, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a28[29]={2,2,2,4,2, 2,4,4,4,2, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a29[29]={2,2,2,4,2, 2,4,4,6,1, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a30[29]={2,2,2,4,2, 2,4,4,6,2, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a31[29]={2,2,2,4,2, 2,4,4,6,2, 1,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a32[29]={2,2,2,4,2, 2,4,4,6,2, 2,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a33[29]={2,2,2,4,2, 2,4,4,6,2, 2,1,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a34[29]={2,2,2,4,2, 2,4,4,6,2, 2,2,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a35[29]={2,2,2,4,2, 2,4,4,6,2, 2,3,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a36[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a37[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,0,0,0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0},
a38[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,0,0,0, 0,2,0,0,0, 0,0,0,0,0, 0,0,0,0},
a39[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,1,0,0, 0,2,0,0,0, 0,0,0,0,0, 0,0,0,0},
a40[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,2,0,0, 0,2,0,0,0, 0,0,0,0,0, 0,0,0,0},
a41[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,0,0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0},
a42[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,1,0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0},
a43[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,1,0, 0,2,0,0,0, 0,0,0,0,0, 0,0,0,0},
a44[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,3,0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0},
a45[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,4,0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0},
a46[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0},
a47[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0},
a48[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,0, 0,2,0,0,0, 0,0,0,0,0, 0,0,0,0},
a49[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,0, 0,2,1,0,0, 0,0,0,0,0, 0,0,0,0},
a50[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,0, 0,2,2,0,0, 0,0,0,0,0, 0,0,0,0},
a51[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,0, 0,2,2,1,0, 0,0,0,0,0, 0,0,0,0},
a52[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,0, 0,2,2,2,0, 0,0,0,0,0, 0,0,0,0},
a53[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,0, 0,2,2,3,0, 0,0,0,0,0, 0,0,0,0},
a54[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,0, 0,2,2,4,0, 0,0,0,0,0, 0,0,0,0},
a55[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,0, 0,2,2,4,0, 0,0,0,1,0, 0,0,0,0},
a56[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,0, 0,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a57[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,0, 0,2,2,4,1, 0,0,0,2,0, 0,0,0,0},
a58[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,2, 0,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a59[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,3, 0,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a60[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,4, 0,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a61[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,5, 0,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a62[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 0,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a63[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 1,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a64[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 1,2,2,4,1, 0,0,0,2,0, 0,0,0,0},
a65[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 3,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a66[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 4,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a67[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 5,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a68[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 6,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a69[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 7,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a70[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,0, 0,0,0,2,0, 0,0,0,0},
a71[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,1, 0,0,0,2,0, 0,0,0,0},
a72[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,2, 0,0,0,2,0, 0,0,0,0},
a73[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,3, 0,0,0,2,0, 0,0,0,0},
a74[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 0,0,0,2,0, 0,0,0,0},
a75[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 1,0,0,2,0, 0,0,0,0},
a76[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 2,0,0,2,0, 0,0,0,0},
a77[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 3,0,0,2,0, 0,0,0,0},
a78[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 5,0,0,1,0, 0,0,0,0},
a79[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,0,0,1,0, 0,0,0,0},
a80[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,0,0,2,0, 0,0,0,0},
a81[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,0,0,2,1, 0,0,0,0},
a82[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,0,0,2,2, 0,0,0,0},
a83[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,0,0,2,2, 1,0,0,0},
a84[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,0,0,2,2, 2,0,0,0},
a85[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,0,0,2,2, 3,0,0,0},
a86[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,0,0,2,2, 4,0,0,0},
a87[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,0,0,2,2, 4,0,0,1},
a88[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,0,0,2,2, 4,0,0,2},
a89[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,0,0,2,2, 4,1,0,2},
a90[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,0,0,2,2, 4,2,0,2},
a91[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,2,0,2,2, 4,1,0,2},
a92[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,3,0,2,2, 4,1,0,2},
a93[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,4,0,2,2, 4,1,0,2},
a94[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,6,0,2,2, 4,0,0,2},
a95[29]={2,2,2,4,2, 2,4,4,6,2, 2,4,4,6,6, 8,2,2,4,4, 6,6,1,2,2, 4,0,0,2};
if(Z== 1) a=a1; else if(Z== 2) a=a2; else if(Z== 3) a=a3; else
if(Z== 4) a=a4; else if(Z== 5) a=a5; else if(Z== 6) a=a6; else
if(Z== 7) a=a7; else if(Z== 8) a=a8; else if(Z== 9) a=a9; else
if(Z==10) a=a10; else
if(Z==11) a=a11; else if(Z==12) a=a12; else if(Z==13) a=a13; else
if(Z==14) a=a14; else if(Z==15) a=a15; else if(Z==16) a=a16; else
if(Z==17) a=a17; else if(Z==18) a=a18; else if(Z==19) a=a19; else
if(Z==20) a=a20; else
if(Z==21) a=a21; else if(Z==22) a=a22; else if(Z==23) a=a23; else
if(Z==24) a=a24; else if(Z==25) a=a25; else if(Z==26) a=a26; else
if(Z==27) a=a27; else if(Z==28) a=a28; else if(Z==29) a=a29; else
if(Z==30) a=a30; else
if(Z==31) a=a31; else if(Z==32) a=a32; else if(Z==33) a=a33; else
if(Z==34) a=a34; else if(Z==35) a=a35; else if(Z==36) a=a36; else
if(Z==37) a=a37; else if(Z==38) a=a38; else if(Z==39) a=a39; else
if(Z==40) a=a40; else
if(Z==41) a=a41; else if(Z==42) a=a42; else if(Z==43) a=a43; else
if(Z==44) a=a44; else if(Z==45) a=a45; else if(Z==46) a=a46; else
if(Z==47) a=a47; else if(Z==48) a=a48; else if(Z==49) a=a49; else
if(Z==50) a=a50; else
if(Z==51) a=a51; else if(Z==52) a=a52; else if(Z==53) a=a53; else
if(Z==54) a=a54; else if(Z==55) a=a55; else if(Z==56) a=a56; else
if(Z==57) a=a57; else if(Z==58) a=a58; else if(Z==59) a=a59; else
if(Z==60) a=a60; else
if(Z==61) a=a61; else if(Z==62) a=a62; else if(Z==63) a=a63; else
if(Z==64) a=a64; else if(Z==65) a=a65; else if(Z==66) a=a66; else
if(Z==67) a=a67; else if(Z==68) a=a68; else if(Z==69) a=a69; else
if(Z==70) a=a70; else
if(Z==71) a=a71; else if(Z==72) a=a72; else if(Z==73) a=a73; else
if(Z==74) a=a74; else if(Z==75) a=a75; else if(Z==76) a=a76; else
if(Z==77) a=a77; else if(Z==78) a=a78; else if(Z==79) a=a79; else
if(Z==80) a=a80; else
if(Z==81) a=a81; else if(Z==82) a=a82; else if(Z==83) a=a83; else
if(Z==84) a=a84; else if(Z==85) a=a85; else if(Z==86) a=a86; else
if(Z==87) a=a87; else if(Z==88) a=a88; else if(Z==89) a=a89; else
if(Z==90) a=a90; else
if(Z==91) a=a91; else if(Z==92) a=a92; else if(Z==93) a=a93; else
if(Z==94) a=a94; else if(Z==95) a=a95;
return a[orb];
}
#endif
#ifdef jga_Rho
#else
#define jga_Rho 1
#define Rho_Zmax 95
#define Rho_imax 231
numero Rho_radius[231]={
0, 0.000158461291, 0.000166585785, 0.000175126814,
0.000184105753, 0.000193545056, 0.000203468328, 0.000213900377,
0.000224867283, 0.000236396474, 0.000248516793, 0.000261258509,
0.000274653517, 0.000288735289, 0.000303539069, 0.000319101848,
0.000335462566, 0.000352662086, 0.000370743481, 0.000389751891,
0.000409734901, 0.000430742453, 0.00045282708, 0.000476044021,
0.000500451308, 0.000526110001, 0.000553084246, 0.000581441505,
0.000611252617, 0.000642592204, 0.000675538613, 0.000710174267,
0.000746585662, 0.000784863951, 0.000825104769, 0.000867408817,
0.000911881798, 0.000958634948, 0.00100778521, 0.00105945545,
0.00111377495, 0.00117087935, 0.0012309117, 0.00129402184,
0.00136036775, 0.00143011531, 0.00150343892, 0.00158052193,
0.00166155689, 0.00174674683, 0.00183630444, 0.00193045381,
0.00202943012, 0.0021334812, 0.00224286737, 0.00235786149,
0.00247875159, 0.0026058401, 0.00273944438, 0.00287989853,
0.00302755414, 0.00318278023, 0.00334596471, 0.00351751619,
0.00369786308, 0.00388745661, 0.00408677058, 0.00429630373,
0.00451658014, 0.00474815024, 0.00499159284, 0.00524751749,
0.00551656308, 0.00579940341, 0.00609674538, 0.00640933216,
0.0067379456, 0.0070834076, 0.0074465815, 0.00782837626,
0.00822974555, 0.00865169335, 0.00909527484, 0.00956160016,
0.0100518344, 0.0105672022, 0.0111089936, 0.0116785653,
0.0122773368, 0.0129068103, 0.0135685559, 0.0142642306,
0.014995574, 0.0157644134, 0.0165726729, 0.0174223706,
0.0183156356, 0.0192546975, 0.0202419069, 0.0212797318,
0.0223707668, 0.0235177409, 0.0247235224, 0.0259911232,
0.0273237173, 0.0287246332, 0.0301973764, 0.0317456312,
0.0333732627, 0.0350843482, 0.0368831605, 0.0387741998,
0.0407621972, 0.0428521186, 0.0450491942, 0.0473589152,
0.0497870594, 0.0523396954, 0.0550232083, 0.0578443073,
0.0608100519, 0.0639278516, 0.0672054961, 0.0706511959,
0.0742735639, 0.0780816525, 0.0820849836, 0.0862935707,
0.0907179341, 0.0953691453, 0.10025882, 0.105399199,
0.110803142, 0.116484128, 0.122456402, 0.128734887,
0.135335267, 0.142274037, 0.149568588, 0.157237142,
0.165298864, 0.173773915, 0.182683483, 0.192049876,
0.201896474, 0.212247923, 0.223130122, 0.234570235,
0.246596918, 0.25924021, 0.272531748, 0.286504745,
0.301194161, 0.316636711, 0.33287102, 0.349937677,
0.367879361, 0.386740953, 0.40656957, 0.427414864,
0.44932887, 0.472366452, 0.49658522, 0.522045672,
0.548811555, 0.576949716, 0.606530547, 0.637628019,
0.670319915, 0.704687953, 0.740818083, 0.778800607,
0.818730593, 0.860707819, 0.904837251, 0.951229215,
0.999999821, 1.05127084, 1.10517073, 1.161834,
1.22140253, 1.28402519, 1.34985852, 1.41906726,
1.49182439, 1.56831193, 1.64872086, 1.73325264,
1.8221184, 1.91554046, 2.01375222, 2.11699963,
2.2255404, 2.33964634, 2.45960259, 2.5857091,
2.71828127, 2.85765052, 3.00416541, 3.1581924,
3.32011628, 3.49034238, 3.66929579, 3.85742474,
4.05519915, 4.2631135, 4.48168802, 4.71146917,
4.95303154, 5.2069788, 5.47394609, 5.75460148,
6.04964638, 6.35981846, 6.68589306, 7.02868605,
7.38905478, 7.76789951, 8.16616821, 8.58485699,
9.02501202, 9.48773384, 9.97418022, 10.485568,
11.0231743, 11.5883436, 12.1824923, 12.8071012,
13.4637346, 14.1540356, 14.8797293};
numero Rho_density_data[21945]={
/* Z= 1 -> H */
0, 1.00456127e-07, 1.11019091e-07, 1.22692654e-07,
1.35593552e-07, 1.4985082e-07, 1.65607034e-07, 1.83019779e-07,
2.02263166e-07, 2.23529611e-07, 2.47031778e-07, 2.73004673e-07,
3.01707928e-07, 3.33428545e-07, 3.68483626e-07, 4.07223638e-07,
4.50035799e-07, 4.97348026e-07, 5.49633285e-07, 6.07413995e-07,
6.71267628e-07, 7.41832366e-07, 8.19813124e-07, 9.05989168e-07,
1.00122134e-06, 1.10646101e-06, 1.22275935e-06, 1.35127766e-06,
1.49329981e-06, 1.65024369e-06, 1.82367626e-06, 2.01532907e-06,
2.22711492e-06, 2.46114769e-06, 2.71976273e-06, 3.00554029e-06,
3.32133141e-06, 3.67028611e-06, 4.05588389e-06, 4.48196988e-06,
4.95279119e-06, 5.47304126e-06, 6.04790375e-06, 6.68310622e-06,
7.38497465e-06, 8.16049942e-06, 9.01739986e-06, 9.96420476e-06,
1.10103356e-05, 1.21661978e-05, 1.34432839e-05, 1.48542904e-05,
1.64132362e-05, 1.81356081e-05, 2.00385093e-05, 2.21408263e-05,
2.44634157e-05, 2.70293131e-05, 2.98639497e-05, 3.29954128e-05,
3.6454705e-05, 4.0276067e-05, 4.44972939e-05, 4.91601131e-05,
5.43105925e-05, 5.99995692e-05, 6.62831735e-05, 7.3223353e-05,
8.08884579e-05, 8.935394e-05, 9.87030435e-05, 0.000109027627,
0.000120429017, 0.000133019028, 0.000146920967, 0.000162270881,
0.000179218754, 0.000197930014, 0.000218587084, 0.000241391055,
0.000266563613, 0.00029434904, 0.000325016677, 0.000358863181,
0.000396215415, 0.000437433482, 0.000482913922, 0.000533093407,
0.000588452618, 0.000649520778, 0.000716880138, 0.000791171391,
0.000873099256, 0.000963438768, 0.00106304185, 0.00117284502,
0.00129387714, 0.00142726838, 0.00157425995, 0.00173621427,
0.00191462599, 0.00211113482, 0.00232753903, 0.00256580836,
0.00282810186, 0.00311678252, 0.00343443733, 0.00378389517,
0.00416824874, 0.00459087733, 0.00505547039, 0.00556605263,
0.00612701382, 0.0067431354, 0.0074196225, 0.00816213712,
0.00897683296, 0.00987038855, 0.0108500477, 0.0119236596,
0.0130997151, 0.0143873906, 0.0157965925, 0.0173379928,
0.0190230776, 0.0208641831, 0.0228745434, 0.0250683185,
0.0274606328, 0.0300676059, 0.0329063721, 0.0359951034,
0.0393530056, 0.0430003256, 0.0469583236, 0.051249247,
0.0558962598, 0.0609233938, 0.0663554221, 0.0722177401,
0.0785361975, 0.0853368938, 0.0926459357, 0.10048914,
0.108891688, 0.117877759, 0.127470016, 0.137689099,
0.148553059, 0.160076678, 0.17227073, 0.185141161,
0.198688269, 0.212905705, 0.227779493, 0.243287057,
0.259396046, 0.276063293, 0.293233812, 0.310839623,
0.32879892, 0.347015172, 0.365376502, 0.383755177,
0.402007371, 0.419973403, 0.437478274, 0.45433253,
0.470333964, 0.485269397, 0.498917788, 0.511053145,
0.521448731, 0.529881775, 0.536138415, 0.540019751,
0.541347742, 0.539971888, 0.535775244, 0.528681159,
0.518658578, 0.50572741, 0.48996228, 0.471494913,
0.450515002, 0.427268982, 0.402056634, 0.375225365,
0.347162366, 0.318284601, 0.289026827, 0.259828627,
0.231120169, 0.203308254, 0.176762715, 0.151804343,
0.128695041, 0.107630543, 0.0887365714, 0.0720684081,
0.0576139838, 0.0453001708, 0.0350018516, 0.0265529528,
0.0197586175, 0.0144076366, 0.0102841826, 0.00717815617,
0.00489353901, 0.00325443409, 0.0021087185, 0.0013294518,
0.00081438123, 0.000483997515, 0.000278641004, 0.000155140442,
8.33947197e-05, 4.32019078e-05, 2.15275886e-05, 1.02979602e-05,
4.71912699e-06, 2.06715026e-06, 8.63534012e-07, 3.43186997e-07,
1.29425828e-07, 4.6194522e-08, 1.55605235e-08, 4.93230257e-09,
1.46668255e-09, 4.07843564e-10, 1.05699609e-10,
/* Z= 2 -> He */
0, 1.13589454e-06, 1.25530335e-06, 1.38726273e-06,
1.53309099e-06, 1.69424561e-06, 1.87233672e-06, 2.06914365e-06,
2.28663271e-06, 2.52697646e-06, 2.79257597e-06, 3.08608355e-06,
3.41043074e-06, 3.76885646e-06, 4.16493958e-06, 4.60263436e-06,
5.08631092e-06, 5.62079595e-06, 6.21142499e-06, 6.86409112e-06,
7.58530723e-06, 8.38226697e-06, 9.26292068e-06, 1.02360509e-05,
1.1311362e-05, 1.24995722e-05, 1.3812526e-05, 1.52633074e-05,
1.68663737e-05, 1.8637691e-05, 2.05949018e-05, 2.27574892e-05,
2.51469864e-05, 2.77871677e-05, 3.0704301e-05, 3.39273975e-05,
3.74885058e-05, 4.14230199e-05, 4.57700335e-05, 5.05727185e-05,
5.58787651e-05, 6.17408296e-05, 6.82170576e-05, 7.53716813e-05,
8.32756123e-05, 9.20071398e-05, 0.000101652717, 0.000112307811,
0.000124077793, 0.000137079012, 0.000151439875, 0.000167302176,
0.000184822376, 0.000204173179, 0.000225545198, 0.000249148754,
0.000275215978, 0.000304002984, 0.000335792254, 0.000370895577,
0.000409656757, 0.000452455075, 0.000499708811, 0.000551879173,
0.000609474839, 0.000673056464, 0.000743242214, 0.000820713409,
0.000906220812, 0.0010005919, 0.0011047381, 0.00121966354,
0.00134647405, 0.00148638745, 0.00164074451, 0.00181102089,
0.00199884083, 0.00220599119, 0.0024344374, 0.00268634153,
0.00296408031, 0.00327026588, 0.00360776903, 0.00397974299,
0.00438965019, 0.00484129321, 0.00533884251, 0.00588687463,
0.00649040798, 0.00715494249, 0.00788650475, 0.00869169179,
0.00957772788, 0.0105525143, 0.0116246901, 0.0128036942,
0.0140998363, 0.0155243669, 0.0170895569, 0.0188087728,
0.0206965767, 0.0227688085, 0.0250426866, 0.0275369156,
0.0302717797, 0.0332692713, 0.0365532003, 0.0401492976,
0.0440853685, 0.0483913869, 0.0530996323, 0.0582448132,
0.063864179, 0.0699976459, 0.0766878873, 0.0839804485,
0.0919238254, 0.100569502, 0.109972037, 0.120189048,
0.131281212, 0.143312156, 0.156348407, 0.170459226,
0.185716346, 0.202193692, 0.219966978, 0.239113286,
0.259710371, 0.281836092, 0.305567503, 0.330979884,
0.358145654, 0.387133032, 0.418004692, 0.450816005,
0.485613376, 0.522432148, 0.561294496, 0.602207065,
0.645158589, 0.69011718, 0.737027764, 0.7858091,
0.836351335, 0.888513088, 0.942119002, 0.996957183,
1.05277741, 1.10928953, 1.16616201, 1.22302175,
1.27945435, 1.33500564, 1.38918328, 1.44146061,
1.49128115, 1.5380646, 1.58121407, 1.62012458,
1.65419304, 1.68282926, 1.70546842, 1.72158372,
1.73070037, 1.73240936, 1.72638035, 1.71237636,
1.69026423, 1.66002572, 1.62176561, 1.57571781,
1.52224755, 1.461851, 1.3951503, 1.32288587,
1.24590361, 1.16513884, 1.08159697, 0.996330559,
0.910414219, 0.824918032, 0.740880013, 0.659279406,
0.581010818, 0.506861448, 0.437491953, 0.373421729,
0.315019578, 0.262500376, 0.215927616, 0.175222009,
0.140175432, 0.110469371, 0.0856969506, 0.0653869659,
0.049028568, 0.036095228, 0.0260665063, 0.0184466112,
0.0127790077, 0.00865659025, 0.00572748017, 0.00369674386,
0.00232465775, 0.00142232596, 0.000845524773, 0.000487636047,
0.000272414298, 0.000147169005, 7.67549645e-05, 3.85756684e-05,
1.86470625e-05, 8.65224047e-06, 3.84551959e-06, 1.63354457e-06,
6.61682236e-07, 2.54949157e-07, 9.3203937e-08, 3.22425073e-08,
1.05249232e-08, 3.23243388e-09, 9.31168087e-10, 2.50797549e-10,
6.2945725e-11, 1.46707004e-11, 3.16385134e-12, 6.28997017e-13,
1.14838464e-13, 1.9179157e-14, 2.91834169e-15,
/* Z= 3 -> Li */
0, 4.37118069e-06, 4.8305501e-06, 5.33818229e-06,
5.89914453e-06, 6.51903747e-06, 7.20404933e-06, 7.96101631e-06,
8.79749405e-06, 9.72182897e-06, 1.07432443e-05, 1.1871929e-05,
1.31191418e-05, 1.44973219e-05, 1.60202126e-05, 1.77029942e-05,
1.95624452e-05, 2.16170974e-05, 2.38874236e-05, 2.63960428e-05,
2.91679426e-05, 3.22307278e-05, 3.56148885e-05, 3.93541159e-05,
4.34856156e-05, 4.80504859e-05, 5.30941361e-05, 5.86667084e-05,
6.48235946e-05, 7.16259674e-05, 7.91413913e-05, 8.74444959e-05,
9.66176958e-05, 0.000106751992, 0.000117947893, 0.000130316374,
0.000143980011, 0.000159074087, 0.00017574802, 0.000194166743,
0.000214512402, 0.000236986001, 0.000261809473, 0.000289227755,
0.00031951128, 0.000352958421, 0.000389898516, 0.000430695014,
0.000475748908, 0.000525502721, 0.000580444525, 0.000641112914,
0.000708101958, 0.000782066782, 0.000863729976, 0.000953888288,
0.00105342036, 0.00116329477, 0.00128457928, 0.0014184505,
0.00156620552, 0.00172927312, 0.00190922769, 0.00210780324,
0.00232690992, 0.00256865029, 0.00283533987, 0.00312952697,
0.00345401559, 0.00381189166, 0.00420654891, 0.00464171916,
0.00512150582, 0.00565041834, 0.00623341277, 0.00687593129,
0.00758395111, 0.00836403295, 0.00922337733, 0.0101698805,
0.0112122009, 0.0123598287, 0.0136231612, 0.0150135821,
0.0165435486, 0.0182266925, 0.0200779103, 0.0221134815,
0.0243511815, 0.0268104076, 0.0295123067, 0.0324799232,
0.0357383527, 0.0393148847, 0.04323918, 0.0475434512,
0.0522626415, 0.0574346073, 0.0631003156, 0.0693040714,
0.0760936886, 0.0835207254, 0.0916406661, 0.10051316,
0.110202193, 0.120776303, 0.132308736, 0.144877598,
0.158566013, 0.173462197, 0.189659536, 0.207256526,
0.226356849, 0.247069106, 0.269506723, 0.293787479,
0.320033342, 0.348369628, 0.378924429, 0.411827773,
0.447210491, 0.485202938, 0.525933564, 0.56952697,
0.616102219, 0.665770113, 0.71863091, 0.774771333,
0.834261179, 0.897149861, 0.963462591, 1.03319609,
1.10631442, 1.18274379, 1.26236844, 1.34502542,
1.43049955, 1.51851881, 1.60875022, 1.70079494,
1.79418564, 1.88838315, 1.98277557, 2.07667708,
2.16932917, 2.25990391, 2.34750891, 2.43119287,
2.50995684, 2.58276439, 2.64855766, 2.70627236,
2.75485945, 2.7933054, 2.8206563, 2.83604407,
2.83871174, 2.82804012, 2.8035748, 2.76504874,
2.71240592, 2.64581919, 2.56570244, 2.47272015,
2.36778736, 2.25206351, 2.12693787, 1.99400628,
1.85504138, 1.71195269, 1.56674206, 1.42145276,
1.27811456, 1.13868833, 1.00501025, 0.878740668,
0.761316955, 0.653916001, 0.557426214, 0.472430438,
0.399202317, 0.337713957, 0.287655681, 0.248465836,
0.219368368, 0.199415877, 0.187534973, 0.182571426,
0.183332443, 0.188624233, 0.197283581, 0.208203018,
0.220349818, 0.232779726, 0.244646654, 0.255209774,
0.263839036, 0.270020127, 0.273359478, 0.273588419,
0.270566821, 0.264284313, 0.254858524, 0.242528975,
0.227645829, 0.210653082, 0.192066744, 0.172448367,
0.152375966, 0.132413641, 0.113082796, 0.0948366374,
0.0780402049, 0.0629576147, 0.0497471541, 0.0384642333,
0.0290716179, 0.0214552432, 0.0154437311, 0.0108292922,
0.00738792494, 0.00489705475, 0.00314934971, 0.0019621423,
0.00118244125, 0.000688092725, 0.000385987078, 0.000208333237,
0.000107984568, 5.36411208e-05, 2.54821152e-05,
/* Z= 4 -> Be */
0, 1.12235603e-05, 1.24026174e-05, 1.37054913e-05,
1.51451768e-05, 1.67360322e-05, 1.84939199e-05, 2.0436366e-05,
2.25827334e-05, 2.49544155e-05, 2.75750463e-05, 3.04707355e-05,
3.3670327e-05, 3.72056893e-05, 4.11120272e-05, 4.54282235e-05,
5.01972427e-05, 5.54665385e-05, 6.12885269e-05, 6.77211137e-05,
7.48282546e-05, 8.26805917e-05, 9.13561526e-05, 0.000100941121,
0.000111530659, 0.000123229896, 0.000136154908, 0.000150433916,
0.000166208454, 0.000183634897, 0.000202885814, 0.000224151852,
0.000247643417, 0.000273592857, 0.000302256696, 0.000333918084,
0.000368889596, 0.000407516258, 0.000450178923, 0.000497297908,
0.00054933707, 0.000606808288, 0.000670276408, 0.00074036466,
0.000817760592, 0.000903222768, 0.000997587922, 0.00110177882,
0.00121681322, 0.00134381349, 0.00148401712, 0.00163878838,
0.00180963136, 0.00199820357, 0.00220633158, 0.00243602879,
0.00268951268, 0.0029692261, 0.00327785918, 0.00361837493,
0.0039940346, 0.00440842891, 0.00486550853, 0.00536962086,
0.0059255478, 0.00653854758, 0.00721440231, 0.00795946736,
0.00878072437, 0.00968584698, 0.0106832562, 0.011782201,
0.0129928291, 0.0143262716, 0.0157947373, 0.0174116064,
0.0191915352, 0.0211505778, 0.0233063046, 0.0256779343,
0.0282864869, 0.0311549231, 0.0343083218, 0.0377740525,
0.0415819585, 0.0457645655, 0.0503572971, 0.0553986803,
0.060930606, 0.0669985637, 0.0736519024, 0.0809441209,
0.0889331102, 0.0976814851, 0.107256837, 0.117732093,
0.129185721, 0.141702116, 0.155371845, 0.17029193,
0.186566085, 0.204304948, 0.22362633, 0.244655281,
0.267524213, 0.292372912, 0.319348484, 0.348605156,
0.380304039, 0.414612651, 0.451704293, 0.491757363,
0.53495425, 0.581480086, 0.631521523, 0.685264409,
0.742892087, 0.804582715, 0.870506346, 0.940821767,
1.01567256, 1.09518301, 1.17945325, 1.26855481,
1.36252367, 1.46135569, 1.5649991, 1.67334831,
1.78623664, 1.90342879, 2.02461457, 2.14940095,
2.2773056, 2.40775061, 2.54005814, 2.67344475,
2.80702019, 2.93978572, 3.07063532, 3.19836044,
3.32165647, 3.43913317, 3.54932737, 3.6507225,
3.74176788, 3.82090712, 3.88660479, 3.93738174,
3.97185063, 3.98875499, 3.98701024, 3.96574521,
3.92434144, 3.86247325, 3.78014088, 3.67770028,
3.55588436, 3.41581464, 3.25900388, 3.08734488,
2.90308762, 2.70880103, 2.50732374, 2.30170059,
2.09510756, 1.89076924, 1.69186831, 1.50145376,
1.32234931, 1.15706742, 1.00773227, 0.876016557,
0.763094068, 0.669611156, 0.595678687, 0.540884018,
0.50432235, 0.484645575, 0.480124861, 0.488724113,
0.508179426, 0.536081493, 0.569956541, 0.607343674,
0.645865917, 0.683293641, 0.717599988, 0.74700731,
0.770025611, 0.785481334, 0.79253757, 0.790704727,
0.779841065, 0.760142148, 0.732119501, 0.696568251,
0.654524326, 0.607212126, 0.555986106, 0.50226754,
0.447480291, 0.39298895, 0.340042859, 0.289728671,
0.242934436, 0.200326711, 0.16234149, 0.129189074,
0.10087131, 0.0772093907, 0.0578791834, 0.0424509794,
0.0304300357, 0.0212948974, 0.0145307416, 0.00965585746,
0.00624031154, 0.00391673716, 0.002383983, 0.00140496797,
0.000800392008, 0.000440010946, 0.00023300288, 0.000118622753,
5.79445805e-05, 2.71006902e-05, 1.21090015e-05, 5.15686543e-06,
2.08809661e-06, 8.01840258e-07, 2.91224268e-07,
/* Z= 5 -> B */
0, 2.28794652e-05, 2.52819827e-05, 2.7936665e-05,
3.08699637e-05, 3.41110936e-05, 3.76923381e-05, 4.16493567e-05,
4.60215488e-05, 5.08524281e-05, 5.61900706e-05, 6.20875871e-05,
6.86036365e-05, 7.58030219e-05, 8.3757317e-05, 9.25455897e-05,
0.000102255151, 0.000112982467, 0.000124834056, 0.000137927564,
0.000152392924, 0.000168373648, 0.000186028192, 0.000205531542,
0.000227076933, 0.000250877754, 0.000277169573, 0.000306212518,
0.000338293787, 0.000373730436, 0.000412872498, 0.000456106296,
0.000503858435, 0.000556599523, 0.000614849268, 0.000679180957,
0.000750227424, 0.000828686869, 0.000915329787, 0.00101100607,
0.00111665356, 0.00123330671, 0.00136210618, 0.00150431064,
0.00166130741, 0.00183462666, 0.00202595559, 0.00223715371,
0.00247027073, 0.00272756605, 0.00301152887, 0.00332490192,
0.00367070711, 0.00405227207, 0.004473262, 0.00493771117,
0.00545006292, 0.00601520482, 0.00663851714, 0.00732591748,
0.00808391441, 0.00891966559, 0.00984103885, 0.0108566787,
0.0119760865, 0.013209695, 0.0145689566, 0.0160664488,
0.0177159607, 0.0195326228, 0.0215330217, 0.0237353314,
0.0261594597, 0.0288272016, 0.0317624025, 0.0349911526,
0.0385419503, 0.042445939, 0.0467371196, 0.0514525808,
0.056632746, 0.0623216666, 0.0685672686, 0.0754216984,
0.0829415843, 0.0911884233, 0.100228868, 0.110135138,
0.120985359, 0.132863939, 0.145861953, 0.160077572,
0.175616369, 0.192591786, 0.211125404, 0.231347367,
0.25339669, 0.277421415, 0.303579003, 0.332036346,
0.362969905, 0.396565646, 0.433018923, 0.47253409,
0.515324056, 0.561609745, 0.611618996, 0.665585399,
0.723747134, 0.786344647, 0.853619039, 0.925809085,
1.00314832, 1.08586144, 1.17416024, 1.26823938,
1.3682704, 1.47439635, 1.58672583, 1.70532441,
1.8302089, 1.96133745, 2.09860229, 2.24181914,
2.39071918, 2.5449388, 2.70401025, 2.86735344,
3.034266, 3.20391679, 3.37534022, 3.54743075,
3.71894145, 3.88848472, 4.05453491, 4.21543789,
4.36942101, 4.51460981, 4.64905167, 4.7707386,
4.87764263, 4.96775293, 5.03911877, 5.08989477,
5.11839628, 5.12314987, 5.10295343, 5.05692577,
4.98456669, 4.88580036, 4.76102114, 4.61112309,
4.43752527, 4.24217367, 4.02753496, 3.79656816,
3.55267763, 3.299649, 3.04156494, 2.78270507,
2.5274322, 2.28006744, 2.04476094, 1.82536161,
1.62529337, 1.44744205, 1.29405975, 1.16669226,
1.06613076, 0.992394924, 0.944742262, 0.92170918,
0.921177208, 0.940462112, 0.976421416, 1.02557361,
1.0842247, 1.14859617, 1.21494865, 1.27969861,
1.33952415, 1.39145756, 1.43296206, 1.4619931,
1.47704196, 1.47716093, 1.46196938, 1.4316411,
1.38687205, 1.32883096, 1.25909138, 1.17955256,
1.09234738, 0.999746323, 0.904058278, 0.807535708,
0.712287724, 0.620205402, 0.532902896, 0.451675922,
0.377480209, 0.310928017, 0.252302974, 0.201589778,
0.158516213, 0.122603163, 0.0932189971, 0.0696340278,
0.0510715432, 0.0367525741, 0.0259323418, 0.017927289,
0.0121326819, 0.00803139713, 0.00519527216, 0.00328066759,
0.00202006195, 0.00121138082, 0.000706519233, 0.000400178134,
0.000219770736, 0.000116819407, 5.99887753e-05, 2.96999751e-05,
1.41460578e-05, 6.46714489e-06, 2.83097779e-06, 1.18359128e-06,
4.71357936e-07, 1.78309506e-07, 6.38870645e-08,
/* Z= 6 -> C */
0, 4.0714538e-05, 4.49878207e-05, 4.97093715e-05,
5.4926164e-05, 6.06901049e-05, 6.70585214e-05, 7.40947435e-05,
8.18687331e-05, 9.04577537e-05, 9.99471522e-05, 0.00011043121,
0.000122014048, 0.000134810674, 0.000148948093, 0.000164566576,
0.000181821059, 0.000200882627, 0.000221940179, 0.000245202391,
0.000270899589, 0.000299286214, 0.000330643059, 0.000365280313,
0.000403540267, 0.000445800921, 0.000492479594, 0.000544036797,
0.000600981002, 0.000663873332, 0.000733333232, 0.000810044177,
0.00089476048, 0.00098831451, 0.00109162449, 0.00120570394,
0.00133167044, 0.00147075707, 0.00162432413, 0.00179387128,
0.0019810528, 0.00218769279, 0.00241580233, 0.00266759819,
0.00294552394, 0.00325227319, 0.00359081314, 0.00396441435,
0.00437667919, 0.00483157486, 0.00533347158, 0.00588718057,
0.00649799826, 0.00717175426, 0.00791486353, 0.00873438362,
0.00963807665, 0.01063448, 0.0117329769, 0.0129438806,
0.0142785236, 0.0157493539, 0.0173700359, 0.0191555731,
0.0211224295, 0.0232886579, 0.0256740525, 0.0283003151,
0.0311912112, 0.0343727656, 0.0378734544, 0.041724436,
0.045959767, 0.0506166518, 0.0557357259, 0.0613613129,
0.0675417557, 0.0743297189, 0.0817825496, 0.0899626091,
0.0989376903, 0.108781397, 0.119573571, 0.131400704,
0.144356415, 0.158541903, 0.174066424, 0.191047713,
0.209612563, 0.229897171, 0.252047658, 0.27622056,
0.302583039, 0.331313431, 0.362601429, 0.396648288,
0.433666974, 0.473882198, 0.517530143, 0.564858317,
0.616124868, 0.671597898, 0.731554449, 0.796279192,
0.86606276, 0.941199422, 1.02198493, 1.10871315,
1.20167255, 1.30114222, 1.4073869, 1.52065134,
1.64115465, 1.76908231, 1.9045794, 2.04774189,
2.19860673, 2.35714316, 2.52324057, 2.69669867,
2.87721562, 3.06437612, 3.25763988, 3.4563303,
3.65962362, 3.86654019, 4.07593489, 4.28649282,
4.49672508, 4.70496798, 4.90938902, 5.10799122,
5.29863167, 5.47903585, 5.64682627, 5.79955292,
5.93473244, 6.04989433, 6.14263391, 6.21066809,
6.25190353, 6.26450062, 6.24694729, 6.19812489,
6.11738157, 6.00459146, 5.86021185, 5.6853261,
5.48167372, 5.25166035, 4.9983511, 4.72543716,
4.43717909, 4.13832712, 3.83401561, 3.52963567,
3.23068929, 2.94262838, 2.67068624, 2.41970658,
2.19397998, 1.99709332, 1.83180165, 1.69992697,
1.60229325, 1.53869748, 1.50792205, 1.50778484,
1.53522897, 1.5864414, 1.6570009, 1.7420435,
1.83644021, 1.93497717, 2.03253412, 2.12425137,
2.20568085, 2.27292037, 2.32271957, 2.3525641,
2.36072969, 2.3463068, 2.309196, 2.25007486,
2.17033482, 2.07199597, 1.95759714, 1.83007252,
1.69261634, 1.54854429, 1.40115809, 1.25361896,
1.10883725, 0.969381273, 0.837409914, 0.714629769,
0.602277756, 0.501127362, 0.41151607, 0.333390117,
0.26636216, 0.209777206, 0.162781686, 0.124391638,
0.0935558602, 0.0692112222, 0.0503282957, 0.0359461084,
0.0251962356, 0.0173167586, 0.0116575742, 0.00767859351,
0.00494270399, 0.0031051999, 0.00190126954, 0.00113284099,
0.000655786716, 0.000368195149, 0.00020013639, 0.000105117593,
5.32419435e-05, 2.59506705e-05, 1.21452331e-05, 5.44541308e-06,
2.33338528e-06, 9.53217352e-07, 3.70272346e-07, 1.36395798e-07,
4.75125326e-08, 1.56051598e-08, 4.81784879e-09,
/* Z= 7 -> N */
0, 6.60882943e-05, 7.30210159e-05, 8.06805256e-05,
8.91429227e-05, 9.84922881e-05, 0.000108821492, 0.00012023309,
0.000132840374, 0.000146768463, 0.000162155557, 0.000179154245,
0.000197933085, 0.000218678237, 0.000241595204, 0.000266910996,
0.000294876227, 0.000325767644, 0.000359890808, 0.00039758315,
0.00043921711, 0.000485203898, 0.000535997504, 0.000592099095,
0.000654061791, 0.000722496188, 0.0007980761, 0.00088154542,
0.00097372476, 0.00107551995, 0.00118793023, 0.0013120583,
0.0014491207, 0.00160045933, 0.00176755432, 0.0019520385,
0.00215571234, 0.00238056132, 0.00262877462, 0.00290276599,
0.00320519623, 0.00353899761, 0.00390740251, 0.00431397185,
0.00476262951, 0.00525769824, 0.00580393802, 0.00640659127,
0.00707143033, 0.00780480914, 0.00861372054, 0.00950585864,
0.0104896883, 0.0115745207, 0.0127705932, 0.0140891569,
0.0155425817, 0.0171444546, 0.0189096984, 0.0208547004,
0.0229974426, 0.0253576618, 0.0279569961, 0.0308191776,
0.033970207, 0.037438564, 0.0412554368, 0.0454549491,
0.0500744246, 0.0551546589, 0.0607402287, 0.066879794,
0.0736264437, 0.0810380653, 0.0891777128, 0.0981140435,
0.10792172, 0.11868187, 0.130482584, 0.1434194,
0.157595798, 0.173123762, 0.190124333, 0.208728135,
0.229075983, 0.251319379, 0.275621086, 0.302155763,
0.331110299, 0.362684369, 0.397090882, 0.434556156,
0.475320399, 0.519637525, 0.567775488, 0.620015621,
0.676652789, 0.737994134, 0.80435878, 0.876075923,
0.95348376, 1.0369271, 1.12675488, 1.22331703,
1.32696104, 1.43802726, 1.55684435, 1.68372262,
1.81894827, 1.96277571, 2.11541867, 2.2770412,
2.44774771, 2.62757134, 2.81646299, 3.01427722,
3.22076058, 3.43553662, 3.6580925, 3.88776588,
4.12373018, 4.36498308, 4.61033583, 4.85840225,
5.10759497, 5.35611916, 5.60197544, 5.84296417,
6.0766964, 6.3006115, 6.51200199, 6.70804548,
6.88584232, 7.04246807, 7.17502737, 7.2807188,
7.35690832, 7.40120554, 7.41154814, 7.38628578,
7.324265, 7.22491074, 7.08830023, 6.91522884,
6.70725679, 6.46674109, 6.19684267, 5.90150881,
5.58542442, 5.25393772, 4.91295099, 4.56878138,
4.22800016, 3.89724422, 3.58301234, 3.29145575,
3.02816629, 2.79797482, 2.6047709, 2.45135117,
2.33930421, 2.26894355, 2.23928571, 2.24808192,
2.2918992, 2.36624861, 2.46575189, 2.58434439,
2.71549582, 2.85244918, 2.98845792, 3.11701822,
3.23208642, 3.32826996, 3.40099239, 3.44662142,
3.46256042, 3.44729924, 3.4004221, 3.32257795,
3.21540737, 3.08143735, 2.92394423, 2.7467916,
2.55425501, 2.35083652, 2.14108086, 1.92940557,
1.719944, 1.51641643, 1.32202828, 1.13940179,
0.970538676, 0.816815376, 0.679006398, 0.557332039,
0.451525003, 0.360910594, 0.284494013, 0.221049413,
0.169205651, 0.127524376, 0.0945676938, 0.0689531937,
0.049395632, 0.0347354971, 0.023955375, 0.0161858089,
0.0107025569, 0.00691741239, 0.0043646032, 0.00268468633,
0.00160750956, 0.000935512362, 0.000528284174, 0.000288972195,
0.000152835812, 7.80094852e-05, 3.83492807e-05, 1.81196647e-05,
8.21072899e-06, 3.5601347e-06, 1.47358628e-06, 5.80812127e-07,
2.17433396e-07, 7.71041258e-08, 2.58266972e-08, 8.14752976e-09,
2.41334908e-09, 6.69062583e-10, 1.73031353e-10,
/* Z= 8 -> O */
0, 0.000100438039, 0.000110967849, 0.000122600773,
0.000135452254, 0.000149649757, 0.000165334102, 0.000182660791,
0.000201801566, 0.000222946066, 0.000246303709, 0.000272105826,
0.000300607731, 0.00033209144, 0.000366868335, 0.000405282161,
0.00044771246, 0.000494578329, 0.000546342286, 0.000603515131,
0.000666660431, 0.000736400601, 0.000813422317, 0.000898483617,
0.000992421061, 0.00109615782, 0.00121071259, 0.00133720948,
0.00147688854, 0.00163111801, 0.0018014072, 0.00198942074,
0.00219699508, 0.00242615491, 0.00267913355, 0.00295839296,
0.00326664769, 0.0036068901, 0.00398241822, 0.00439686654,
0.00485424139, 0.00535895443, 0.00591586763, 0.00653033471,
0.00720825186, 0.0079561118, 0.00878105965, 0.00969096273,
0.0106944749, 0.011801118, 0.0130213648, 0.014366732,
0.015849879, 0.0174847208, 0.0192865431, 0.0212721396,
0.0234599467, 0.025870204, 0.0285251196, 0.0314490497,
0.0346687064, 0.0382133573, 0.0421150699, 0.0464089587,
0.0511334501, 0.0563305803, 0.0620463081, 0.0683308393,
0.0752390102, 0.0828306526, 0.0911710113, 0.100331172,
0.110388562, 0.12142738, 0.133539185, 0.146823347,
0.161387727, 0.177349165, 0.194834173, 0.213979483,
0.23493278, 0.25785327, 0.282912374, 0.3102943,
0.340196848, 0.372831792, 0.40842548, 0.447219461,
0.48947069, 0.535452068, 0.585452378, 0.639776468,
0.698745012, 0.76269418, 0.831974924, 0.906952024,
0.988002658, 1.07551479, 1.16988504, 1.27151525,
1.38081014, 1.49817228, 1.62399805, 1.75867152,
1.90255833, 2.05599809, 2.21929622, 2.39271402,
2.57645893, 2.77067304, 2.97541928, 3.19066978,
3.41629004, 3.65202451, 3.89748049, 4.15211248,
4.41520596, 4.68586254, 4.96298361, 5.24525833,
5.5311532, 5.81890154, 6.1065011, 6.39171124,
6.67206049, 6.94485474, 7.2071991, 7.45602179,
7.68810987, 7.90015459, 8.08880424, 8.25073147,
8.38270092, 8.48165703, 8.5448122, 8.56974125,
8.55448341, 8.4976387, 8.39846706, 8.25697422,
8.07399559, 7.85125065, 7.59138775, 7.29799652,
6.97559023, 6.62955904, 6.26608181, 5.89200449,
5.51468229, 5.1417861, 4.78108644, 4.44020844,
4.12638187, 3.84618521, 3.60529971, 3.40828705,
3.25839925, 3.15743375, 3.10564089, 3.10169101,
3.14270592, 3.22435069, 3.34098577, 3.48587084,
3.65141225, 3.82944059, 4.01150846, 4.18919277,
4.35438967, 4.4995923, 4.61813831, 4.70441818,
4.75404167, 4.7639513, 4.73248339, 4.65937567,
4.54571962, 4.39386368, 4.20727205, 3.99034071,
3.74819088, 3.48643827, 3.21095872, 2.92765641,
2.64224625, 2.36006308, 2.08589935, 1.82388318,
1.57739449, 1.34902275, 1.14056265, 0.953044772,
0.786796212, 0.641522825, 0.516408086, 0.41022101,
0.321425438, 0.248286113, 0.188966006, 0.141611308,
0.104421958, 0.0757064298, 0.0539208874, 0.0376936644,
0.0258366689, 0.0173458848, 0.0113932518, 0.00731229875,
0.00457976153, 0.00279515958, 0.00165997457, 0.000957741751,
0.000535960949, 0.000290406169, 0.000152083085, 7.68309692e-05,
3.73690964e-05, 1.74627148e-05, 7.82339703e-06, 3.35261052e-06,
1.37104132e-06, 5.33736568e-07, 1.97284677e-07, 6.90526107e-08,
2.28225971e-08, 7.10185599e-09, 2.07428497e-09, 5.66847624e-10,
1.44450993e-10, 3.4208171e-11, 7.50134416e-12,
/* Z= 9 -> F */
0, 0.000145245256, 0.000160462718, 0.000177273207,
0.00019584324, 0.00021635677, 0.000239016896, 0.000264047936,
0.000291697506, 0.000322239153, 0.0003559748, 0.00039323789,
0.000434396527, 0.000479857117, 0.000530068413, 0.000585525704,
0.000646775821, 0.000714422378, 0.000789131562, 0.000871638767,
0.000962755526, 0.0010633776, 0.00117449334, 0.0012971937,
0.00143268181, 0.00158228562, 0.00174747012, 0.00192985113,
0.00213121134, 0.00235351641, 0.00259893527, 0.00286985817,
0.00316892215, 0.0034990334, 0.00386339659, 0.00426554354,
0.00470936671, 0.0051991553, 0.00573963625, 0.00633601611,
0.00699402951, 0.00771999313, 0.00852086022, 0.00940428954,
0.0103787063, 0.0114533864, 0.0126385307, 0.0139453681,
0.0153862387, 0.0169747155, 0.0187257156, 0.020655632,
0.0227824729, 0.0251260139, 0.0277079679, 0.0305521619,
0.033684738, 0.037134368, 0.0409324728, 0.0451134965,
0.0497151501, 0.0547787249, 0.0603494048, 0.0664765909,
0.0732142925, 0.0806214884, 0.0887625813, 0.097707808,
0.10753376, 0.118323848, 0.13016887, 0.14316757,
0.157427222, 0.173064291, 0.190205038, 0.208986282,
0.229555964, 0.252074063, 0.276713073, 0.303658992,
0.333111912, 0.365286767, 0.40041405, 0.438740402,
0.480529338, 0.526061654, 0.57563585, 0.629568577,
0.688194573, 0.751866698, 0.820955753, 0.895849705,
0.97695303, 1.06468523, 1.15947914, 1.26177919,
1.37203801, 1.49071336, 1.61826396, 1.75514472,
1.90180039, 2.05865979, 2.22612715, 2.40457416,
2.59432912, 2.79566669, 3.00879455, 3.23384118,
3.47083998, 3.7197144, 3.98026109, 4.25213242,
4.5348177, 4.82762718, 5.12967205, 5.43984747,
5.75681829, 6.07900238, 6.40456152, 6.73139238,
7.05712414, 7.3791194, 7.69448423, 8.00008392,
8.29256725, 8.5684042, 8.82392502, 9.05538273,
9.25901508, 9.43112564, 9.56817055, 9.66685963,
9.72425938, 9.73790741, 9.70592499, 9.62713242,
9.50115204, 9.32851124, 9.11071682, 8.85031986,
8.55094242, 8.21727943, 7.85506248, 7.47097731,
7.07254505, 6.66795826, 6.26587486, 5.87517738,
5.50470257, 5.16295004, 4.85778189, 4.59612799,
4.38370705, 4.22478294, 4.12196636, 4.07607317,
4.08605337, 4.14899063, 4.26018095, 4.41328096,
4.60052919, 4.81302309, 5.0410409, 5.2743969,
5.50281096, 5.71627617, 5.9054122, 6.06178427,
6.1781826, 6.24884701, 6.26963043, 6.23809624,
6.15354872, 6.01699257, 5.83102989, 5.59969759,
5.3282547, 5.02292967, 4.69064283, 4.33871651,
3.9745841, 3.60551882, 3.23838711, 2.87943935,
2.53414536, 2.20707822, 1.90184724, 1.62107921,
1.36644125, 1.1387037, 0.937830389, 0.76309222,
0.613192797, 0.486400068, 0.380675972, 0.293797851,
0.223467767, 0.167405516, 0.123424374, 0.0894883648,
0.0637520552, 0.0445840396, 0.0305763241, 0.0205419566,
0.0135034733, 0.00867480226, 0.00543893501, 0.00332357036,
0.00197649584, 0.00114213396, 0.000640272745, 0.000347618188,
0.000182455769, 9.24108026e-05, 4.50768275e-05, 2.11332499e-05,
9.5025016e-06, 4.08886081e-06, 1.67976589e-06, 6.572335e-07,
2.44291556e-07, 8.60314273e-08, 2.86255855e-08, 8.97292374e-09,
2.64163669e-09, 7.28101412e-10, 1.8726333e-10, 4.47879615e-11,
9.92585181e-12, 2.0308102e-12, 3.82131935e-13,
/* Z=10 -> Ne */
0, 0.000202054522, 0.00022320899, 0.000246576208,
0.000272387289, 0.00030089746, 0.000332388532, 0.000367171597,
0.000405590254, 0.000448023755, 0.000494890846, 0.000546653871,
0.000603823166, 0.000666962063, 0.000736692513, 0.000813700841,
0.000898744678, 0.000992660294, 0.00109637028, 0.00121089327,
0.00133735279, 0.00147698878, 0.00163116946, 0.00180140405,
0.00198935741, 0.00219686655, 0.00242595701, 0.00267886301,
0.0029580486, 0.00326623046, 0.00360640418, 0.003981872,
0.00439627422, 0.00485362299, 0.00535834022, 0.00591529766,
0.00652986346, 0.00720795011, 0.00795607176, 0.00878139865,
0.00969182793, 0.0106960526, 0.0118036401, 0.013025118,
0.0143720694, 0.0158572327, 0.017494617, 0.0192996245,
0.0212891828, 0.0234818906, 0.0258981809, 0.0285604857,
0.0314934328, 0.034724053, 0.0382819921, 0.0421997607,
0.0465129949, 0.0512607358, 0.0564857461, 0.0622348227,
0.0685591772, 0.0755148008, 0.0831628889, 0.0915702656,
0.10080988, 0.110961311, 0.122111283, 0.134354264,
0.147793025, 0.162539363, 0.178714722, 0.196450844,
0.215890646, 0.237188846, 0.260512829, 0.286043406,
0.313975662, 0.344519794, 0.377901882, 0.414364755,
0.454168707, 0.497592241, 0.544932723, 0.596506953,
0.652651727, 0.713723898, 0.780100763, 0.852179885,
0.930378556, 1.01513338, 1.10689914, 1.20614755,
1.31336439, 1.4290483, 1.55370653, 1.68785167,
1.83199644, 1.9866488, 2.15230417, 2.32943916,
2.51850152, 2.71990132, 2.93399858, 3.16109109,
3.4014008, 3.65505815, 3.92208552, 4.20238018,
4.49569416, 4.80161667, 5.11955214, 5.44870186,
5.78804255, 6.13630772, 6.49197102, 6.85323048,
7.21799612, 7.58388329, 7.94820929, 8.3079977,
8.65998745, 9.00065899, 9.32625771, 9.6328392,
9.91631794, 10.1725388, 10.3973494, 10.5866909,
10.7367058, 10.8438435, 10.9049826, 10.9175673,
10.8797178, 10.7903757, 10.6494122, 10.4577332,
10.2173738, 9.93154907, 9.60468674, 9.24241734,
8.85151577, 8.43980312, 8.01599693, 7.58950949,
7.17020178, 6.76809978, 6.39307594, 6.05450821,
5.76093626, 5.51972151, 5.33673525, 5.21608829,
5.15991306, 5.16822386, 5.23885155, 5.36746931,
5.54770803, 5.77135468, 6.02863455, 6.30855513,
6.59930372, 6.88867712, 7.16452456, 7.41518593,
7.62990475, 7.7991991, 7.91517496, 7.97177505,
7.96494532, 7.89272499, 7.75524473, 7.55465269,
7.29495335, 6.9817872, 6.6221509, 6.22407532,
5.79628325, 5.34783602, 4.88779116, 4.42488527,
3.96725726, 3.52221465, 3.09606194, 2.69398451,
2.31999016, 1.97690785, 1.66643286, 1.3892138,
1.14497101, 0.932635844, 0.750502765, 0.596383929,
0.46775949, 0.361917019, 0.276075065, 0.207487971,
0.153530374, 0.111761093, 0.0799670815, 0.0561894588,
0.0387337096, 0.0261667743, 0.0173038561, 0.0111876931,
0.00706293201, 0.0043479749, 0.00260630855, 0.00151896977,
0.000859355379, 0.000471172563, 0.000249931123, 0.000128029104,
6.32155279e-05, 3.00266001e-05, 1.36916751e-05, 5.98044971e-06,
2.49662025e-06, 9.93757794e-07, 3.76216178e-07, 1.35111264e-07,
4.59048337e-08, 1.47129171e-08, 4.43524062e-09, 1.25360589e-09,
3.31146305e-10, 8.14753195e-11, 1.86061114e-11, 3.9294349e-12,
7.64573843e-13, 1.36536805e-13, 2.22895382e-14,
/* Z=11 -> Na */
0, 0.000273550104, 0.000302168075, 0.000333776901,
0.000368688692, 0.000407247979, 0.000449835206, 0.000496870372,
0.000548817101, 0.00060618727, 0.000669545901, 0.000739516632,
0.000816787884, 0.0009021195, 0.000996350078, 0.00110040512,
0.00121530588, 0.0013421796, 0.00148226961, 0.0016369482,
0.00180772913, 0.00199628249, 0.00220445031, 0.0024342651,
0.00268796762, 0.00296802958, 0.00327717676, 0.00361841451,
0.0039950558, 0.00441075349, 0.0048695337, 0.00537583418,
0.00593454437, 0.00655105198, 0.00723129371, 0.00798180699,
0.00880979374, 0.0097231837, 0.010730708, 0.0118419761,
0.0130675649, 0.0144191142, 0.0159094259, 0.0175525844,
0.0193640757, 0.0213609189, 0.0235618278, 0.0259873588,
0.0286600925, 0.0316048227, 0.0348487683, 0.0384217948,
0.0423566736, 0.0466893241, 0.0514591262, 0.0567092225,
0.0624868646, 0.068843767, 0.0758365095, 0.0835269615,
0.0919827372, 0.101277687, 0.111492403, 0.12271481,
0.135040745, 0.148574561, 0.163429856, 0.179730132,
0.197609574, 0.217213795, 0.238700673, 0.262241215,
0.288020372, 0.316237986, 0.347109675, 0.38086772,
0.417762071, 0.458061099, 0.502052605, 0.550044417,
0.602365434, 0.659365952, 0.721418381, 0.788917542,
0.862280846, 0.941948056, 1.02838111, 1.1220634,
1.22349834, 1.33320808, 1.45173144, 1.5796206,
1.71743822, 1.86575282, 2.02513361, 2.19614458,
2.37933707, 2.57524109, 2.78435588, 3.00713944,
3.24399471, 3.49525762, 3.76117921, 4.0419116,
4.33748722, 4.6478014, 4.97258997, 5.311409,
5.66361094, 6.02832508, 6.40443182, 6.79054499,
7.18499088, 7.58579159, 7.99065065, 8.39694691,
8.8017292, 9.20172215, 9.59333706, 9.9726963,
10.3356667, 10.6779022, 10.9949064, 11.2821007,
11.5349188, 11.7488966, 11.9197979, 12.0437307,
12.1172915, 12.1376963, 12.1029377, 12.0119171,
11.864583, 11.6620464, 11.4066811, 11.1021872,
10.7536249, 10.3673983, 9.95119381, 9.51386547,
9.06525898, 8.61598587, 8.17713833, 7.75996208,
7.37548876, 7.03414583, 6.74535513, 6.51714325,
6.35577726, 6.26544905, 6.24802685, 6.30288935,
6.42685223, 6.6142025, 6.85683632, 7.14450169,
7.46513939, 7.80529976, 8.15063095, 8.48640156,
8.79804993, 9.0717268, 9.29480076, 9.45632458,
9.54742527, 9.56160831, 9.49495888, 9.34624863,
9.1169157, 8.81095123, 8.43467903, 7.99644518,
7.50623369, 6.97523212, 6.4153614, 5.838799,
5.257514, 4.68284035, 4.12510538, 3.5933249,
3.09498072, 2.63588238, 2.22011399, 1.85006249,
1.52651763, 1.24883115, 1.01512277, 0.822514594,
0.667379439, 0.545587838, 0.452740431, 0.384374678,
0.336139709, 0.30393374, 0.284004658, 0.273014754,
0.268074125, 0.266748607, 0.267047912, 0.267400444,
0.266619921, 0.263868004, 0.258615553, 0.250604331,
0.239809483, 0.226402283, 0.210712954, 0.193192944,
0.174376294, 0.154841036, 0.135171324, 0.115922071,
0.0975879431, 0.0805787295, 0.065202266, 0.0516563915,
0.040029645, 0.0303101279, 0.0224010423, 0.0161406845,
0.0113245118, 0.00772683416, 0.00512009906, 0.00329023856,
0.00204735063, 0.00123163359, 0.000715099042, 0.000400017307,
0.000215184511, 0.000111099413, 5.49395663e-05,
/* Z=12 -> Mg */
0, 0.000361421058, 0.000399200799, 0.000440925272,
0.000487005687, 0.000537895947, 0.00059409719, 0.000656162505,
0.000724702433, 0.000800391019, 0.000883971981, 0.000976266398,
0.00107818015, 0.00119071337, 0.00131496915, 0.00145216507,
0.00160364457, 0.00177088974, 0.0019555355, 0.00215938571,
0.00238443026, 0.00263286335, 0.00290710549, 0.00320982584,
0.00354396761, 0.00391277578, 0.00431982847, 0.00476906914,
0.00526484521, 0.00581194693, 0.00641565397, 0.00708178338,
0.00781674311, 0.00862759165, 0.0095221037, 0.010508839,
0.0115972208, 0.0127976257, 0.01412147, 0.0155813163,
0.0171909854, 0.0189656802, 0.0209221132, 0.0230786614,
0.0254555214, 0.0280748829, 0.0309611186, 0.0341409966,
0.0376438983, 0.041502066, 0.0457508676, 0.0504290946,
0.0555792563, 0.0612479337, 0.0674861446, 0.0743497312,
0.0818997994, 0.0902031511, 0.0993328243, 0.10936857,
0.120397471, 0.132514492, 0.145823181, 0.160436332,
0.176476687, 0.194077775, 0.213384613, 0.234554693,
0.257758737, 0.283181727, 0.311023802, 0.341501206,
0.374847353, 0.411313802, 0.451171219, 0.494710475,
0.542243481, 0.594104111, 0.650649071, 0.712258637,
0.779337287, 0.852313936, 0.931642413, 1.01780128,
1.11129355, 1.21264589, 1.3224076, 1.44114888,
1.56945872, 1.70794189, 1.85721529, 2.01790357,
2.19063354, 2.37602758, 2.5746963, 2.78722906,
3.014184, 3.2560761, 3.51336408, 3.78643489,
4.07558775, 4.38101625, 4.70278788, 5.04082251,
5.39487171, 5.76449299, 6.14902782, 6.54757452,
6.95896673, 7.38174677, 7.81414795, 8.25407124,
8.69907379, 9.14635372, 9.59275055, 10.0347452,
10.4684715, 10.8897448, 11.2940874, 11.6767817,
12.0329342, 12.3575478, 12.6456194, 12.8922462,
13.0927525, 13.2428217, 13.3386536, 13.3771143,
13.355896, 13.2736826, 13.1302938, 12.9268217,
12.6657476, 12.351017, 11.9880829, 11.5839014,
11.1468668, 10.6866951, 10.2142305, 9.74120808,
9.27993107, 8.84291267, 8.44246101, 8.09023762,
7.79679918, 7.57114458, 7.42029238, 7.34890556,
7.35898876, 7.44968081, 7.61715174, 7.85462236,
8.15251064, 8.49870014, 8.87892532, 9.27726746,
9.67672157, 10.0598316, 10.4093552, 10.7089233,
10.9436798, 11.1008606, 11.17029, 11.1447639,
11.0203276, 10.7963982, 10.4757557, 10.064395,
9.57123184, 9.00769901, 8.38723564, 7.72470713,
7.03576994, 6.33623028, 5.64141607, 4.96559954,
4.32149315, 3.71984911, 3.16916871, 2.67553949,
2.242594, 1.87159145, 1.56160271, 1.3097831,
1.11170924, 0.961754739, 0.853479385, 0.780007541,
0.73437655, 0.709839046, 0.700109482, 0.699550748,
0.703300476, 0.707342148, 0.708527386, 0.704558551,
0.693938971, 0.675899565, 0.650309324, 0.617573857,
0.578528106, 0.534326911, 0.486336768, 0.436031997,
0.38489908, 0.334352016, 0.285661131, 0.239898384,
0.197900355, 0.160249591, 0.127273902, 0.0990620181,
0.0754928365, 0.0562745184, 0.0409895629, 0.0291412994,
0.0201979559, 0.0136309844, 0.00894531142, 0.00570042385,
0.00352228107, 0.00210704259, 0.00121827784, 0.00067966833,
0.000365207874, 0.000188646765, 9.34879281e-05, 4.43552162e-05,
2.01027633e-05, 8.68317966e-06, 3.56576311e-06,
/* Z=13 -> Al */
0, 0.000467162929, 0.000515953114, 0.000569832744,
0.000629331684, 0.00069503492, 0.000767588033, 0.000847703544,
0.000936167955, 0.0010338492, 0.00114170508, 0.00126079272,
0.00139227835, 0.00153744884, 0.00169772422, 0.00187467085,
0.00207001693, 0.00228566886, 0.00252372934, 0.00278651761,
0.00307659106, 0.00339677045, 0.00375016569, 0.00414020615,
0.00457067136, 0.00504572922, 0.0055699721, 0.00614846172,
0.00678677624, 0.007491061, 0.00826808624, 0.00912530906,
0.0100709433, 0.011114032, 0.012264532, 0.0135334032,
0.0149327088, 0.0164757203, 0.0181770436, 0.0200527329,
0.0221204534, 0.0243996195, 0.0269115698, 0.0296797529,
0.0327299275, 0.036090374, 0.0397921503, 0.0438693315,
0.0483593009, 0.0533030592, 0.0587455519, 0.064736031,
0.0713284314, 0.07858181, 0.0865607932, 0.0953360572,
0.10498485, 0.115591571, 0.127248377, 0.140055791,
0.154123455, 0.169570774, 0.186527804, 0.205135971,
0.225549012, 0.24793385, 0.272471547, 0.299358338,
0.328806609, 0.361045927, 0.396324247, 0.434908867,
0.477087557, 0.523169756, 0.573487401, 0.628396213,
0.68827635, 0.753533483, 0.824599385, 0.901932478,
0.986018181, 1.07736886, 1.17652404, 1.28404915,
1.40053475, 1.52659512, 1.66286576, 1.81000078,
1.96866918, 2.13954997, 2.32332706, 2.52068233,
2.73228765, 2.95879579, 3.20082974, 3.45897031,
3.733742, 4.02559757, 4.33490133, 4.66190863,
5.00674582, 5.3693881, 5.74963379, 6.14708233,
6.56110382, 6.99081564, 7.43505478, 7.89235163,
8.3609066, 8.83856487, 9.3228054, 9.81071758,
10.2990036, 10.7839708, 11.2615499, 11.7273064,
12.1764812, 12.6040363, 13.004715, 13.373126,
13.7038336, 13.9914789, 14.2309046, 14.417305,
14.5463829, 14.614522, 14.6189623, 14.5579739,
14.4310284, 14.2389526, 13.9840641, 13.670269,
13.3031235, 12.889842, 12.4392509, 11.9616699,
11.4687309, 10.9731178, 10.4882441, 10.0278511,
9.60557175, 9.23442936, 8.92633152, 8.69155025,
8.53823376, 8.4719553, 8.49534893, 8.60783291,
8.80545902, 9.08089066, 9.42353153, 9.81980038,
10.2535419, 10.7065754, 11.159338, 11.5916281,
11.9833794, 12.3154602, 12.5704517, 12.7333622,
12.7922564, 12.7387571, 12.5684052, 12.2808514,
11.8798637, 11.3731689, 10.7721052, 10.0911207,
9.34714127, 8.55881691, 7.74572134, 6.92750549,
6.12308359, 5.34987116, 4.62312603, 3.95542169,
3.35627842, 2.83196664, 2.3854847, 2.01670551,
1.72267115, 1.49800766, 1.33542681, 1.22627699,
1.16110373, 1.1301862, 1.12402046, 1.13372588,
1.15136445, 1.17016315, 1.18464684, 1.19068456,
1.18546295, 1.16740179, 1.13602138, 1.09178042,
1.03589344, 0.970140815, 0.89668113, 0.817872941,
0.736114979, 0.653708458, 0.572746456, 0.495031953,
0.422025144, 0.354818791, 0.29413861, 0.240365028,
0.193571374, 0.153573051, 0.119982883, 0.0922675431,
0.0698012263, 0.0519134626, 0.0379291624, 0.0271998998,
0.0191264693, 0.0131733082, 0.00887588784, 0.00584246451,
0.00375151099, 0.00234612287, 0.00142656185, 0.000841868867,
0.000481269788, 0.000265988259, 0.000141830067, 7.28069135e-05,
3.5901001e-05, 1.69654377e-05, 7.66488029e-06,
/* Z=14 -> Si */
0, 0.000592864642, 0.000654725125, 0.000723031757,
0.000798454974, 0.000881734595, 0.000973687158, 0.00107521378,
0.00118730881, 0.00131106959, 0.00144770672, 0.00159855606,
0.00176509155, 0.00194893905, 0.00215189205, 0.00237592915,
0.00262323255, 0.00289620901, 0.00319751259, 0.00353007065,
0.00389711, 0.00430218875, 0.00474923011, 0.0052425568,
0.00578693533, 0.00638761744, 0.00705039082, 0.00778163131,
0.00858836435, 0.00947832596, 0.0104600396, 0.0115428884,
0.0127372034, 0.0140543552, 0.0155068627, 0.0171084981,
0.0188744143, 0.0208212752, 0.0229674131, 0.0253329743,
0.0279401094, 0.0308131557, 0.0339788496, 0.0374665558,
0.0413085073, 0.0455400981, 0.0502001382, 0.055331219,
0.0609800145, 0.0671976879, 0.0740402788, 0.081569165,
0.0898514986, 0.0989607573, 0.108977258, 0.119988777,
0.132091165, 0.145389035, 0.159996465, 0.176037803,
0.193648472, 0.212975815, 0.234180033, 0.257435173,
0.282930076, 0.310869545, 0.341475219, 0.374987036,
0.411664069, 0.451785862, 0.495653629, 0.54359138,
0.595947146, 0.653093874, 0.715430915, 0.783384502,
0.857409, 0.937987328, 1.02563143, 1.12088263,
1.22431135, 1.33651721, 1.45812714, 1.58979475,
1.73219788, 1.88603616, 2.05202746, 2.23090267,
2.42340136, 2.63026452, 2.8522265, 3.09000611,
3.3442955, 3.61574793, 3.90496325, 4.21247196,
4.53871775, 4.88403749, 5.24863863, 5.63257742,
6.03573179, 6.45777559, 6.89815187, 7.35604143,
7.83033562, 8.31960964, 8.82209015, 9.33563614,
9.8577137, 10.3853798, 10.9152708, 11.4436007,
11.9661646, 12.4783592, 12.9752064, 13.4514046,
13.9013891, 14.3194027, 14.6995993, 15.0361576,
15.3234148, 15.5560188, 15.7290955, 15.8384304,
15.8806562, 15.8534498, 15.7557154, 15.5877638,
15.3514719, 15.0504084, 14.6899137, 14.2771473,
13.8210478, 13.3322506, 12.8229084, 12.3064432,
11.7972202, 11.3101368, 10.8601522, 10.4617586,
10.128418, 9.87198162, 9.70212555, 9.62582779,
9.64691162, 9.76568794, 9.97872734, 10.2787743,
10.6548223, 11.0923624, 11.5737944, 12.0790005,
12.586051, 13.0720282, 13.513916, 13.8895435,
14.1785059, 14.3630438, 14.4288311, 14.3656273,
14.1677675, 13.8344498, 13.3698158, 12.7828035,
12.0867825, 11.298975, 10.439703, 9.53148174,
8.59801292, 7.66313267, 6.7497673, 5.87895155,
5.06897068, 4.33466911, 3.68696117, 3.13257432,
2.67402267, 2.30981112, 2.03484011, 1.84097946,
1.71775663, 1.65311468, 1.63417959, 1.64799058,
1.68215203, 1.72537243, 1.76787519, 1.80167127,
1.82069683, 1.82082844, 1.79979384, 1.75699639,
1.6932795, 1.6106497, 1.51198208, 1.40072465,
1.28061903, 1.15544927, 1.02882969, 0.904036164,
0.783884823, 0.670657516, 0.566069841, 0.471277267,
0.386911988, 0.313142091, 0.249745756, 0.196192533,
0.151725456, 0.115438528, 0.0863461569, 0.0634417832,
0.0457450412, 0.0323370472, 0.0223847087, 0.0151551683,
0.0100218868, 0.00646395609, 0.00406021671, 0.00247974182,
0.00147007324, 0.000844462833, 0.000469170569, 0.000251625519,
0.000130011729, 6.45815089e-05, 3.07742739e-05, 1.40358216e-05,
6.11269206e-06, 2.5357208e-06, 9.9937165e-07,
/* Z=15 -> P */
0, 0.000740636024, 0.000817838358, 0.000903076841,
0.000997186173, 0.00110108731, 0.0012157968, 0.00134243595,
0.00148224225, 0.00163658115, 0.00180695835, 0.00199503545,
0.00220264564, 0.00243181037, 0.00268475921, 0.00296395156,
0.00327209942, 0.00361219281, 0.00398752932, 0.00440174388,
0.00485884398, 0.00536324689, 0.00591982156, 0.00653393334,
0.00721149426, 0.00795901846, 0.00878368318, 0.00969339162,
0.0106968507, 0.0118036484, 0.0130243357, 0.0143705346,
0.0158550348, 0.0174919032, 0.0192966275, 0.021286238,
0.0234794635, 0.0258968957, 0.0285611749, 0.031497173,
0.0347322263, 0.0382963493, 0.0422225073, 0.0465468802,
0.0513091721, 0.0565529391, 0.0623259284, 0.068680495,
0.07567399, 0.0833692253, 0.0918349549, 0.101146422,
0.111385897, 0.122643299, 0.135016873, 0.14861384,
0.163551196, 0.179956526, 0.197968751, 0.21773918,
0.239432365, 0.263227105, 0.289317608, 0.317914486,
0.349245936, 0.383558989, 0.421120703, 0.462219387,
0.507165909, 0.556294978, 0.609966457, 0.668566465,
0.73250854, 0.802235067, 0.878217757, 0.960958898,
1.05099177, 1.14888132, 1.25522363, 1.37064636,
1.49580789, 1.63139582, 1.77812529, 1.93673682,
2.10799241, 2.29267216, 2.49156785, 2.70547748,
2.93519759, 3.18151331, 3.44518828, 3.72695303,
4.02748871, 4.34741306, 4.68726158, 5.04746723,
5.42833805, 5.83003378, 6.25253916, 6.69563723,
7.15887737, 7.64154816, 8.14264393, 8.66083527,
9.19443893, 9.74138832, 10.2992077, 10.864994,
11.4353971, 12.0066147, 12.5743923, 13.1340313,
13.6804171, 14.2080584, 14.7111387, 15.1835966,
15.6192112, 16.0117188, 16.3549519, 16.6429825,
16.8703041, 17.0320168, 17.1240215, 17.1432362,
17.0878029, 16.9572792, 16.7528324, 16.4773846,
16.1357441, 15.734664, 15.2828541, 14.7909174,
14.2712078, 13.737606, 13.2051983, 12.6898746,
12.2078514, 11.7751112, 11.406805, 11.1166153,
10.9161148, 10.8141661, 10.8163614, 10.9245672,
11.1365957, 11.446022, 11.8421707, 12.3103065,
12.8320036, 13.3857069, 13.9474688, 14.4918318,
14.9928207, 15.4250059, 15.7645874, 15.9904528,
16.085146, 16.0357075, 15.8343391, 15.4788456,
14.9728298, 14.3256168, 13.551918, 12.671217,
11.7069273, 10.6853371, 9.63441849, 8.5825386,
7.55715942, 6.58359528, 5.68390274, 4.87596273,
4.17281675, 3.58228779, 3.10690594, 2.7441349,
2.48686981, 2.32416701, 2.24213624, 2.22493482,
2.25578451, 2.3179431, 2.39557457, 2.47446847,
2.54258108, 2.59038544, 2.61103368, 2.60034466,
2.55664372, 2.48048592, 2.37429166, 2.24193478,
2.08830929, 1.91890645, 1.73942161, 1.55541492,
1.37203085, 1.19378972, 1.02444625, 0.866917729,
0.723270595, 0.594757378, 0.481892198, 0.384553939,
0.30210492, 0.233515173, 0.177483857, 0.132551104,
0.0971955359, 0.0699145645, 0.0492866151, 0.0340152122,
0.0229564272, 0.0151317073, 0.00972862635, 0.00609235093,
0.00371057494, 0.00219450681, 0.00125820772, 0.000698123302,
0.000374183088, 0.000193365966, 9.61509068e-05, 4.59090916e-05,
2.10024446e-05, 9.18497608e-06, 3.83080305e-06, 1.51993436e-06,
5.72207568e-07, 2.03842717e-07, 6.85196682e-08,
/* Z=16 -> S */
0, 0.00091274752, 0.00100779033, 0.00111271499,
0.00122854637, 0.0013564158, 0.00149757077, 0.00165338814,
0.00182538654, 0.00201524119, 0.00222480041, 0.00245610229,
0.00271139457, 0.0029931569, 0.00330412271, 0.0036473074,
0.00402603392, 0.00444396771, 0.00490514748, 0.00541402632,
0.00597551186, 0.00659501273, 0.00727848848, 0.0080325054,
0.00886429753, 0.00978183281, 0.0107938861, 0.0119101228,
0.0131411841, 0.0144987796, 0.0159958061, 0.0176464487,
0.0194663201, 0.0214725919, 0.0236841496, 0.0261217616,
0.0288082585, 0.0317687318, 0.0350307524, 0.0386246033,
0.0425835475, 0.0469440892, 0.0517463088, 0.0570341609,
0.0628558695, 0.0692642853, 0.0763173401, 0.0840784833,
0.0926171988, 0.102009527, 0.11233864, 0.123695493,
0.136179447, 0.149899021, 0.164972648, 0.181529537,
0.199710444, 0.219668716, 0.241571262, 0.265599489,
0.291950524, 0.320838362, 0.352494895, 0.387171477,
0.425139904, 0.466693878, 0.512150407, 0.561851144,
0.616163611, 0.67548269, 0.740231991, 0.810864806,
0.887865603, 0.971750736, 1.06306946, 1.16240442,
1.27037215, 1.38762248, 1.51483941, 1.65273857,
1.80206692, 1.96360004, 2.13813949, 2.32650852,
2.52954793, 2.74810934, 2.9830482, 3.23521495,
3.505445, 3.7945466, 4.10328627, 4.43237543,
4.78244781, 5.1540451, 5.54759026, 5.96336555,
6.40148449, 6.86186409, 7.34419537, 7.8479104,
8.37214851, 8.91572666, 9.47710133, 10.0543451,
10.6451054, 11.2465906, 11.8555431, 12.4682245,
13.0804119, 13.6874027, 14.28403, 14.8646946,
15.4234161, 15.9538908, 16.4495888, 16.9038544,
17.3100357, 17.6616402, 17.9525051, 18.1769886,
18.3301792, 18.4081135, 18.4079971, 18.3284321,
18.1696262, 17.9335728, 17.6242199, 17.2475643,
16.8117142, 16.3268623, 15.8051939, 15.2606869,
14.7088366, 14.1662731, 13.6502857, 13.1782684,
12.7670841, 12.4323969, 12.1879616, 12.044939,
12.0112352, 12.0909376, 12.2838593, 12.585228,
12.9855642, 13.4707537, 14.0223455, 14.6180544,
15.2324743, 15.8379927, 16.4058475, 16.9072914,
17.3148327, 17.6034641, 17.7518444, 17.7433586,
17.5669937, 17.2179985, 16.6982479, 16.0163269,
15.1872616, 14.2319593, 13.1763077, 12.0500317,
10.8853197, 9.71530819, 8.57251072, 7.48727083,
6.48633814, 5.59166098, 4.81946135, 4.17965841,
3.67566919, 3.30459619, 3.05777526, 2.92163873,
2.87881637, 2.90938902, 2.9921999, 3.10612512,
3.2312274, 3.34971929, 3.44669271, 3.51059222,
3.53343177, 3.51076841, 3.44147086, 3.32732391,
3.17251444, 2.98305154, 2.76616383, 2.52971792,
2.2816875, 2.02970147, 1.78068399, 1.54059505,
1.31426895, 1.1053462, 0.916284442, 0.748433888,
0.602161884, 0.477008641, 0.371858925, 0.28511709,
0.214873254, 0.159053236, 0.115546107, 0.0823070109,
0.0574336685, 0.039218165, 0.026176095, 0.0170564465,
0.0108360397, 0.00670265267, 0.00403066538, 0.0023527944,
0.0013309276, 0.000728349201, 0.000384903193, 0.000196049819,
9.60551552e-05, 4.51762317e-05, 2.03511081e-05, 8.76121703e-06,
3.59585897e-06, 1.40351801e-06, 5.19607454e-07, 1.81964765e-07,
6.01051937e-08, 1.86703115e-08, 5.43689627e-09,
/* Z=17 -> Cl */
0, 0.00111159275, 0.00122721237, 0.00135483884,
0.00149571558, 0.00165121513, 0.00182285078, 0.00201229239,
0.00222138152, 0.00245214929, 0.00270683598, 0.00298791216,
0.00329810171, 0.00364040839, 0.00401814422, 0.00443496043,
0.00489488151, 0.00540234428, 0.00596223772, 0.00657995045,
0.0072614206, 0.00801318977, 0.00884246547, 0.00975718629,
0.0107660964, 0.0118788239, 0.0131059708, 0.0144592104,
0.0159513876, 0.0175966416, 0.0194105301, 0.0214101691,
0.0236143805, 0.0260438677, 0.0287213884, 0.0316719599,
0.0349230692, 0.0385049246, 0.0424506888, 0.0467967838,
0.0515831858, 0.0568537675, 0.0626566485, 0.0690445825,
0.0760754123, 0.083812505, 0.0923252702, 0.101689681,
0.11198888, 0.12331377, 0.135763749, 0.149447396,
0.164483249, 0.181000665, 0.199140653, 0.219056934,
0.240916833, 0.264902383, 0.291211486, 0.320059091,
0.351678342, 0.386322051, 0.424263865, 0.465799779,
0.511249483, 0.560957849, 0.615296304, 0.674664497,
0.739491463, 0.81023705, 0.887393355, 0.971485853,
1.06307423, 1.16275334, 1.27115428, 1.38894355,
1.51682365, 1.65553296, 1.80584347, 1.96855986,
2.14451694, 2.33457589, 2.53962016, 2.76054978,
2.99827528, 3.2537086, 3.52775407, 3.82129669,
4.13518953, 4.47023678, 4.827178, 5.20666838,
5.60925627, 6.03535843, 6.48523378, 6.95895672,
7.45638227, 7.97711706, 8.52048206, 9.08548164,
9.67076302, 10.2745867, 10.8947906, 11.52876,
12.1733999, 12.825119, 13.4798126, 14.132863,
14.7791424, 15.4130392, 16.0284977, 16.6190681,
17.1779919, 17.6982918, 18.1728954, 18.5947876,
18.9571648, 19.2536373, 19.4784374, 19.6266384,
19.6944008, 19.679203, 19.5800838, 19.3978558,
19.1352997, 18.7973251, 18.3910561, 17.9258785,
17.4133797, 16.8672295, 16.3029346, 15.7375021,
15.1890001, 14.6760092, 14.2169981, 13.8296156,
13.5299473, 13.3317442, 13.2456808, 13.2786608,
13.4332314, 13.7071228, 14.0929823, 14.5782957,
15.1455545, 15.7726536, 16.4335423, 17.0990982,
17.7382011, 18.3189812, 18.8101635, 19.1824818,
19.4100513, 19.4716816, 19.3520069, 19.0424023,
18.5416145, 17.8560371, 16.9996529, 15.9935503,
14.8650942, 13.6467266, 12.374485, 11.086277,
9.82003975, 8.61186886, 7.4942317, 6.49439001,
5.63312721, 4.92386723, 4.37224722, 3.97616935,
3.72631812, 3.60710049, 3.59792686, 3.67472887,
3.81159472, 3.98239851, 4.16230583, 4.32906342,
4.46399832, 4.55268478, 4.58527422, 4.55649281,
4.46536398, 4.3146925, 4.11038971, 3.86070514,
3.57542229, 3.26508594, 2.94029999, 2.61113477,
2.28666115, 1.97462106, 1.68123245, 1.41111565,
1.16732478, 0.951462448, 0.7638551, 0.603766382,
0.469628483, 0.359273106, 0.270149827, 0.199519709,
0.144619003, 0.102788813, 0.071570605, 0.0487689488,
0.032485377, 0.0211275276, 0.0133989165, 0.00827483274,
0.00496924715, 0.00289734756, 0.00163752632, 0.000895611709,
0.000473172491, 0.000241033966, 0.000118153213, 5.56198902e-05,
2.50898647e-05, 1.08211161e-05, 4.45171054e-06, 1.742569e-06,
6.47348088e-07, 2.27611622e-07, 7.55316591e-08, 2.35860327e-08,
6.90920077e-09, 1.8925419e-09, 4.83111384e-10,
/* Z=18 -> Ar */
0, 0.00133971556, 0.00147889985, 0.00163251965,
0.0018020682, 0.00198919256, 0.00219570962, 0.00242362265,
0.00267514121, 0.00295270234, 0.00325899269, 0.00359697454,
0.00396991428, 0.00438141311, 0.00483543938, 0.00533636892,
0.00588902319, 0.00649871631, 0.0071713035, 0.00791323651,
0.00873162225, 0.00963429082, 0.0106298644, 0.0117278378,
0.012938669, 0.0142738689, 0.0157461073, 0.0173693337,
0.0191588905, 0.0211316627, 0.0233062208, 0.0257029906,
0.0283444282, 0.0312552229, 0.0344625004, 0.0379960723,
0.0418886915, 0.0461763106, 0.0508984104, 0.0560983121,
0.0618235618, 0.0681262836, 0.0750636458, 0.0826982856,
0.0910988376, 0.100340441, 0.110505342, 0.121683538,
0.133973435, 0.147482544, 0.162328333, 0.178639024,
0.196554467, 0.216227174, 0.237823248, 0.261523515,
0.2875247, 0.316040516, 0.347303122, 0.3815642,
0.419096619, 0.46019569, 0.505180657, 0.554396272,
0.608214319, 0.667035162, 0.731289208, 0.801438451,
0.877978027, 0.961437345, 1.05238152, 1.15141225,
1.25916874, 1.37632847, 1.5036068, 1.64175737,
1.79157126, 1.9538753, 2.12953067, 2.3194294,
2.52449131, 2.7456584, 2.9838903, 3.2401545,
3.51541924, 3.81064296, 4.12676048, 4.4646697,
4.82521486, 5.209167, 5.61720324, 6.04988337,
6.5076232, 6.99066544, 7.49904966, 8.03257942,
8.59078693, 9.17289543, 9.77778435, 10.4039488,
11.049469, 11.7119675, 12.3885832, 13.0759459,
13.770153, 14.4667568, 15.1607666, 15.8466597,
16.5184078, 17.1695175, 17.7931042, 18.3819656,
18.9287033, 19.4258461, 19.8660202, 20.2421207,
20.5475311, 20.7763424, 20.9236012, 20.9855614,
20.959938, 20.8461552, 20.6455784, 20.3617077,
20.0003319, 19.5696163, 19.0801315, 18.5447674,
17.9785786, 17.3984985, 16.8229542, 16.2713585,
15.7635088, 15.3188791, 14.9558506, 14.6908951,
14.5377407, 14.5065765, 14.603323, 14.8290148,
15.1793613, 15.6444893, 16.208931, 16.8518715,
17.5476608, 18.2665939, 18.9759541, 19.6412621,
20.2276955, 20.7016373, 21.0322399, 21.1929798,
21.163065, 20.9286613, 20.4838295, 19.8311119,
18.9817276, 17.9553223, 16.779274, 15.4875593,
14.1192303, 12.7165642, 11.3229771, 9.98083973,
8.72929573, 7.60225439, 6.62667513, 5.82126474,
5.19569063, 4.75036097, 4.47678614, 4.3584919,
4.37240887, 4.4906168, 4.68230772, 4.9158144,
5.16054201, 5.38867569, 5.57655668, 5.70564699,
5.76306581, 5.74169493, 5.63989687, 5.46092463,
5.21208477, 4.90376902, 4.54842377, 4.15954733,
3.750772, 3.33508945, 2.92423534, 2.5282557,
2.15524697, 1.81125629, 1.50031841, 1.22460055,
0.984626889, 0.779551446, 0.607453465, 0.465633929,
0.350893915, 0.259782642, 0.188806787, 0.134596705,
0.0940291137, 0.0643085167, 0.0430115573, 0.028100213,
0.0179103538, 0.0111223357, 0.00672012288, 0.0039446149,
0.00224594655, 0.00123835925, 0.000660077203, 0.000339511345,
0.000168188824, 8.00856578e-05, 3.65777341e-05, 1.59892934e-05,
6.67409404e-06, 2.65374138e-06, 1.00260695e-06, 3.58971192e-07,
1.21462506e-07, 3.87275527e-08, 1.16005303e-08, 3.2541867e-09,
8.52084625e-10, 2.0754376e-10, 4.68574658e-11,
/* Z=19 -> K */
0, 0.00160090986, 0.00176702545, 0.00195034686,
0.00215265132, 0.00237589888, 0.0026222507, 0.00289409002,
0.00319404528, 0.0035250138, 0.00389019004, 0.00429309579,
0.00473761233, 0.00522801885, 0.00576903112, 0.00636584545,
0.00702418759, 0.00775036775, 0.00855133589, 0.00943474751,
0.0104090367, 0.0114834914, 0.0126683349, 0.0139748268,
0.0154153621, 0.0170035791, 0.0187544916, 0.0206846129,
0.0228121132, 0.0251569748, 0.0277411733, 0.0305888653,
0.0337266028, 0.0371835679, 0.0409918129, 0.0451865494,
0.0498064309, 0.0548938997, 0.0604955181, 0.0666623712,
0.0734504759, 0.0809212402, 0.0891419575, 0.098186329,
0.108135067, 0.119076468, 0.131107166, 0.144332737,
0.158868626, 0.174840868, 0.192387, 0.211657077,
0.23281464, 0.256037831, 0.281520486, 0.309473515,
0.340125918, 0.373726457, 0.410544842, 0.450873256,
0.4950279, 0.543350637, 0.59621042, 0.654005051,
0.717162848, 0.786144137, 0.861442983, 0.943588436,
1.03314626, 1.13072026, 1.23695266, 1.35252607,
1.478163, 1.61462665, 1.76272035, 1.9232868,
2.09720683, 2.28539681, 2.48880529, 2.70841026,
2.94521189, 3.20022798, 3.47448397, 3.76900506,
4.08480358, 4.42286634, 4.7841382, 5.16950464,
5.579772, 6.01564407, 6.47769642, 6.96635008,
7.4818387, 8.0241766, 8.59312439, 9.18815041,
9.80839157, 10.4526167, 11.1191874, 11.8060131,
12.5105228, 13.2296324, 13.9597073, 14.6965561,
15.4354095, 16.170927, 16.8972073, 17.6078186,
18.2958546, 18.9540005, 19.5746288, 20.1499157,
20.6719933, 21.1331196, 21.525877, 21.8433952,
22.0795956, 22.2294559, 22.2892685, 22.2569275,
22.1321774, 21.9168549, 21.6150951, 21.2334843,
20.7811451, 20.2697372, 19.7133751, 19.1284237,
18.5331802, 17.9474468, 17.3919563, 16.8877125,
16.4552155, 16.1136208, 15.8798552, 15.7677097,
15.7869978, 15.9427748, 16.2347012, 16.6565952,
17.1961937, 17.8351974, 18.5495872, 19.3102531,
20.0839081, 20.8342819, 21.5235577, 22.113987,
22.5696163, 22.8580494, 22.9521561, 22.8316135,
22.4842205, 21.9068565, 21.1060371, 20.0979996,
18.9082661, 17.5706997, 16.1260395, 14.6200294,
13.1011467, 11.6181393, 10.2174416, 8.94069099,
7.82247162, 6.88847637, 6.15420628, 5.62432194,
5.29269505, 5.1431675, 5.15094566, 5.28452969,
5.50801325, 5.78356409, 6.07389736, 6.34454298,
6.56575584, 6.71394205, 6.772542, 6.73234653,
6.59128046, 6.35373449, 6.02953434, 5.63268042,
5.1799674, 4.68960667, 4.17994165, 3.6683383,
3.17030001, 2.69883275, 2.2640636, 1.87310314,
1.5301168, 1.23656869, 0.991590142, 0.792429626,
0.634935737, 0.514036953, 0.424183816, 0.359732181,
0.315251946, 0.285756409, 0.266854376, 0.254832804,
0.246681541, 0.240074098, 0.233317003, 0.225279927,
0.215315476, 0.203175858, 0.188930139, 0.172885045,
0.155510679, 0.137371987, 0.119067319, 0.101175249,
0.0842110366, 0.0685943887, 0.0546291657, 0.0424957424,
0.0322547443, 0.0238607489, 0.0171831399, 0.01203107,
0.00817923527, 0.00539160939, 0.00344093936, 0.00212279591,
0.00126384653, 0.000724899641, 0.000399815792,
/* Z=20 -> Ca */
0, 0.00189792144, 0.00209460221, 0.00231162622,
0.0025510916, 0.00281531201, 0.00310683809, 0.00342848175,
0.00378334359, 0.0041748411, 0.00460674195, 0.00508319773,
0.0056087845, 0.00618854584, 0.00682803756, 0.00753338262,
0.00831132568, 0.00916929543, 0.0101154773, 0.0111588798,
0.0123094311, 0.0135780536, 0.0149767781, 0.0165188406,
0.0182188135, 0.0200927258, 0.0221582167, 0.0244346838,
0.0269434601, 0.0297080074, 0.0327541046, 0.0361100957,
0.0398071148, 0.0438793637, 0.0483644083, 0.0533034876,
0.0587418601, 0.0647291914, 0.0713199526, 0.0785738751,
0.0865564197, 0.0953393206, 0.105001129, 0.115627863,
0.127313614, 0.140161306, 0.154283434, 0.169802964,
0.186854094, 0.205583319, 0.226150379, 0.248729363,
0.27350992, 0.30069831, 0.330518931, 0.363215506,
0.39905262, 0.43831709, 0.481319636, 0.528396547,
0.579911172, 0.636255622, 0.69785279, 0.7651577,
0.838659286, 0.91888231, 1.00638855, 1.10177886,
1.20569384, 1.31881511, 1.44186676, 1.57561529,
1.72086978, 1.87848198, 2.04934478, 2.23439121,
2.43459129, 2.65095019, 2.8845017, 3.1363039,
3.40743232, 3.69897056, 4.01200056, 4.34758949,
4.70677757, 5.09055805, 5.49986219, 5.93553448,
6.39831018, 6.88878679, 7.40739727, 7.95437479,
8.52971745, 9.13315487, 9.76410484, 10.4216337,
11.1044159, 11.8106918, 12.538229, 13.2842798,
14.0455542, 14.8181849, 15.5977116, 16.3790703,
17.1565914, 17.9240208, 18.6745453, 19.4008656,
20.0952492, 20.7496548, 21.3558426, 21.9055481,
22.3906517, 22.8034039, 23.136652, 23.3841152,
23.5406475, 23.6025314, 23.5677586, 23.4363174,
23.2104263, 22.8947582, 22.4965935, 22.0259018,
21.4953403, 20.9201469, 20.3179073, 19.7082195,
19.1121979, 18.5518684, 18.0494423, 17.6264725,
17.302948, 17.0963326, 17.0206032, 17.0853424,
17.2949009, 17.6477413, 18.1359768, 18.7451344,
19.4542561, 20.2362728, 21.0587349, 21.8848686,
22.6749153, 23.3877544, 23.9827061, 24.421463,
24.6700363, 24.7006454, 24.4933968, 24.0376854,
23.3331985, 22.3904362, 21.2306728, 19.8853416,
18.3948097, 16.8065948, 15.1730738, 13.5488186,
11.9876881, 10.5398579, 9.24900341, 8.14980793,
7.26601219, 6.60914755, 6.17807627, 5.95937729,
5.92856407, 6.05204439, 6.28965616, 6.59757996,
6.93138027, 7.24894047, 7.51305008, 7.69347715,
7.76837873, 7.72500181, 7.55967093, 7.2771349,
6.8893795, 6.41405725, 5.87269688, 5.28884602,
4.68629599, 4.08751631, 3.51237226, 2.97719741,
2.49422908, 2.07140684, 1.7124933, 1.41746485,
1.18310189, 1.00370657, 0.871871829, 0.779237151,
0.717175186, 0.677370071, 0.65226388, 0.635364115,
0.621417046, 0.606463492, 0.587798774, 0.563860238,
0.534066916, 0.498632729, 0.458369374, 0.414493918,
0.368450671, 0.321754307, 0.275858998, 0.232056737,
0.191405147, 0.154685274, 0.122387007, 0.0947189406,
0.0716383681, 0.0528957993, 0.0380881317, 0.0267143175,
0.0182281937, 0.012084079, 0.00777220773, 0.00484274188,
0.00291859009, 0.0016985205, 0.000952854462, 0.000514330168,
0.000266609801, 0.00013244756, 6.29237111e-05,
/* Z=21 -> Sc */
0, 0.00223217905, 0.00246318663, 0.00271805376,
0.00299923681, 0.00330944429, 0.00365166203, 0.00402918132,
0.00444562966, 0.00490500545, 0.00541171478, 0.00597061403,
0.00658705365, 0.00726692798, 0.00801673159, 0.00884361845,
0.009755468, 0.0107609574, 0.011869642, 0.0130920429,
0.014439743, 0.0159254912, 0.017563317, 0.0193686616,
0.0213585123, 0.0235515516, 0.0259683337, 0.0286314543,
0.0315657593, 0.0347985551, 0.0383598469, 0.0422826037,
0.0466030352, 0.0513609014, 0.0565998517, 0.0623677894,
0.0687172636, 0.0757059082, 0.0833969191, 0.0918595418,
0.101169661, 0.111410342, 0.122672543, 0.135055751,
0.148668811, 0.163630635, 0.180071175, 0.198132306,
0.217968792, 0.239749461, 0.263658255, 0.289895445,
0.318679065, 0.350245982, 0.384853631, 0.422781378,
0.464332104, 0.509833872, 0.55964154, 0.614138722,
0.673739254, 0.738889277, 0.810068905, 0.887794137,
0.972618282, 1.06513417, 1.16597509, 1.2758168,
1.39537799, 1.52542186, 1.66675651, 1.82023454,
1.98675346, 2.16725445, 2.36272001, 2.5741725,
2.80266976, 3.04930091, 3.31518006, 3.601439,
3.90921807, 4.23965597, 4.59387541, 4.97296906,
5.37798309, 5.80989456, 6.2695899, 6.75784159,
7.27527571, 7.8223443, 8.39928913, 9.00610447,
9.64250088, 10.3078613, 11.0011988, 11.7211132,
12.4657469, 13.2327461, 14.0192146, 14.8216848,
15.6360865, 16.4577198, 17.2812576, 18.1007328,
18.9095669, 19.7006016, 20.4661598, 21.1981258,
21.8880501, 22.5272999, 23.1072006, 23.6192608,
24.0553703, 24.4080734, 24.6708298, 24.838316,
24.9067192, 24.8740482, 24.7404118, 24.5082932,
24.1827679, 23.7716579, 23.2856312, 22.7381802,
22.1455097, 21.5262928, 20.9012814, 20.2928085,
19.7241135, 19.2185688, 18.7987881, 18.4856453,
18.2972507, 18.2479305, 18.3472519, 18.5991459,
19.0012112, 19.5442238, 20.2119255, 20.9811325,
21.8221855, 22.6997585, 23.5740185, 24.4021358,
25.1400337, 25.7443962, 26.1747646, 26.3956718,
26.3786793, 26.1041908, 25.5629387, 24.7570171,
23.7003574, 22.4185886, 20.9482365, 19.3352547,
17.6329155, 15.8991737, 14.1936321, 12.5742521,
11.0940733, 9.79811859, 8.72075462, 7.88368988,
7.29480267, 6.947896, 6.82342768, 6.89016294,
7.10762119, 7.42912102, 7.805161, 8.18685627,
8.52915382, 8.79357338, 8.95027351, 8.97933769,
8.87121391, 8.62636948, 8.2542429, 7.77165556,
7.20086622, 6.56746149, 5.89825583, 5.21937513,
4.55463505, 3.92430329, 3.34428549, 2.8257339,
2.37505245, 1.99423218, 1.68144488, 1.43180525,
1.23821485, 1.09221101, 0.984749019, 0.90687418,
0.85025084, 0.807538986, 0.772621512, 0.740700424,
0.708284676, 0.673096716, 0.633924007, 0.5904392,
0.543006599, 0.49249053, 0.440075576, 0.387104928,
0.334942192, 0.284859151, 0.237950429, 0.195075914,
0.156829625, 0.123533197, 0.095250845, 0.0718215555,
0.0529035032, 0.038025178, 0.0266378131, 0.0181643143,
0.0120407473, 0.00774801103, 0.00483263843, 0.00291712931,
0.0017013289, 0.000957036391, 0.000518302142, 0.000269722776,
0.000134603106, 6.42795203e-05, 2.9308947e-05,
/* Z=22 -> Ti */
0, 0.00260778167, 0.00287727988, 0.00317457109,
0.00350251189, 0.00386425178, 0.00426326133, 0.00470336573,
0.0051887813, 0.00572415255, 0.00631459849, 0.00696575874,
0.0076838457, 0.00847570319, 0.00934886746, 0.0103116408,
0.0113731651, 0.0125435032, 0.013833737, 0.0152560631,
0.0168239046, 0.0185520351, 0.0204567071, 0.0225558039,
0.0248689894, 0.0274178907, 0.0302262884, 0.0333203189,
0.0367287174, 0.0404830426, 0.0446179733, 0.0491715893,
0.0541857108, 0.059706226, 0.0657835007, 0.0724727809,
0.0798346549, 0.0879355371, 0.0968482122, 0.106652409,
0.117435433, 0.129292816, 0.142329127, 0.156658635,
0.172406316, 0.189708591, 0.20871447, 0.229586497,
0.252501905, 0.277653813, 0.305252522, 0.335526824,
0.368725389, 0.405118406, 0.444999069, 0.488685191,
0.536521018, 0.58887893, 0.646161318, 0.708802462,
0.777270317, 0.852068543, 0.933738291, 1.02286005,
1.12005556, 1.2259891, 1.34136915, 1.4669497,
1.60353112, 1.75196052, 1.91313255, 2.0879879,
2.27751398, 2.48274136, 2.70474219, 2.94462562,
3.2035346, 3.48263741, 3.78312206, 4.10618544,
4.453022, 4.82481098, 5.2227006, 5.64778852,
6.10110378, 6.58357906, 7.09602833, 7.63911295,
8.2133131, 8.81888771, 9.45584202, 10.1238794,
10.8223629, 11.5502701, 12.3061457, 13.0880594,
13.8935547, 14.7196159, 15.5626249, 16.4183331,
17.2818394, 18.1475735, 19.0093079, 19.8601665,
20.6926689, 21.4987907, 22.2700424, 22.9975948,
23.6724091, 24.2854195, 24.8277359, 25.2908764,
25.6670361, 25.9493752, 26.1323242, 26.2119026,
26.1860352, 26.0548553, 25.8209877, 25.4897766,
25.0694618, 24.5712605, 24.0093689, 23.4008312,
22.7652817, 22.1245441, 21.5020905, 20.9223404,
20.4098377, 19.9882946, 19.6795712, 19.502573,
19.4721699, 19.5981579, 19.8843346, 20.3277493,
20.91819, 21.6379642, 22.4620209, 23.3584328,
24.2893009, 25.2119904, 26.0807781, 26.8487606,
27.4700108, 27.9018669, 28.1072369, 28.0567932,
27.7309322, 27.1213398, 26.2320709, 25.0800095,
23.6946297, 22.1170425, 20.3982754, 18.5968933,
16.7760162, 14.9999237, 13.33043, 11.8232737,
10.5247898, 9.46910095, 8.67608833, 8.15029526,
7.88089561, 7.84274626, 7.9984436, 8.30122948,
8.69849586, 9.13559628, 9.55963326, 9.92291451,
10.1858158, 10.3188295, 10.3037157, 10.1337042,
9.81283665, 9.35457993, 8.77988625, 8.11493683,
7.38877487, 6.63102198, 5.86985826, 5.13038445,
4.43342829, 3.79483891, 3.22523808, 2.73018169,
2.31065226, 1.96379077, 1.68376637, 1.46269345,
1.29151475, 1.16078866, 1.06133795, 0.984740257,
0.923657775, 0.872019708, 0.825078726, 0.77937007,
0.732600987, 0.68349576, 0.631618083, 0.577186644,
0.520896018, 0.463749707, 0.406911761, 0.351578653,
0.298874706, 0.249771237, 0.20503059, 0.165173918,
0.13047199, 0.100955911, 0.0764447376, 0.0565851778,
0.0408986397, 0.0288303923, 0.0197962895, 0.013223161,
0.00858027115, 0.00540063996, 0.00329229725, 0.00194070255,
0.00110429549, 0.000605480571, 0.000319290615, 0.000161615724,
7.83590658e-05, 3.63122963e-05, 1.60464515e-05,
/* Z=23 -> V */
0, 0.00302829151, 0.00334078679, 0.0036854588,
0.00406560861, 0.00448487559, 0.00494726934, 0.00545720849,
0.00601956155, 0.00663969247, 0.00732350908, 0.00807752088,
0.00890889671, 0.00982553046, 0.010836117, 0.0119502284,
0.0131784016, 0.014532241, 0.0160245113, 0.0176692642,
0.0194819625, 0.0214796141, 0.0236809272, 0.0261064824,
0.0287789013, 0.0317230597, 0.0349663012, 0.0385386646,
0.0424731597, 0.0468060486, 0.0515771471, 0.056830164,
0.06261307, 0.0689785182, 0.0759842396, 0.083693549,
0.0921758413, 0.101507172, 0.111770831, 0.123058014,
0.135468528, 0.149111569, 0.164106503, 0.18058382,
0.198685989, 0.218568593, 0.240401343, 0.264369279,
0.290673971, 0.319534987, 0.351191103, 0.385901928,
0.42394945, 0.465639591, 0.51130414, 0.561302245,
0.616022587, 0.675885022, 0.741342723, 0.812884033,
0.891034544, 0.97635895, 1.06946301, 1.17099547,
1.28164959, 1.40216494, 1.53332818, 1.67597485,
1.83098948, 1.99930584, 2.18190622, 2.37982178,
2.59412885, 2.82594728, 3.07643723, 3.34679222,
3.63823485, 3.95200729, 4.28936243, 4.65155172,
5.03981066, 5.4553442, 5.89930582, 6.37277699,
6.87674284, 7.41206312, 7.97944307, 8.57939816,
9.21221733, 9.87792492, 10.5762329, 11.3065023,
12.0676918, 12.8583136, 13.6763811, 14.5193663,
15.3841572, 16.2670135, 17.1635418, 18.0686626,
18.9766026, 19.8808956, 20.7744045, 21.6493511,
22.4973888, 23.3096771, 24.0770149, 24.7899723,
25.4390869, 26.0150566, 26.5090065, 26.9127483,
27.2190914, 27.4221535, 27.517704, 27.5034904,
27.3795605, 27.1485558, 26.8159618, 26.3902836,
25.8831558, 25.3093338, 24.6865635, 24.0353241,
23.3784142, 22.7403774, 22.14678, 21.6233425,
21.1949444, 20.8845329, 20.7119732, 20.6928978,
20.8375988, 21.1500511, 21.6271038, 22.2579231,
23.0237637, 23.8980713, 24.8470116, 25.8304043,
26.8030624, 27.7165375, 28.5211658, 29.1683979,
29.6132412, 29.8167515, 29.7483845, 29.3881073,
28.7280693, 27.7737484, 26.5444031, 25.0727825,
23.4040222, 21.5937309, 19.7053356, 17.8067989,
15.9668694, 14.2511311, 12.7180834, 11.4155521,
10.3777332, 9.62308979, 9.15332603, 8.95353603,
8.993536, 9.23029613, 9.61126423, 10.0783033,
10.5718966, 11.0352736, 11.4180984, 11.6794453,
11.789856, 11.7323732, 11.5025368, 11.1074638,
10.564147, 9.89722347, 9.13643742, 8.31404495,
7.46236992, 6.61169434, 5.78858757, 5.01475143,
4.30638981, 3.67406535, 3.12298203, 2.65359211,
2.26243043, 1.94306135, 1.68705046, 1.48487425,
1.32671237, 1.20308673, 1.10533011, 1.02589345,
0.958505213, 0.898211241, 0.841324329, 0.785310566,
0.728638411, 0.670608819, 0.611181259, 0.550805449,
0.490264446, 0.430533499, 0.372656882, 0.317644536,
0.266390145, 0.219611004, 0.177810326, 0.141260996,
0.11000926, 0.0838954151, 0.0625875592, 0.0456240922,
0.0324599445, 0.0225119591, 0.0151994573, 0.00997701101,
0.00635782769, 0.00392734911, 0.00234793499, 0.00135627261,
0.000755655812, 0.000405340776, 0.000208928934, 0.000103271093,
4.88467667e-05, 2.2059623e-05, 9.48951947e-06,
/* Z=24 -> Cr */
0, 0.00349577097, 0.00385595392, 0.004253163,
0.00469119055, 0.00517421588, 0.00570684299, 0.00629414432,
0.00694170734, 0.00765568763, 0.00844286382, 0.00931070186,
0.0102674216, 0.0113220774, 0.0124846334, 0.0137660578,
0.015178428, 0.0167350303, 0.0184504874, 0.0203408841,
0.0224239212, 0.0247190576, 0.0272476971, 0.0300333723,
0.0331019498, 0.0364818648, 0.0402043462, 0.044303719,
0.0488176718, 0.0537875853, 0.0592589006, 0.0652814731,
0.0719099939, 0.0792044699, 0.0872306749, 0.0960607007,
0.105773553, 0.116455749, 0.128202006, 0.141115978,
0.155311063, 0.170911208, 0.188051894, 0.206881076,
0.227560237, 0.250265598, 0.275189251, 0.302540421,
0.332547039, 0.365456909, 0.401539564, 0.441087633,
0.48441869, 0.531876981, 0.583835483, 0.64069742,
0.702898622, 0.770909488, 0.845236957, 0.92642653,
1.01506436, 1.11177957, 1.21724558, 1.33218229,
1.45735753, 1.59358883, 1.74174368, 1.90274143,
2.07755232, 2.26719761, 2.47274923, 2.69532681,
2.93609619, 3.19626379, 3.47707391, 3.77979994,
4.10573769, 4.4561944, 4.83247709, 5.23587942,
5.66766214, 6.1290369, 6.62114096, 7.14501476,
7.70157051, 8.29156208, 8.91555119, 9.57386589,
10.2665625, 10.9933758, 11.7536821, 12.5464401,
13.3701496, 14.2227964, 15.1018047, 16.0039978,
16.9255428, 17.8619328, 18.8079472, 19.7576466,
20.7043629, 21.6407261, 22.5587025, 23.449646,
24.3043976, 25.1134033, 25.8668575, 26.5548954,
27.1678104, 27.6963062, 28.1317787, 28.4666309,
28.6946087, 28.8111439, 28.8136997, 28.7021179,
28.4789181, 28.1495667, 27.7226772, 27.2101212,
26.6270351, 25.9916973, 25.3252754, 24.6513901,
23.9955502, 23.3843918, 22.8447876, 22.4028034,
22.0825672, 21.9050579, 21.8868961, 22.0391712,
22.3663979, 22.8656502, 23.5259609, 24.3280334,
25.2443562, 26.2397156, 27.2721577, 28.2943993,
29.2556458, 30.1037617, 30.7877197, 31.2602119,
31.4802856, 31.4158611, 31.0459824, 30.3626003,
29.3717995, 28.0942726, 26.5650101, 24.8320904,
22.9546223, 20.9998837, 19.0397873, 17.146862,
15.3900204, 13.8303881, 12.5175056, 11.486227,
10.7545624, 10.3226824, 10.1731901, 10.2726593,
10.5743237, 11.0216951, 11.5527906, 12.1046104,
12.6174631, 13.0387983, 13.3262367, 13.4496088,
13.3918886, 13.149066, 12.7290545, 12.1498365,
11.4370832, 10.6215115, 9.73622513, 8.8142643,
7.88650894, 6.98007774, 6.11724663, 5.31489372,
4.58442593, 3.9321022, 3.35965347, 2.86509776,
2.44363904, 2.08856583, 1.79207587, 1.54597723,
1.34223986, 1.17339075, 1.03276086, 0.914607465,
0.814136565, 0.727456212, 0.651486516, 0.583849609,
0.522755265, 0.466893524, 0.415339351, 0.367471337,
0.322902918, 0.281424493, 0.242953405, 0.207490489,
0.175081566, 0.14578405, 0.119638793, 0.0966482013,
0.0767613202, 0.0598662794, 0.0457901582, 0.0343054123,
0.0251416303, 0.0180007499, 0.0125737227, 0.00855665654,
0.00566475047, 0.00364283333, 0.00227194838, 0.00137198356,
0.000800846552, 0.000451050902, 0.000244662486, 0.000127563457,
6.3798856e-05, 3.05418507e-05, 1.39635513e-05,
/* Z=25 -> Mn */
0, 0.00401948253, 0.00443296554, 0.00488888146,
0.00539156888, 0.00594580779, 0.00655686157, 0.00723053003,
0.00797319971, 0.00879190397, 0.00969438814, 0.0106891794,
0.0117856665, 0.0129941842, 0.0143261068, 0.0157939568,
0.0174115058, 0.0191939119, 0.0211578496, 0.0233216584,
0.025705507, 0.0283315722, 0.0312242359, 0.0344102904,
0.0379191898, 0.0417832844, 0.0460381135, 0.0507227108,
0.0558799282, 0.0615568012, 0.0678049475, 0.074680984,
0.0822470114, 0.0905711129, 0.0997278988, 0.109799117,
0.120874301, 0.13305144, 0.146437794, 0.161150664,
0.177318275, 0.195080757, 0.214591175, 0.236016557,
0.259539157, 0.285357624, 0.313688397, 0.344767153,
0.378850222, 0.416216284, 0.457168013, 0.50203383,
0.551169813, 0.604961574, 0.663826287, 0.728214741,
0.798613489, 0.875546813, 0.959579229, 1.05131733,
1.15141165, 1.26055956, 1.37950599, 1.50904608,
1.6500262, 1.80334508, 1.96995485, 2.15086126,
2.34712291, 2.55985165, 2.79020929, 3.03940535,
3.30869365, 3.59936714, 3.91275048, 4.25019312,
4.61305666, 5.00270605, 5.42049217, 5.86773682,
6.34571028, 6.85561085, 7.39853811, 7.97546387,
8.58719826, 9.23435593, 9.91731453, 10.6361732,
11.390707, 12.180316, 13.0039797, 13.8602028,
14.7469616, 15.6616592, 16.6010666, 17.5612946,
18.5377407, 19.5250721, 20.5172024, 21.5072918,
22.4877644, 23.4503422, 24.3861065, 25.2855873,
26.1388855, 26.9358253, 27.6661358, 28.3196831,
28.8867264, 29.3582115, 29.7260895, 29.9836712,
30.1259766, 30.1501122, 30.0556126, 29.8447781,
29.5229588, 29.0987625, 28.5841999, 27.9946938,
27.3489799, 26.6688442, 25.9787102, 25.3050404,
24.6755791, 24.1184254, 23.6609535, 23.3286266,
23.1437397, 23.1241322, 23.2819462, 23.6225014,
24.1433563, 24.833643, 25.6737213, 26.6352444,
27.6816673, 28.7692242, 29.848381, 30.8657284,
31.7662811, 32.4960632, 33.0048943, 33.2492256,
33.1948433, 32.8193054, 32.1139145, 31.0850353,
29.7546864, 28.1601906, 26.3529339, 24.3961353,
22.3617649, 20.3267078, 18.3684025, 16.5602283,
14.966958, 13.6406317, 12.6171789, 11.9141016,
11.5294342, 11.4421043, 11.6136951, 11.9914894,
12.5125141, 13.1082678, 13.7096863, 14.2519331,
14.6786098, 14.9450502, 15.020484, 14.8889732,
14.5491371, 14.0128069, 13.3028402, 12.4503632,
11.4917297, 10.4655018, 9.40966225, 8.35927773,
7.34471416, 6.39046288, 5.5145731, 4.72863245,
4.03820229, 3.44358754, 2.94082403, 2.52275705,
2.18011284, 1.90247881, 1.67913735, 1.49972415,
1.35470271, 1.23566759, 1.13550031, 1.04840708,
0.9698717, 0.89654994, 0.826131821, 0.757187486,
0.689009488, 0.621459424, 0.554822564, 0.489673823,
0.426756322, 0.366874665, 0.310804486, 0.259219676,
0.212639153, 0.171393409, 0.135610744, 0.105221599,
0.0799785256, 0.0594878756, 0.0432493016, 0.0306981467,
0.0212466568, 0.0143202916, 0.0093865525, 0.00597495493,
0.00368797616, 0.00220386451, 0.00127294369, 0.000709429325,
0.000380798127, 0.000196488094, 9.72659982e-05, 4.60948941e-05,
2.08664333e-05, 9.00192572e-06, 3.69191321e-06,
/* Z=26 -> Fe */
0, 0.00459854677, 0.00507081486, 0.0055914633,
0.00616542948, 0.00679815048, 0.00749561517, 0.00826441869,
0.00911182258, 0.0100458227, 0.0110752219, 0.0122097088,
0.0134599488, 0.0148376813, 0.0163558219, 0.0180285797,
0.0198715925, 0.0219020564, 0.0241388846, 0.0266028736,
0.029316891, 0.0323060714, 0.0355980359, 0.039223142,
0.0432147346, 0.0476094373, 0.0524474718, 0.0577729903,
0.0636344478, 0.0700850263, 0.0771830454, 0.0849924684,
0.0935834125, 0.103032723, 0.113424577, 0.12485116,
0.137413383, 0.151221663, 0.166396767, 0.183070704,
0.201387748, 0.221505418, 0.24359569, 0.267846137,
0.294461221, 0.323663771, 0.355696321, 0.390822709,
0.429329813, 0.471529156, 0.517758846, 0.568385303,
0.623805642, 0.684449315, 0.750780404, 0.823299885,
0.902547777, 0.989105403, 1.08359754, 1.18669474,
1.29911506, 1.42162669, 1.55504918, 1.70025527,
1.85817218, 2.02978206, 2.2161231, 2.41828895,
2.63742781, 2.87474084, 3.1314795, 3.40894127,
3.70846581, 4.03142691, 4.3792243, 4.75327492,
5.15499926, 5.58580542, 6.04707527, 6.54014158,
7.06626415, 7.62660599, 8.2222023, 8.85392666,
9.52245426, 10.2282219, 10.971386, 11.75177,
12.568821, 13.4215536, 14.3085012, 15.2276554,
16.1764183, 17.1515522, 18.149128, 19.1644917,
20.1922283, 21.2261467, 22.2592716, 23.2838554,
24.2914143, 25.2727928, 26.2182388, 27.1175385,
27.9601536, 28.735424, 29.4327888, 30.0420456,
30.5536613, 30.9590969, 31.2511578, 31.4243774,
31.475399, 31.4033337, 31.2101231, 30.9008369,
30.4839134, 29.9713135, 29.3785648, 28.7246666,
28.0318527, 27.3251762, 26.6319313, 25.9808693,
25.4012604, 24.9217949, 24.5693512, 24.3676796,
24.3360615, 24.4879894, 24.8299713, 25.3605042,
26.0693245, 26.9369984, 27.9349327, 29.025835,
30.1646805, 31.3001823, 32.3767395, 33.3368149,
34.1236382, 34.6841583, 34.9720192, 34.950489,
34.5950623, 33.8956108, 32.8578568, 31.5040646,
29.8727589, 28.0174465, 26.0043221, 23.9090176,
21.8125362, 19.7966232, 17.9388237, 16.307621,
14.9579964, 13.9277925, 13.2352057, 12.8776522,
12.8321428, 13.0571766, 13.4960003, 14.080965,
14.7386084, 15.3949957, 15.9808712, 16.4361629,
16.7135105, 16.7805672, 16.6209583, 16.2339516,
15.6329765, 14.843236, 13.8987226, 12.8389406,
11.7056589, 10.5399389, 9.3796339, 8.257514,
7.20002842, 6.22672415, 5.35024834, 4.5768218,
3.9070704, 3.33707309, 2.85950398, 2.46476007,
2.14198899, 1.87996125, 1.66775692, 1.49526179,
1.35348618, 1.23473144, 1.1326369, 1.04213989,
0.959377646, 0.881555974, 0.806801796, 0.734011948,
0.662704527, 0.592877388, 0.524875998, 0.459271461,
0.396751195, 0.338023424, 0.283737689, 0.234423116,
0.190445587, 0.151984483, 0.119027764, 0.0913837254,
0.0687063783, 0.0505302213, 0.0363102779, 0.0254629273,
0.0174036287, 0.0115784509, 0.00748754106, 0.00469976198,
0.00285890047, 0.00168273016, 0.000956738601, 0.000524529256,
0.000276782812, 0.000140299555, 6.81761885e-05, 3.16909282e-05,
1.40598959e-05, 5.93941468e-06, 2.38307257e-06,
/* Z=27 -> Co */
0, 0.00523932744, 0.00577647844, 0.00636855653,
0.00702115521, 0.00774043472, 0.0085331779, 0.0094068516,
0.0103696771, 0.011430705, 0.0125998948, 0.0138882091,
0.0153077114, 0.016871674, 0.018594699, 0.0204928499,
0.0225837883, 0.0248869453, 0.0274236798, 0.0302174706,
0.0332941264, 0.0366820134, 0.0404122844, 0.0445191748,
0.0490402728, 0.0540168583, 0.0594942421, 0.0655221418,
0.0721551254, 0.0794530213, 0.087481454, 0.0963123515,
0.106024519, 0.1167043, 0.128446251, 0.141353846,
0.155540317, 0.17112948, 0.188256741, 0.207069978,
0.227730751, 0.250415325, 0.27531603, 0.302642554,
0.332623273, 0.365506858, 0.401563883, 0.441088408,
0.484399885, 0.531844974, 0.583799541, 0.640670657,
0.70289892, 0.770960271, 0.845368683, 0.926678181,
1.01548529, 1.11243129, 1.21820426, 1.33354199,
1.45923305, 1.59611952, 1.74509811, 1.90712214,
2.08320165, 2.274405, 2.48185778, 2.70674253,
2.95029759, 3.2138133, 3.49862957, 3.80612993,
4.13773537, 4.49489641, 4.8790822, 5.29176712,
5.73441982, 6.20848083, 6.71534538, 7.25634003,
7.8326931, 8.445508, 9.09572697, 9.78409576,
10.511117, 11.2770147, 12.0816774, 12.9246101,
13.8048849, 14.7210789, 15.6712227, 16.6527462,
17.6624203, 18.6963158, 19.7497501, 20.8172684,
21.8925991, 22.9686661, 24.0375919, 25.0907173,
26.1186771, 27.1114731, 28.0585899, 28.9491558,
29.7721214, 30.5164986, 31.1716194, 31.7274437,
32.1748962, 32.5062332, 32.7154274, 32.7985611,
32.7542229, 32.5838661, 32.2921486, 31.8871803,
31.3807201, 30.788229, 30.1288128, 29.4249973,
28.7023411, 27.9888458, 27.3142014, 26.7088203,
26.2027302, 25.824297, 25.598875, 25.5473976,
25.6849842, 26.0196686, 26.5512714, 27.2705727,
28.1588058, 29.1875896, 30.3193264, 31.5081367,
32.7013092, 33.8412933, 34.8681068, 35.7221756,
36.3473969, 36.6943092, 36.7231865, 36.4068489,
35.7330284, 34.7060204, 33.3475151, 31.6964207,
29.8076344, 27.7496986, 25.6014423, 23.4477348,
21.3745918, 19.4639416, 17.7884159, 16.4065838,
15.3590078, 14.6654844, 14.3237514, 14.309803,
14.5798311, 15.0736513, 15.7193232, 16.4385548,
17.1524277, 17.786911, 18.2777271, 18.5741501,
18.6415024, 18.4622211, 18.0355301, 17.3758659,
16.5103321, 15.4755087, 14.3139448, 13.0706749,
11.7900248, 10.5129509, 9.27500343, 8.10501194,
7.02444744, 6.04741526, 5.18114948, 4.4268856,
3.78096581, 3.23604059, 2.78225827, 2.40834951,
2.10254931, 1.85332477, 1.64990497, 1.48262453,
1.34310997, 1.22434175, 1.12062478, 1.02750015,
0.941620648, 0.860610127, 0.78291738, 0.707672119,
0.634546578, 0.563624263, 0.495277762, 0.430056244,
0.36858508, 0.31147939, 0.259273469, 0.212368339,
0.170998216, 0.135215521, 0.104893707, 0.0797449127,
0.0593491681, 0.0431910753, 0.0306994505, 0.0212858766,
0.0143787032, 0.00945000257, 0.00603416376, 0.00373795768,
0.00224290695, 0.00130149303, 0.000729096122, 0.000393605675,
0.000204386917, 0.000101882673, 4.86518293e-05, 2.22075323e-05,
9.6673175e-06, 4.00376075e-06, 1.57357044e-06,
/* Z=28 -> Ni */
0, 0.00594680198, 0.00655539893, 0.0072261109,
0.00796525087, 0.00877976976, 0.00967731792, 0.0106663182,
0.0117560402, 0.0129566845, 0.0142794782, 0.0157367717,
0.0173421577, 0.0191105809, 0.0210584812, 0.0232039429,
0.0255668443, 0.0281690415, 0.0310345571, 0.0341897942,
0.0376637653, 0.0414883383, 0.0456985272, 0.050332766,
0.0554332621, 0.061046347, 0.0672228485, 0.074018538,
0.0814945921, 0.0897180587, 0.0987624601, 0.108708329,
0.119643912, 0.131665796, 0.144879743, 0.159401417,
0.175357327, 0.192885801, 0.212137923, 0.233278707,
0.256488264, 0.28196305, 0.309917241, 0.340584159,
0.374217868, 0.411094695, 0.451515198, 0.495805651,
0.544320285, 0.597443223, 0.655590415, 0.719212115,
0.788794935, 0.864864171, 0.947986484, 1.03877175,
1.13787603, 1.24600315, 1.36390829, 1.49239874,
1.6323365, 1.78464055, 1.95028734, 2.13031316,
2.32581306, 2.53794289, 2.76791692, 3.01700783,
3.28654289, 3.5779016, 3.89250994, 4.23183393,
4.59737253, 4.99064541, 5.41318274, 5.86650896,
6.35212708, 6.87149572, 7.42600727, 8.0169611,
8.64553165, 9.31273556, 10.019393, 10.7660866,
11.5531158, 12.3804445, 13.247654, 14.1538858,
15.097784, 16.0774384, 17.0903263, 18.1332626,
19.2023373, 20.2928791, 21.3994122, 22.5156345,
23.6343994, 24.7477283, 25.8468285, 26.9221592,
27.9634972, 28.9600639, 29.9006634, 30.7738838,
31.568306, 32.2727928, 32.8767776, 33.3706169,
33.7459717, 33.9961777, 34.1166878, 34.1054573,
33.9633408, 33.6944351, 33.306385, 32.8105774,
32.2222404, 31.5604248, 30.8477783, 30.1102142,
29.3763237, 28.6766357, 28.0426559, 27.5057392,
27.0958042, 26.839922, 26.7608662, 26.8756466,
27.1941376, 27.7178802, 28.4391289, 29.3402481,
30.3935509, 31.5616112, 32.7981262, 34.0493393,
35.256012, 36.3559036, 37.2866516, 37.9889832,
38.4100304, 38.5066185, 38.2483139, 37.619976,
36.623661, 35.2796249, 33.6263008, 31.7191753,
29.6284466, 27.435627, 25.2291412, 23.0992146,
21.1323471, 19.4057713, 17.9823151, 16.9061203,
16.1995544, 15.8616972, 15.8684988, 16.1747093,
16.7173824, 17.4207115, 18.2017422, 18.9764481,
19.665659, 20.2002945, 20.5255299, 20.6035347,
20.4147339, 19.9575291, 19.2467117, 18.3107891,
17.1886139, 15.9256449, 14.5702276, 13.1701632,
11.7698154, 10.4079189, 9.11612225, 7.91826677,
6.830338, 5.86095715, 5.01227951, 4.281147,
3.66035199, 3.13989115, 2.70811772, 2.35272336,
2.0615201, 1.82301402, 1.62678516, 1.46370161,
1.32600152, 1.20727861, 1.10240495, 1.00741386,
0.919366837, 0.836211026, 0.75663954, 0.679955602,
0.605942369, 0.534740031, 0.466730863, 0.402433902,
0.342411727, 0.287191451, 0.237202317, 0.192731574,
0.15389888, 0.120649122, 0.0927614346, 0.0698717237,
0.0515046604, 0.0371112078, 0.0261071101, 0.0179088134,
0.011963645, 0.00777243217, 0.00490372907, 0.00300000072,
0.00177688233, 0.00101723499, 0.00056189613, 0.000298931554,
0.000152875145, 7.5002863e-05, 3.52270581e-05, 1.58040202e-05,
6.75674983e-06, 2.74613785e-06, 1.05828644e-06,
/* Z=29 -> Cu */
0, 0.00672325259, 0.00741004106, 0.00816678908,
0.00900059007, 0.00991925504, 0.0109313782, 0.01204642,
0.013274787, 0.0146279344, 0.0161184594, 0.0177602228,
0.0195684694, 0.0215599611, 0.0237531345, 0.0261682533,
0.0288275983, 0.031755656, 0.0349793285, 0.0385281816,
0.0424346849, 0.0467345081, 0.0514668077, 0.0566745736,
0.0624049902, 0.068709828, 0.0756458789, 0.0832754225,
0.0916667506, 0.10089469, 0.11104124, 0.12219622,
0.134457946, 0.147934079, 0.162742332, 0.179011479,
0.196882278, 0.216508493, 0.238058075, 0.26171428,
0.287677079, 0.316164374, 0.347413689, 0.381683528,
0.419255197, 0.460434496, 0.505553663, 0.554973185,
0.609084129, 0.668310046, 0.733109355, 0.803977668,
0.881450176, 0.966103852, 1.05856049, 1.15948844,
1.26960564, 1.38968182, 1.52054048, 1.66306162,
1.81818318, 1.98690259, 2.17027831, 2.36943054,
2.58554149, 2.8198545, 3.07367301, 3.34835863,
3.64532685, 3.96604347, 4.31201696, 4.68479109,
5.08593607, 5.51703358, 5.97966528, 6.4753933,
7.00574017, 7.57216644, 8.17604256, 8.81861877,
9.50098896, 10.2240572, 10.9884892, 11.7946701,
12.6426535, 13.5321083, 14.4622641, 15.4318485,
16.4390354, 17.4813766, 18.5557499, 19.6583023,
20.7844048, 21.9286003, 23.0845871, 24.2451916,
25.4023743, 26.5472527, 27.6701469, 28.7606506,
29.8077545, 30.7999763, 31.7255516, 32.5726585,
33.3296852, 33.9855423, 34.5299873, 34.9540405,
35.2503548, 35.4136658, 35.4411888, 35.3330536,
35.0926628, 34.7270164, 34.2469559, 33.6672783,
33.0067596, 32.2879753, 31.5369835, 30.7827816,
30.0565758, 29.3908443, 28.8182049, 28.3701077,
28.0754147, 27.9588795, 28.0396347, 28.3297291,
28.8328266, 29.5431557, 30.4447823, 31.5113392,
32.7062187, 33.9833488, 35.2885513, 36.56147,
37.7380371, 38.7534256, 39.5453148, 40.0573654,
40.2426643, 40.0669861, 39.5115738, 38.575264,
37.2757378, 35.6496849, 33.7518463, 31.6527672,
29.4354305, 27.1907902, 25.0125446, 22.9913769,
21.2091446, 19.7334194, 18.6128502, 17.8737583,
17.5182991, 17.5244007, 17.8475323, 18.4241753,
19.1767006, 20.0192299, 20.8639565, 21.6273537,
22.2357216, 22.6296597, 22.7671013, 22.6247749,
22.1981106, 21.4997349, 20.5568256, 19.4077072,
18.0980473, 16.6770229, 15.1937828, 13.6944523,
12.2198143, 10.8037729, 9.47254848, 8.24456215,
7.13086939, 6.13601923, 5.25915861, 4.49526453,
3.83636904, 3.27267718, 2.79352903, 2.38815498,
2.04623151, 1.75824165, 1.51567149, 1.31108141,
1.13808215, 0.991257131, 0.866054714, 0.758673429,
0.665954053, 0.58528477, 0.514521897, 0.451925486,
0.396105468, 0.34597519, 0.300709218, 0.259702146,
0.222527996, 0.188899443, 0.158628106, 0.131587014,
0.107677303, 0.0868005008, 0.0688379183, 0.0536376387,
0.0410092473, 0.0307254996, 0.0225295536, 0.0161460824,
0.0112942234, 0.00770051079, 0.00511020282, 0.00329589355,
0.00206282083, 0.00125087425, 0.000733686436, 0.000415528833,
0.000226829725, 0.000119119861, 6.006084e-05, 2.90146272e-05,
1.34002139e-05, 5.90308809e-06, 2.47442199e-06,
/* Z=30 -> Zn */
0, 0.00758356694, 0.00835675746, 0.00920854881,
0.0101468964, 0.0111805508, 0.0123191448, 0.0135732768,
0.0149546033, 0.0164759494, 0.0181514192, 0.0199965239,
0.0220283233, 0.0242655687, 0.0267288741, 0.0294409003,
0.032426551, 0.0357131809, 0.0393308513, 0.0433125719,
0.0476946011, 0.0525167435, 0.0578226894, 0.0636603907,
0.0700824484, 0.0771465674, 0.0849160329, 0.0934602171,
0.102855131, 0.113184072, 0.124538258, 0.137017578,
0.150731325, 0.165799081, 0.182351604, 0.200531811,
0.220495895, 0.24241434, 0.266473293, 0.292875737,
0.321843058, 0.353616327, 0.388458163, 0.42665419,
0.468515009, 0.514378071, 0.564609528, 0.619606674,
0.679799855, 0.745654881, 0.817675412, 0.896405458,
0.98243171, 1.07638621, 1.17894912, 1.29085076,
1.41287434, 1.5458585, 1.69069958, 1.84835303,
2.01983571, 2.20622754, 2.40867162, 2.62837481,
2.86660838, 3.12470531, 3.40405941, 3.70612192,
4.03239632, 4.38443279, 4.76382017, 5.17217684,
5.61113739, 6.08233976, 6.58740616, 7.12792492,
7.70542622, 8.32135487, 8.97703838, 9.67365646,
10.4121981, 11.1934214, 12.0178061, 12.8855038,
13.7962837, 14.7494745, 15.743906, 16.7778473,
17.8489456, 18.9541626, 20.0897274, 21.2510662,
22.4327774, 23.628582, 24.8313065, 26.0328789,
27.2243538, 28.3959332, 29.5370655, 30.6365223,
31.6825504, 32.6630554, 33.565815, 34.3787422,
35.0902023, 35.6893539, 36.1665306, 36.5136604,
36.7246971, 36.7960663, 36.7270737, 36.5203362,
36.1821098, 35.7225685, 35.1559677, 34.5006943,
33.7791481, 33.0174294, 32.2448692, 31.4933033,
30.7961578, 30.1873283, 29.6998749, 29.3645439,
29.2082367, 29.2524014, 29.5114975, 29.9915829,
30.6891346, 31.5902023, 32.6699829, 33.8929062,
35.2132759, 36.5765419, 37.9211655, 39.1810951,
40.2887421, 41.1783295, 41.7895317, 42.0711174,
41.9844475, 41.5065384, 40.6324844, 39.3769798,
37.7747612, 35.8798294, 33.7633553, 31.5103321,
29.2150574, 26.9756966, 24.8882465, 23.0403271,
21.5052719, 20.3369961, 19.5661182, 19.1977043,
19.2108955, 19.5604935, 20.1804256, 20.9887905,
21.8940449, 22.8017826, 23.6214981, 24.2727242,
24.690052, 24.8266621, 24.6561546, 24.1726494,
23.3893356, 22.3357201, 21.0539761, 19.5947819,
18.0130844, 16.3641319, 14.7000408, 13.067132,
11.5040817, 10.0409126, 8.69875908, 7.49026728,
6.42049551, 5.48813009, 4.6868639, 4.00679636,
3.43573952, 2.96035767, 2.56709218, 2.24286032,
1.97553825, 1.75425458, 1.56953263, 1.41331816,
1.27893066, 1.16096592, 1.05517399, 0.958327234,
0.868085802, 0.782866061, 0.701712489, 0.624174297,
0.550186515, 0.479956865, 0.413860708, 0.35234639,
0.295853883, 0.244749114, 0.199276358, 0.159528747,
0.125437275, 0.0967761576, 0.0731818676, 0.0541823246,
0.0392319411, 0.0277485177, 0.0191481132, 0.0128748761,
0.00842383876, 0.00535572739, 0.00330392527, 0.001974585,
0.00114143849, 0.000637121266, 0.000342774845, 0.000177418246,
8.8172601e-05, 4.1987023e-05, 1.91159888e-05, 8.30204226e-06,
3.43111788e-06, 1.34602396e-06, 4.99903308e-07,
/* Z=31 -> Ga */
0, 0.00852765702, 0.00939538423, 0.0103511401,
0.0114038112, 0.0125631774, 0.0138399927, 0.0152460942,
0.0167944934, 0.0184995029, 0.0203768611, 0.0224438738,
0.0247195587, 0.0272248294, 0.0299826581, 0.0330182984,
0.0363594852, 0.0400366969, 0.0440833867, 0.0485363081,
0.0534357913, 0.0588261187, 0.0647558719, 0.0712783411,
0.0784519985, 0.0863409266, 0.0950153992, 0.104552411,
0.115036309, 0.126559496, 0.139223069, 0.153137743,
0.168424577, 0.18521595, 0.203656614, 0.223904639,
0.246132687, 0.270529181, 0.297299653, 0.326668203,
0.35887897, 0.394197792, 0.432913929, 0.475341916,
0.521823466, 0.572729468, 0.628462255, 0.689457893,
0.756188214, 0.82916379, 0.908935785, 0.996099114,
1.09129465, 1.19521224, 1.30859292, 1.43223155,
1.56697965, 1.71374738, 1.87350595, 2.04728913,
2.23619533, 2.44138789, 2.66409683, 2.90561724,
3.16730976, 3.45059752, 3.75696421, 4.0879488,
4.44514084, 4.83017111, 5.24470425, 5.69042587,
6.16902924, 6.68219566, 7.23157883, 7.81877804,
8.44531345, 9.1125946, 9.82188702, 10.5742712,
11.3706026, 12.2114649, 13.0971174, 14.0274382,
15.0018721, 16.0193634, 17.0783005, 18.1764431,
19.3108673, 20.4779015, 21.6730728, 22.8910522,
24.1256256, 25.3696556, 26.6150837, 27.852932,
29.0733395, 30.2656345, 31.418417, 32.5197067,
33.5570984, 34.5179977, 35.3898659, 36.1605339,
36.8185387, 37.3535347, 37.7566719, 38.0210876,
38.1423149, 38.1187744, 37.9521637, 37.6478615,
37.2152252, 36.6677933, 36.0233841, 35.3040123,
34.5356483, 33.747757, 32.9726257, 32.2444992,
31.5984364, 31.0690384, 30.6889477, 30.4872684,
30.4879093, 30.7079563, 31.1561527, 31.8316021,
32.7227669, 33.8068962, 35.0499611, 36.4071579,
37.8240509, 39.238369, 40.5824127, 41.7860374,
42.7800941, 43.5001793, 43.890461, 43.9074287,
43.5232506, 42.7285004, 41.5340157, 39.9716415,
38.0937195, 35.9712067, 33.690403, 31.3484421,
29.0477142, 26.8895741, 24.9677486, 23.3619576,
22.1322498, 21.3145809, 20.9180527, 20.9241257,
21.2879238, 21.9416008, 22.799469, 23.7644787,
24.7354374, 25.6143532, 26.3132248, 26.7597027,
26.9012203, 26.7072792, 26.1698704, 25.3021564,
24.1356525, 22.7163563, 21.1002407, 19.3485489,
17.5233383, 15.6835661, 13.8819456, 12.1627388,
10.5604572, 9.09944725, 7.79423141, 6.65043068,
5.66610003, 4.83328152, 4.13962412, 3.56993246,
3.10754323, 2.73547864, 2.43734455, 2.19797802,
2.00386906, 1.84338927, 1.70686793, 1.58655405,
1.47649825, 1.3723805, 1.2713052, 1.17157912,
1.07248294, 0.974046946, 0.876836419, 0.781755924,
0.689876378, 0.602290452, 0.519999146, 0.443830609,
0.374389559, 0.312035769, 0.256886154, 0.208835483,
0.167590007, 0.132708296, 0.103644118, 0.0797877386,
0.0605023578, 0.0451543592, 0.0331367068, 0.0238855854,
0.0168911163, 0.0117031559, 0.00793317705, 0.0052531953,
0.00339253829, 0.00213308423, 0.00130346103, 0.000772663741,
0.000443458732, 0.000245938398, 0.00013152929, 6.769006e-05,
3.34491815e-05, 1.58351522e-05, 7.16499653e-06,
/* Z=32 -> Ge */
0, 0.00956309866, 0.0105341999, 0.0116036041,
0.012781214, 0.0140779186, 0.0155057013, 0.017077731,
0.0188084971, 0.0207139235, 0.0228115208, 0.0251205303,
0.0276621059, 0.0304594841, 0.0335382037, 0.0369263142,
0.0406546257, 0.0447569638, 0.0492704771, 0.0542359389,
0.0596980937, 0.065706037, 0.0723136291, 0.0795799345,
0.0875697061, 0.0963539258, 0.106010377, 0.116624273,
0.128288895, 0.141106412, 0.155188575, 0.17065765,
0.187647358, 0.206303835, 0.226786688, 0.249270275,
0.273944885, 0.301018, 0.330715984, 0.363285333,
0.398994505, 0.438135654, 0.481026441, 0.528011978,
0.579466999, 0.635797977, 0.697445393, 0.76488632,
0.838636518, 0.919253469, 1.00733852, 1.10354006,
1.20855594, 1.32313585, 1.44808495, 1.58426535,
1.73259926, 1.89407134, 2.0697298, 2.26068926,
2.46813154, 2.69330621, 2.93753028, 3.20218897,
3.48873234, 3.79867363, 4.13358545, 4.49509239,
4.88486719, 5.3046174, 5.75607777, 6.24099398,
6.76110697, 7.31813383, 7.91374445, 8.54953384,
9.22699547, 9.94748116, 10.7121696, 11.5220194,
12.3777199, 13.2796488, 14.2278051, 15.2217598,
16.2605915, 17.3428154, 18.4663296, 19.6283455,
20.8253155, 22.0528927, 23.3058586, 24.5780907,
25.8625298, 27.1511574, 28.4350147, 29.7042122,
30.947998, 32.1548462, 33.3125725, 34.4085159,
35.4297295, 36.3632393, 37.1963654, 37.9170303,
38.5141754, 38.9781723, 39.3012772, 39.4780998,
39.5060577, 39.3858528, 39.1218491, 38.7224464,
38.2003059, 37.5724945, 36.8604622, 36.0898438,
35.2900505, 34.4936523, 33.7355309, 33.0518074,
32.4785271, 32.0502052, 31.7981815, 31.7489357,
31.9223652, 32.3301697, 32.974411, 33.8463821,
34.9258499, 36.1808281, 37.5679245, 39.0333176,
40.5144424, 41.9423256, 43.2445335, 44.3486481,
45.1861229, 45.6962967, 45.8303566, 45.5550232,
44.8555984, 43.7381897, 42.2308273, 40.3832664,
38.2653694, 35.9640236, 33.5786705, 31.2156677,
28.9817562, 26.9771118, 25.2884769, 23.9829292,
23.1028404, 22.6625137, 22.6468811, 23.0124207,
23.6903152, 24.5915928, 25.6138363, 26.6488571,
27.5906372, 28.3428307, 28.8251896, 28.9783802,
28.7668781, 28.1798077, 27.2298222, 25.9503078,
24.3912926, 22.6145477, 20.6883907, 18.6826401,
16.6640873, 14.692812, 12.8194723, 11.0836477,
9.51318455, 8.12442589, 6.92317629, 5.90617275,
5.0628767, 4.37738991, 3.83033085, 3.40054822,
3.06658769, 2.80786514, 2.60553789, 2.44308591,
2.30663776, 2.18508101, 2.07000089, 1.95549023,
1.83786941, 1.71534836, 1.58765924, 1.45568454,
1.32110023, 1.18604922, 1.05285943, 0.923811674,
0.800964117, 0.686030746, 0.580312252, 0.484671324,
0.399544358, 0.324980497, 0.260698467, 0.206152767,
0.160602391, 0.123176686, 0.0929344669, 0.0689144433,
0.0501761921, 0.0358314328, 0.0250664186, 0.0171563402,
0.0114727039, 0.00748487888, 0.00475682272, 0.00294012576,
0.00176442915, 0.00102629955, 0.000577547122, 0.000313851546,
0.00016437372, 8.27989352e-05, 4.00292702e-05, 1.85322497e-05,
8.19730849e-06, 3.45587e-06, 1.38512553e-06,
/* Z=33 -> As */
0, 0.0106970547, 0.0117810154, 0.0129744587,
0.0142883882, 0.0157349017, 0.0173273031, 0.0190802179,
0.0210097227, 0.0231334921, 0.0254709497, 0.0280434396,
0.0308744106, 0.0339896269, 0.037417382, 0.0411887541,
0.0453378633, 0.0499021634, 0.0549227707, 0.0604447946,
0.066517733, 0.0731958821, 0.0805387571, 0.08861164,
0.0974860564, 0.107240386, 0.117960483, 0.129740342,
0.14268288, 0.156900704, 0.172516987, 0.189666405,
0.208496153, 0.229167074, 0.251854748, 0.276750803,
0.304064363, 0.334023327, 0.366876066, 0.402893037,
0.442368507, 0.485622585, 0.533002973, 0.584887326,
0.641685307, 0.703840911, 0.77183497, 0.84618777,
0.927461326, 1.01626241, 1.11324513, 1.21911383,
1.3346256, 1.46059346, 1.59788859, 1.7474432,
1.91025293, 2.0873785, 2.27994871, 2.48916078,
2.71628118, 2.9626472, 3.2296648, 3.51880932,
3.83162022, 4.16970062, 4.53470898, 4.92835522,
5.35238886, 5.80859041, 6.29875803, 6.82468891,
7.38816309, 7.99091864, 8.6346283, 9.32086658,
10.0510778, 10.826539, 11.6483126, 12.5172081,
13.4337187, 14.3979797, 15.4096956, 16.4680901,
17.5718288, 18.7189598, 19.9068489, 21.132103,
22.3905201, 23.6770248, 24.9856186, 26.309351,
27.6402931, 28.9695301, 30.2871914, 31.5824909,
32.843811, 34.058815, 35.2146111, 36.2979393,
37.2954292, 38.1938972, 38.9806633, 39.6439743,
40.1733856, 40.5602608, 40.798214, 40.8836174,
40.8160591, 40.5987968, 40.2391205, 39.748661,
39.1435623, 38.4445152, 37.6766129, 36.8690186,
36.0543747, 35.2680397, 34.5470161, 33.9286957,
33.4493828, 33.1426659, 33.0376434, 33.1571846,
33.5161629, 34.1199226, 34.9629745, 36.0280647,
37.2857704, 38.6946411, 40.2020226, 41.7455711,
43.2554817, 44.6573601, 45.8757401, 46.8379593,
47.4783707, 47.7425194, 47.591114, 47.0034599,
45.9800606, 44.5441399, 42.7418556, 40.6409988,
38.3281746, 35.9044609, 33.4797516, 31.1660748,
29.0702839, 27.2867222, 25.890379, 24.9311733,
24.4299126, 24.3763313, 24.7295208, 25.4207458,
26.3585052, 27.4353943, 28.5361843, 29.5463886,
30.3605328, 30.8894272, 31.0658112, 30.8479671,
30.2211285, 29.1966763, 27.8094196, 26.1133423,
24.1763172, 22.0743446, 19.8858452, 17.6864281,
15.5445194, 13.5180521, 11.6523371, 9.97909164,
8.51652718, 7.27033091, 6.23531103, 5.39748621,
4.7363801, 4.22732782, 3.84362626, 3.55840993,
3.34617591, 3.18392992, 3.05195475, 2.93422794,
2.81853795, 2.69635224, 2.56249619, 2.41469955,
2.25306392, 2.07949781, 1.89715981, 1.70994186,
1.52201581, 1.33746016, 1.15997362, 0.992677689,
0.838000119, 0.697631419, 0.572540164, 0.463032812,
0.368844569, 0.289247364, 0.223163977, 0.169279978,
0.126146287, 0.0922683477, 0.0661795288, 0.0464977436,
0.0319656767, 0.0214757733, 0.0140818423, 0.0089993896,
0.00559721515, 0.00338271121, 0.00198329031, 0.00112615211,
0.000618192425, 0.000327459391, 0.000167052596, 8.19083216e-05,
3.8517559e-05, 1.73332683e-05, 7.44704357e-06, 3.04728474e-06,
1.18457558e-06, 4.36291373e-07, 1.51825333e-07,
/* Z=34 -> Se */
0, 0.0119372932, 0.0131442985, 0.0144729353,
0.0159353968, 0.0175450891, 0.0193167478, 0.0212665647,
0.023412345, 0.0257736463, 0.0283719618, 0.0312309004,
0.0343763977, 0.0378369316, 0.0416437835, 0.0458312817,
0.0504371151, 0.0555026494, 0.061073266, 0.0671987459,
0.0739337057, 0.0813379958, 0.0894772559, 0.0984234065,
0.10825526, 0.119059108, 0.13092947, 0.143969774,
0.158293247, 0.174023628, 0.191296324, 0.210259274,
0.231074095, 0.253917247, 0.278981388, 0.306476593,
0.336631954, 0.369697094, 0.405943871, 0.445668072,
0.489191413, 0.536863565, 0.589064121, 0.646205068,
0.708732963, 0.777131438, 0.851923883, 0.933675826,
1.02299809, 1.12054908, 1.22703815, 1.3432281,
1.46993816, 1.60804641, 1.75849342, 1.92228353,
2.10048819, 2.29424763, 2.50477171, 2.73334241,
2.98131371, 3.25011039, 3.54122901, 3.85623431,
4.19675541, 4.56448317, 4.96116066, 5.38857746,
5.84855843, 6.34294891, 6.87360287, 7.44236088,
8.05102921, 8.70135498, 9.39499664, 10.1334896,
10.918211, 11.7503338, 12.630785, 13.5601883,
14.5388126, 15.566514, 16.6426678, 17.7661018,
18.9350376, 20.1470051, 21.3987942, 22.6863728,
24.0048294, 25.3483276, 26.7100582, 28.0822124,
29.4559669, 30.8215065, 32.1680565, 33.4839478,
34.7567368, 35.9733429, 37.1202393, 38.1836853,
39.1500206, 40.0060005, 40.7391586, 41.3382568,
41.7937317, 42.0981712, 42.2468376, 42.2381363,
42.0741005, 41.7608032, 41.3086815, 40.7327843,
40.0528526, 39.2932434, 38.4826393, 37.6535606,
36.8416176, 36.0845184, 35.4208412, 34.8885841,
34.5235138, 34.3573875, 34.4161263, 34.7179756,
35.2718391, 36.0758018, 37.1160431, 38.3662148,
39.787384, 41.32864, 42.9284286, 44.5166397,
46.0173683, 47.3523903, 48.4450989, 49.2248039,
49.6311607, 49.6184044, 49.1591606, 48.2474632,
46.9007454, 45.1604805, 43.0912971, 40.7785072,
38.3239784, 35.840538, 33.4451866, 31.2515278,
29.3619385, 27.8601265, 26.8046837, 26.2242584,
26.1148643, 26.4396534, 27.1312809, 28.0967312,
29.2242565, 30.3917904, 31.4761124, 32.3619385,
32.9501152, 33.1642113, 32.954998, 32.3025703,
31.2159939, 29.7307854, 27.9045391, 25.8112793,
23.5351162, 21.1637859, 18.7826118, 16.4693298,
14.2900476, 12.2965269, 10.5247993, 8.99505806,
7.71264791, 6.66990852, 5.84862137, 5.22278023,
4.76143408, 4.43138313, 4.1995635, 4.03500366,
3.91029024, 3.80253935, 3.69388771, 3.5715704,
3.42765212, 3.25850177, 3.0640893, 2.84719229,
2.61257672, 2.36621928, 2.11460829, 1.86416125,
1.62076914, 1.38947725, 1.17429018, 0.978091836,
0.802656949, 0.648735344, 0.51618439, 0.404131949,
0.311150461, 0.235428765, 0.174931139, 0.127536133,
0.0911508054, 0.0637990758, 0.0436841026, 0.0292266831,
0.0190826375, 0.012142837, 0.00751986308, 0.00452540815,
0.0026422774, 0.00149435073, 0.000817191729, 0.00043132162,
0.000219308145, 0.000107205211, 5.02776493e-05, 2.25724998e-05,
9.67904725e-06, 3.95448069e-06, 1.5355223e-06, 5.65180528e-07,
1.96645132e-07, 6.44895337e-08, 1.98743635e-08,
/* Z=35 -> Br */
0, 0.0132921264, 0.0146331051, 0.0161088984,
0.0177329853, 0.0195201822, 0.0214867741, 0.0236506481,
0.0260314662, 0.028650824, 0.0315324441, 0.0347023793,
0.0381892398, 0.0420244336, 0.0462424457, 0.0508811139,
0.0559819713, 0.0615905747, 0.0677568987, 0.0745357424,
0.0819871947, 0.0901771039, 0.0991776586, 0.109067902,
0.119934432, 0.131872043, 0.144984514, 0.159385353,
0.175198764, 0.192560494, 0.21161893, 0.232536137,
0.255489141, 0.28067106, 0.308292657, 0.338583678,
0.371794492, 0.408197671, 0.448090017, 0.491794199,
0.53966099, 0.592071295, 0.649438441, 0.712210596,
0.780873239, 0.855951786, 0.93801415, 1.02767372,
1.12559199, 1.23248196, 1.34911025, 1.4763006,
1.61493695, 1.76596534, 1.93039775, 2.10931349,
2.30386162, 2.51526356, 2.74481344, 2.99387908,
3.26390195, 3.5563972, 3.87295103, 4.21521711,
4.58491421, 4.9838171, 5.41375208, 5.87658453,
6.37420702, 6.90852499, 7.48143864, 8.09482002,
8.75049114, 9.45019245, 10.1955519, 10.9880457,
11.8289614, 12.7193441, 13.6599522, 14.6511993,
15.6930943, 16.7851753, 17.9264507, 19.1153183,
20.3495064, 21.6259899, 22.9409332, 24.2896233,
25.6664085, 27.0646553, 28.4767075, 29.8938789,
31.3064423, 32.7036819, 34.0739288, 35.4046707,
36.6826897, 37.8942223, 39.0252113, 40.0615616,
40.9894714, 41.7958069, 42.4685249, 42.9971275,
43.3731651, 43.5907364, 43.647007, 43.5426941,
43.2825279, 42.8756256, 42.3357697, 41.6815605,
40.9364128, 40.128315, 39.2894249, 38.4553833,
37.6643944, 36.9560318, 36.3698311, 35.9436417,
35.7118492, 35.7034721, 35.9402695, 36.4349174,
37.1894226, 38.1938171, 39.4253311, 40.848114,
42.41362, 44.0617104, 45.7225609, 47.3192902,
48.7713394, 49.9984169, 50.9248772, 51.4843483,
51.6242218, 51.309845, 50.527977, 49.2892532,
47.6293411, 45.6085396, 43.3097267, 40.8345222,
38.2978897, 35.821312, 33.5249863, 31.5196171,
29.8983116, 28.7293987, 28.0507507, 27.8662281,
28.1446857, 28.8216991, 29.8040543, 30.9765835,
32.2108383, 33.3748245, 34.3428879, 35.0049133,
35.2739792, 35.0918694, 34.4320297, 33.2998734,
31.7305603, 29.7846355, 27.5420494, 25.0952187,
22.5417709, 19.9776058, 17.4907646, 15.1565361,
13.0340099, 11.1641788, 9.56955624, 8.25513554,
7.2104497, 6.41243458, 5.82876015, 5.42131615,
5.14956951, 4.97355556, 4.8563447, 4.76587725,
4.67614365, 4.56773186, 4.42781687, 4.24969149,
4.03196096, 3.77752399, 3.49245358, 3.18488503,
2.86398768, 2.53907728, 2.21890688, 1.91114998,
1.62207043, 1.3563602, 1.11712253, 0.905964971,
0.72317332, 0.567933977, 0.438579828, 0.332836568,
0.248053551, 0.181407914, 0.130074203, 0.091356881,
0.0627857521, 0.0421763659, 0.0276597235, 0.0176865794,
0.0110120801, 0.00666654622, 0.00391813368, 0.00223209057,
0.00123046106, 0.000655213196, 0.000336397381, 0.000166201702,
7.88584803e-05, 3.58563702e-05, 1.55890593e-05, 6.46537183e-06,
2.55166083e-06, 9.55858468e-07, 3.3895185e-07, 1.13457773e-07,
3.57440975e-08, 1.05660556e-08, 2.92123437e-09,
/* Z=36 -> Kr */
0, 0.0147705059, 0.0162571836, 0.0178929605,
0.0196927078, 0.0216727629, 0.0238510743, 0.0262473654,
0.0288832951, 0.0317826569, 0.0349715725, 0.0384787247,
0.0423356034, 0.0465767719, 0.0512401536, 0.0563673638,
0.0620040484, 0.0682002753, 0.0750109479, 0.0824962482,
0.0907221287, 0.0997608677, 0.109691642, 0.120601147,
0.132584304, 0.145744994, 0.160196885, 0.176064253,
0.193483025, 0.212601721, 0.233582556, 0.256602705,
0.281855494, 0.309551865, 0.339921743, 0.373215765,
0.409706801, 0.449691921, 0.493494183, 0.541464806,
0.59398514, 0.651469171, 0.714365721, 0.783161163,
0.858381927, 0.940597057, 1.0304215, 1.12851858,
1.23560321, 1.35244453, 1.47986948, 1.61876547,
1.77008295, 1.93483865, 2.1141181, 2.30907798,
2.52094722, 2.75103045, 3.00070715, 3.2714324,
3.56473708, 3.88222599, 4.22557497, 4.59652662,
4.99688578, 5.42851114, 5.89330673, 6.3932085,
6.93017197, 7.50615311, 8.12308884, 8.78287315,
9.48732758, 10.2381706, 11.0369816, 11.8851566,
12.7838678, 13.7340097, 14.7361422, 15.7904348,
16.8966026, 18.0538311, 19.2607212, 20.5151997,
21.8144569, 23.1548748, 24.5319576, 25.9402637,
27.3733692, 28.8238068, 30.2830582, 31.7415371,
33.1886215, 34.6126862, 36.0012054, 37.3408623,
38.6177216, 39.8174477, 40.9255447, 41.9277,
42.8101387, 43.5600281, 44.1659584, 44.618412,
44.910305, 45.0375061, 44.9993439, 44.7991104,
44.4444695, 43.9477844, 43.3263397, 42.6023865,
41.8030052, 40.9597511, 40.1080513, 39.2863617,
38.5350342, 37.8949509, 37.4059029, 37.1048088,
37.0237885, 37.1881752, 37.6146202, 38.3093147,
39.2665291, 40.4675598, 41.8802147, 43.4589272,
45.1456528, 46.8715096, 48.5592613, 50.1265335,
51.4897461, 52.5685196, 53.2904396, 53.5958176,
53.4422264, 52.8083992, 51.6972198, 50.1374054,
48.1836891, 45.9152451, 43.4322739, 40.8508568,
38.2962341, 35.8948631, 33.7658081, 32.0121231,
30.7128391, 29.9164047, 29.6361732, 29.8484726,
30.4935913, 31.4796867, 32.6894112, 33.9887085,
35.2370071, 36.2979202, 37.0494576, 37.3928757,
37.2593117, 36.6138382, 35.4565506, 33.8208466,
31.7691936, 29.3869152, 26.7746868, 24.0404415,
21.2914333, 18.6270638, 16.1329403, 13.8765774,
11.9048424, 10.2431936, 8.8965559, 7.85158587,
7.07998753, 6.54248142, 6.19303942, 5.9830122,
5.86483717, 5.79509354, 5.73676443, 5.66064692,
5.54593754, 5.38009739, 5.15812206, 4.88139343,
4.55628014, 4.19264507, 3.8023994, 3.39820099,
2.99237514, 2.59608626, 2.2187736, 1.86783135,
1.54850328, 1.26394939, 1.01544094, 0.802638113,
0.623913646, 0.476687282, 0.357747257, 0.263539672,
0.190414235, 0.134820879, 0.0934552029, 0.0633558258,
0.0419584028, 0.0271130092, 0.0170728061, 0.0104618277,
0.00622956781, 0.00359909236, 0.00201425515, 0.00109015417,
0.000569563126, 0.000286725786, 0.000138807649, 6.44898537e-05,
2.86924333e-05, 1.21972798e-05, 4.94256983e-06, 1.90441835e-06,
6.95930453e-07, 2.40538498e-07, 7.84124552e-08, 2.40368365e-08,
6.90739466e-09, 1.85477467e-09, 4.63815708e-10,
/* Z=37 -> Rb */
0, 0.016384406, 0.0180295967, 0.0198393706,
0.0218301006, 0.0240197647, 0.0264281165, 0.0290768482,
0.0319897793, 0.0351930633, 0.0387154147, 0.0425883457,
0.0468464456, 0.0515276603, 0.0566736236, 0.0623300038,
0.0685468763, 0.0753791481, 0.0828870013, 0.0911363885,
0.10019958, 0.110155709, 0.12109147, 0.133101717,
0.146290302, 0.160770789, 0.176667437, 0.194116026,
0.213264972, 0.234276414, 0.257327348, 0.282610983,
0.31033805, 0.340738356, 0.37406233, 0.410582662,
0.450596213, 0.494425863, 0.542422593, 0.594967723,
0.652475059, 0.715393364, 0.784209073, 0.859448552,
0.941681385, 1.03152275, 1.12963641, 1.23673844,
1.35359907, 1.48104692, 1.61997116, 1.77132511,
1.93612885, 2.11547232, 2.3105166, 2.52249813,
2.75272822, 3.0025959, 3.27356791, 3.56718802,
3.88507724, 4.22893, 4.60051107, 5.00165176,
5.43424082, 5.90021706, 6.40155792, 6.94026518,
7.51834965, 8.13780975, 8.80060863, 9.50864792,
10.2637358, 11.0675516, 11.9216061, 12.8271923,
13.7853441, 14.796773, 15.8618135, 16.98036,
18.1517925, 19.3749123, 20.6478653, 21.968071,
23.3321419, 24.7358208, 26.1739082, 27.6402073,
29.1274757, 30.6273937, 32.1305504, 33.626461,
35.1035919, 36.5494385, 37.9506454, 39.2931404,
40.5623512, 41.7434425, 42.8216209, 43.7824974,
44.6124878, 45.2992668, 45.8322601, 46.2031822,
46.406559, 46.4402771, 46.3061028, 46.0101204,
45.5631523, 44.9809837, 44.2845192, 43.4997063,
42.6572647, 41.7921677, 40.9428825, 40.1502991,
39.4564362, 38.902874, 38.5289497, 38.3698311,
38.4544907, 38.803688, 39.4280548, 40.3264656,
41.4847488, 42.8749237, 44.4550667, 46.1699028,
47.9522095, 49.7250671, 51.4048958, 52.9053001,
54.1414795, 55.0350647, 55.5191307, 55.543045,
55.0768166, 54.1146126, 52.6770477, 50.8119621,
48.5934296, 46.1188889, 43.5043335, 40.8778114,
38.3714333, 36.1125069, 34.2143517, 32.7675476,
31.8324318, 31.4335213, 31.5565434, 32.1484718,
33.1207199, 34.3553429, 35.7137947, 37.0474815,
38.2092171, 39.0644684, 39.5014496, 39.4390793,
38.8322487, 37.6739235, 35.9941063, 33.8558884,
31.3490906, 28.5822468, 25.6736469, 22.7423134,
19.8996277, 17.2422371, 14.846715, 12.7662144,
11.0292349, 9.64038086, 8.58285141, 7.82228708,
7.31151199, 6.99567366, 6.8173089, 6.7209177,
6.65673113, 6.58345604, 6.46992779, 6.29568291,
6.05059004, 5.73372078, 5.35168791, 4.91668797,
4.44446611, 3.95238495, 3.45773935, 2.97640157,
2.52184391, 2.10453963, 1.73171222, 1.4073801,
1.132635, 0.906080246, 0.724364817, 0.58274883,
0.475652605, 0.397148907, 0.341374457, 0.302846611,
0.276684344, 0.258738846, 0.245647579, 0.234826341,
0.224417076, 0.213205993, 0.200525284, 0.186148554,
0.170186684, 0.152989283, 0.135054633, 0.116950028,
0.0992445722, 0.0824552476, 0.0670074001, 0.0532102846,
0.0412470363, 0.0311778542, 0.0229541399, 0.0164404195,
0.0114405444, 0.00772457942, 0.0050533074, 0.00319810049,
0.00195492571, 0.00115227827, 0.000653731928,
/* Z=38 -> Sr */
0, 0.0181436762, 0.0199610479, 0.021959763,
0.0241578054, 0.0265749283, 0.0292328242, 0.0321553051,
0.035368517, 0.038901154, 0.0427847095, 0.0470537432,
0.051746171, 0.0569035783, 0.0625715703, 0.0688001737,
0.0756442025, 0.0831637457, 0.0914246589, 0.100499056,
0.110465974, 0.12141189, 0.133431494, 0.146628395,
0.161115929, 0.177018076, 0.194470316, 0.213620707,
0.234630987, 0.257677764, 0.282953739, 0.310669214,
0.341053367, 0.374356061, 0.410849363, 0.450829417,
0.494618386, 0.542566597, 0.595054448, 0.652494967,
0.715336204, 0.784063697, 0.8592031, 0.941323221,
1.03103864, 1.12901282, 1.23596096, 1.35265374,
1.47991979, 1.61864865, 1.76979494, 1.93438041,
2.11349678, 2.30830884, 2.52005696, 2.75005817,
2.99970841, 3.27048302, 3.56393671, 3.88170314,
4.22549343, 4.5970912, 4.9983511, 5.43118811,
5.89757442, 6.39952421, 6.93908358, 7.51831436,
8.13927269, 8.80399132, 9.51444626, 10.2725353,
11.0800352, 11.9385681, 12.8495541, 13.8141623,
14.8332596, 15.9073486, 17.0365067, 18.2203102,
19.4577808, 20.7472858, 22.0864868, 23.4722481,
24.9005661, 26.3665028, 27.8641205, 29.3864288,
30.9253407, 32.4716606, 34.0150719, 35.5441856,
37.046566, 38.5088654, 39.9169273, 41.2560005,
42.5109482, 43.6665573, 44.7078705, 45.620575,
46.391468, 47.0089302, 47.4634666, 47.7482491,
47.8596687, 47.7978935, 47.5673447, 47.1771545,
46.6414642, 45.979641, 45.2162704, 44.3810005,
43.5080948, 42.6357422, 41.8051262, 41.0591469,
40.4409294, 39.9920692, 39.750679, 39.7493362,
40.01297, 40.5568466, 41.3847351, 42.4874191,
43.8416824, 45.4098587, 47.1401787, 48.9678307,
50.8169746, 52.6035614, 54.239006, 55.6345482,
56.7061462, 57.3796616, 57.5959892, 57.3158646,
56.5238876, 55.2314377, 53.4781303, 51.3314819,
48.8846474, 46.2521248, 43.5635414, 40.9557877,
38.5639534, 36.5117035, 34.9017944, 33.8076134,
33.2664871, 33.275547, 33.7906456, 34.7286263,
35.9729004, 37.3819466, 38.800106, 40.0696182,
41.042942, 41.5940895, 41.6280708, 41.0875206,
39.9560814, 38.2582359, 36.0558662, 33.4419479,
30.5320683, 27.4546623, 24.3408566, 21.3147945,
18.48522, 15.9389238, 13.736454, 11.9102602,
10.4652357, 9.38140297, 8.61832047, 8.12067604,
7.82445002, 7.66306543, 7.57295513, 7.49814272,
7.39353895, 7.2268281, 6.9789834, 6.64356279,
6.22503757, 5.73646736, 5.19682932, 4.62830639,
4.05377293, 3.4946723, 2.96939373, 2.49220228,
2.0727129, 1.71585464, 1.4222368, 1.18881059,
1.00971508, 0.877196789, 0.782509506, 0.716719747,
0.671366751, 0.638949931, 0.613238871, 0.589419246,
0.56409812, 0.535202682, 0.501803458, 0.463895261,
0.422161162, 0.377741486, 0.332022369, 0.286454201,
0.242405787, 0.20105648, 0.163326055, 0.129839987,
0.100925893, 0.0766359642, 0.0567885265, 0.0410217904,
0.0288528223, 0.0197351631, 0.0131097864, 0.00844580494,
0.00526900776, 0.00317814341, 0.00185033865, 0.00103800255,
0.000560028711, 0.000290027499, 0.000143877318,
/* Z=39 -> Y */
0, 0.0200563129, 0.0220601913, 0.0242634956,
0.0266859476, 0.0293492004, 0.0322770253, 0.0354955159,
0.0390333086, 0.0429218262, 0.0471955426, 0.0518922769,
0.0570535026, 0.0627247021, 0.0689557493, 0.0758012906,
0.0833212286, 0.0915811956, 0.10065309, 0.110615619,
0.121554993, 0.13356553, 0.146750465, 0.161222726,
0.177105755, 0.19453451, 0.213656485, 0.234632745,
0.257639199, 0.282867759, 0.310527802, 0.340847671,
0.374076128, 0.410484135, 0.450366735, 0.494044781,
0.541867197, 0.594213009, 0.651493669, 0.714155734,
0.782682955, 0.857599497, 0.939472318, 1.02891433,
1.12658715, 1.23320484, 1.34953618, 1.4764086,
1.61471081, 1.76539648, 1.92948723, 2.10807514,
2.3023262, 2.51348281, 2.74286461, 2.99187231,
3.26198721, 3.55477238, 3.87187099, 4.21500731,
4.58598089, 4.98666573, 5.4190011, 5.88498688,
6.38667202, 6.92614269, 7.50550747, 8.12687778,
8.79235077, 9.50397682, 10.2637358, 11.0735054,
11.9350119, 12.849802, 13.8191833, 14.8441753,
15.9254503, 17.0632725, 18.2574253, 19.5071449,
20.8110428, 22.1670265, 23.5722275, 25.0229168,
26.5144386, 28.0411377, 29.5963039, 31.1721191,
32.7596359, 34.3487663, 35.9282875, 37.4859009,
39.0083046, 40.4813347, 41.8901024, 43.2192421,
44.4531708, 45.5764122, 46.5739899, 47.4318504,
48.1373596, 48.6798248, 49.0510559, 49.2459259,
49.2629395, 49.1047745, 48.7787476, 48.2971992,
47.6777611, 46.9434471, 46.1225662, 45.2483711,
44.3585052, 43.4940948, 42.6986275, 42.0164986,
41.4913063, 41.1639252, 41.0704346, 41.2399406,
41.6924591, 42.4369125, 43.4694366, 44.7721062,
46.3122177, 48.0422783, 49.9007988, 51.813942,
53.6981163, 55.4634247, 57.0178833, 58.2723389,
59.1457138, 59.5704193, 59.4975357, 58.9013443,
57.7828827, 56.1720772, 54.1281853, 51.7381973,
49.1131897, 46.3825645, 43.6864471, 41.1665878,
38.95644, 37.1710358, 35.8976212, 35.187851,
35.0523872, 35.4585457, 36.3314323, 37.5586319,
38.9982033, 40.4893951, 41.8651237, 42.9651375,
43.6486282, 43.8051262, 43.3627129, 42.2928085,
40.6112556, 38.3756409, 35.6793175, 32.6427689,
29.4031906, 26.1033344, 22.8805408, 19.8569527,
17.1316013, 14.7749882, 12.8263788, 11.2938967,
10.157176, 9.37213421, 8.87726498, 8.60072613,
8.46750355, 8.40597534, 8.35332108, 8.25942039,
8.0890522, 7.82242727, 7.45425272, 6.99163246,
6.45119429, 5.85585213, 5.23155689, 4.60436583,
3.99802661, 3.43222523, 2.92152834, 2.47499084,
2.09633827, 1.7845943, 1.53500891, 1.34013617,
1.19093335, 1.07777035, 0.991275728, 0.92297554,
0.865714252, 0.813868105, 0.763384223, 0.711682856,
0.657467425, 0.600480437, 0.541240156, 0.480782866,
0.42042914, 0.361584693, 0.305582374, 0.253565818,
0.206414267, 0.164704666, 0.128706619, 0.0984039232,
0.0735362172, 0.0536536872, 0.0381776541, 0.0264606923,
0.0178408138, 0.0116857383, 0.00742503908, 0.0045696306,
0.00271960627, 0.00156256941, 0.000865183189, 0.000460785843,
0.000235589978, 0.000115393501, 5.40289911e-05,
/* Z=40 -> Zr */
0, 0.0221357103, 0.0243416056, 0.0267664306,
0.0294317771, 0.0323613398, 0.0355811268, 0.0391196758,
0.0430082865, 0.0472813137, 0.05197642, 0.0571349151,
0.0628020912, 0.0690275952, 0.0758658424, 0.0833764598,
0.091624774, 0.100682311, 0.11062742, 0.121545874,
0.133531496, 0.146687001, 0.161124706, 0.176967382,
0.194349304, 0.213417113, 0.234330997, 0.257265896,
0.282412648, 0.309979469, 0.340193421, 0.373301893,
0.40957433, 0.449304104, 0.492810369, 0.540440142,
0.592570484, 0.649610698, 0.712005019, 0.780234873,
0.854821861, 0.936330378, 1.02537072, 1.12260175,
1.22873485, 1.34453607, 1.4708302, 1.60850358,
1.75850761, 1.92186201, 2.09965754, 2.29305935,
2.50330949, 2.73172879, 2.97972012, 3.24876785,
3.54044032, 3.85638905, 4.19834709, 4.56812716,
4.96761942, 5.39878368, 5.86364508, 6.36428261,
6.90281868, 7.48140574, 8.10220718, 8.76737881,
9.47904301, 10.2392607, 11.0500011, 11.9131012,
12.830225, 13.8028183, 14.8320532, 15.9187727,
17.0634308, 18.266016, 19.5259914, 20.8422127,
22.2128468, 23.6353016, 25.1061382, 26.6210041,
28.1745472, 29.7603607, 31.3709316, 32.9975929,
34.6305122, 36.2587013, 37.8700256, 39.4513054,
40.9883957, 42.4663582, 43.8696442, 45.1823692,
46.3885994, 47.4727402, 48.4199486, 49.2166176,
49.8508873, 50.3132095, 50.5969276, 50.6988564,
50.6198578, 50.3653412, 49.9457169, 49.376709,
48.679554, 47.88097, 47.0129433, 46.1122398,
45.2196312, 44.3788643, 43.6352806, 43.0341949,
42.6190071, 42.4291229, 42.4977493, 42.8496704,
43.4991264, 44.4479065, 45.6838264, 47.1797409,
48.8931618, 50.7667542, 52.7296219, 54.6995659,
56.5862999, 58.2954674, 59.7334595, 60.8127327,
61.4573936, 61.6086922, 61.230072, 60.3113213,
58.8714447, 56.9598579, 54.6556244, 52.0645065,
49.3138428, 46.5453186, 43.9060478, 41.5384445,
39.5696106, 38.1011505, 37.2002258, 36.8928642,
37.1602058, 37.9383125, 39.1217155, 40.570652,
42.1214294, 43.5990982, 44.831337, 45.6621971,
45.9645157, 45.6497955, 44.6746635, 43.043396,
40.8063622, 38.0546722, 34.9116058, 31.5217896,
28.0391026, 24.6144695, 21.3845844, 18.4625473,
15.9310389, 13.8385553, 12.1987963, 10.9930611,
10.1752167, 9.67856216, 9.42379665, 9.32722664,
9.30837727, 9.29636002, 9.23449898, 9.08298016,
8.81954384, 8.43842697, 7.94793081, 7.36708641,
6.72189283, 6.04158354, 5.35527945, 4.68929434,
4.06522131, 3.49885154, 2.99984527, 2.57205224,
2.21430516, 1.92150831, 1.68585634, 1.49802744,
1.34824383, 1.22712755, 1.12631583, 1.03883827,
0.959281027, 0.883778036, 0.809877396, 0.736328065,
0.662828028, 0.589764833, 0.517971456, 0.44851172,
0.382502854, 0.320977837, 0.264787287, 0.214538515,
0.170567349, 0.132938504, 0.101468757, 0.0757670552,
0.0552853309, 0.039373979, 0.027336264, 0.0184769854,
0.0121419011, 0.00774597656, 0.00479002018, 0.00286664558,
0.00165750389, 0.000924294232, 0.000496173277, 0.000255902996,
0.000126544939, 5.98694314e-05, 2.70378823e-05,
/* Z=41 -> Nb */
0, 0.0243913997, 0.0268155895, 0.0294797029,
0.0324073322, 0.0356243588, 0.039159175, 0.0430429392,
0.0473098159, 0.0519972704, 0.0571463853, 0.062802203,
0.0690140724, 0.0758361071, 0.0833275542, 0.0915533379,
0.100584559, 0.110499062, 0.121382028, 0.133326724,
0.146435127, 0.160818815, 0.176599726, 0.193911195,
0.212898865, 0.233721778, 0.25655365, 0.281583935,
0.309019446, 0.339085549, 0.372027874, 0.408114046,
0.447635293, 0.490908563, 0.538278401, 0.590119302,
0.64683789, 0.708875299, 0.776709974, 0.850860059,
0.931886554, 1.02039599, 1.11704385, 1.22253704,
1.33763826, 1.46316803, 1.60000873, 1.7491082,
1.91148245, 2.08821893, 2.28048015, 2.48950553,
2.7166152, 2.96321106, 3.23077869, 3.52088904,
3.83519721, 4.17544413, 4.54345131, 4.94112158,
5.37043238, 5.83342838, 6.33221626, 6.86895084,
7.44582319, 8.0650444, 8.72882652, 9.4393568,
10.1987753, 11.0091391, 11.8723888, 12.790307,
13.764473, 14.7962103, 15.8865318, 17.0360794,
18.2450523, 19.5131397, 20.839447, 22.2224121,
23.6597271, 25.1482601, 26.6839695, 28.2618313,
29.8757725, 31.5186043, 33.1819839, 34.8563728,
36.5310516, 38.1941109, 39.8325424, 41.4322853,
42.9784088, 44.4552574, 45.8466988, 47.1364288,
48.3082962, 49.3467293, 50.2372017, 50.9667244,
51.5244293, 51.9021339, 52.0949478, 52.1018639,
51.9263153, 51.5766525, 51.0665436, 50.4152336,
49.6476212, 48.7941284, 47.8903313, 46.9763031,
46.0956726, 45.2943726, 44.6190834, 44.1154099,
43.8258438, 43.7875137, 44.0299301, 44.5727234,
45.4235611, 46.576416, 48.0102386, 49.6883087,
51.5583229, 53.5533257, 55.5936127, 57.5896034,
59.4456291, 61.0645866, 62.3531914, 63.2277069,
63.6196747, 63.4814072, 62.7907181, 61.5545006,
59.8107605, 57.628685, 55.1065521, 52.3673553,
49.5521431, 46.8114433, 44.2951355, 42.1415405,
40.4664955, 39.3534164, 38.8452835, 38.9394188,
39.5857964, 40.6892166, 42.1154633, 43.7010078,
45.2655525, 46.6263123, 47.6127663, 48.080452,
47.9225655, 47.078228, 45.5367393, 43.3374748,
40.5655327, 37.343647, 33.8212738, 30.1618347,
26.5294437, 23.0762138, 19.9313087, 17.1925831,
14.9214563, 13.1412373, 11.8388929, 10.9698334,
10.465024, 10.2395754, 10.2018137, 10.2619104,
10.3392296, 10.3678436, 10.2998505, 10.1064987,
9.77732658, 9.31770039, 8.74531746, 8.08617783,
7.37056208, 6.62941313, 5.89140511, 5.18086052,
4.51652861, 3.91117048, 3.3717916, 2.90035939,
2.49480772, 2.15016055, 1.85962808, 1.61557746,
1.41030991, 1.23662591, 1.08818007, 0.959656298,
0.846800327, 0.746353209, 0.655924261, 0.573837101,
0.498970896, 0.430613995, 0.368336737, 0.311887085,
0.261107981, 0.215875104, 0.176051736, 0.141458571,
0.111856401, 0.0869397745, 0.0663399473, 0.0496352874,
0.0363672227, 0.0260592792, 0.0182371754, 0.0124476021,
0.00827398151, 0.00534795178, 0.00335600157, 0.00204130239,
0.00120143581, 0.000683011778, 0.00037435125, 0.000197427435,
9.99829499e-05, 4.85182754e-05, 2.25098047e-05,
/* Z=42 -> Mo */
0, 0.0268441532, 0.0295047909, 0.0324280001,
0.035639517, 0.0391675718, 0.0430431254, 0.0473001339,
0.0519758314, 0.0571110286, 0.0627504662, 0.0689431652,
0.0757428557, 0.0832083747, 0.0914041698, 0.100400843,
0.110275619, 0.121113077, 0.133005753, 0.146054834,
0.16037102, 0.17607531, 0.193299934, 0.212189376,
0.232901394, 0.255608261, 0.280497909, 0.307775438,
0.337664306, 0.370408237, 0.406272501, 0.445546031,
0.488543153, 0.535605669, 0.587104976, 0.643444479,
0.705061853, 0.77243185, 0.84606874, 0.926529348,
1.01441586, 1.11037922, 1.21512163, 1.32940066,
1.45403218, 1.58989358, 1.73792756, 1.89914501,
2.07462907, 2.2655375, 2.47310638, 2.69865227,
2.94357467, 3.20935822, 3.49757385, 3.80987906,
4.14801788, 4.51382017, 4.90919733, 5.33614063,
5.79671288, 6.29304361, 6.82731581, 7.40175724,
8.01862144, 8.68017197, 9.38866043, 10.1462984,
10.9552279, 11.8174896, 12.7349806, 13.7094107,
14.7422523, 15.8346863, 16.9875393, 18.2012234,
19.4756546, 20.8101902, 22.2035427, 23.6536942,
25.1578274, 26.7122307, 28.3122215, 29.9520721,
31.6249542, 33.3228645, 35.0365982, 36.7557411,
38.4686584, 40.1625519, 41.823513, 43.4366646,
44.9863091, 46.4561501, 47.8295593, 49.0899162,
50.2209892, 51.2073784, 52.0350456, 52.6918259,
53.1680489, 53.4571266, 53.5561714, 53.4665756,
53.1945686, 52.7516365, 52.1548805, 51.427166,
50.5971146, 49.6988258, 48.7713547, 47.8578796,
47.0045509, 46.2590675, 45.6689148, 45.2793465,
45.1311989, 45.2585602, 45.6864052, 46.4283867,
47.4848518, 48.8412704, 50.4672318, 52.3161659,
54.3258896, 56.4201126, 58.5109482, 60.5023804,
62.294693, 63.7896385, 64.8961639, 65.5363922,
65.6514435, 65.2067337, 64.1962433, 62.6454048,
60.6120605, 58.1853104, 55.4819679, 52.6406593,
49.8136978, 47.1571579, 44.8197708, 42.9314346,
41.5922966, 40.8634529, 40.7602081, 41.2487259,
42.2466621, 43.6279793, 45.23172, 46.874157,
48.3633041, 49.5144615, 50.1653786, 50.1896172,
49.5067787, 48.0887184, 45.9611626, 43.2006645,
39.927269, 36.2936821, 32.4720459, 28.6395588,
24.9643135, 21.5926228, 18.6388798, 16.1788254,
14.2465954, 12.8356562, 11.9032927, 11.3779516,
11.1685085, 11.1743708, 11.2953072, 11.4400291,
11.5327883, 11.5175428, 11.3596096, 11.0449924,
10.577836, 9.97660065, 9.26957417, 8.49032879,
7.67359781, 6.85192776, 6.05326509, 5.29952955,
4.60608625, 3.98196077, 3.43058991, 2.95089936,
2.53851032, 2.1869216, 1.88855135, 1.63557506,
1.42053366, 1.23672283, 1.07839191, 0.940796435,
0.820149124, 0.713509083, 0.618643999, 0.533887982,
0.458010107, 0.390100867, 0.329478741, 0.275615603,
0.228078485, 0.186485246, 0.150471449, 0.119667351,
0.0936834067, 0.0721039176, 0.0544875115, 0.0403736494,
0.0292933956, 0.0207828488, 0.0143972905, 0.00972423237,
0.00639391271, 0.00408630027, 0.00253417785, 0.00152247713,
0.000884514069, 0.000496023451, 0.000267984811, 0.000139206924,
6.93818947e-05, 3.31067822e-05, 1.50896549e-05,
/* Z=43 -> Tc */
0, 0.0295106377, 0.0324273147, 0.0356309786,
0.0391496755, 0.0430141538, 0.0472581275, 0.0519185588,
0.0570359565, 0.0626547262, 0.0688235164, 0.0755956173,
0.0830294192, 0.0911888406, 0.10014388, 0.109971151,
0.120754488, 0.13258563, 0.145564899, 0.159802005,
0.175416887, 0.192540556, 0.211316213, 0.2319002,
0.254463166, 0.279191345, 0.306287885, 0.335974246,
0.368491828, 0.404103488, 0.443095446, 0.485779136,
0.532493234, 0.583605707, 0.639516354, 0.700658977,
0.767504096, 0.840561509, 0.920383334, 1.00756681,
1.10275745, 1.20665205, 1.32000256, 1.44361889,
1.57837236, 1.72519934, 1.88510525, 2.05916667,
2.24853587, 2.45444322, 2.67820048, 2.92120337,
3.18493319, 3.47095847, 3.78093672, 4.11661386,
4.47982359, 4.87248468, 5.29659796, 5.75424194,
6.24756479, 6.77877522, 7.35013199, 7.9639287,
8.62247753, 9.3280859, 10.0830355, 10.8895483,
11.7497616, 12.6656818, 13.6391459, 14.671772,
15.7649031, 16.9195518, 18.1363354, 19.4154034,
20.7563629, 22.1581993, 23.6191978, 25.1368542,
26.7077999, 28.3277054, 29.9912109, 31.6918564,
33.4220123, 35.1728401, 36.9342651, 38.6949577,
40.4423866, 42.1628456, 43.8415756, 45.4628983,
47.0104179, 48.4672623, 49.8164101, 51.0410385,
52.1249695, 53.0531502, 53.8122063, 54.3910103,
54.7813034, 54.9783134, 54.9813919, 54.7945633,
54.4270477, 53.8936539, 53.2150497, 52.41782,
51.5343208, 50.6022682, 49.6640358, 48.7656441,
47.95541, 47.2823181, 46.7940636, 46.5348778,
46.5432014, 46.849247, 47.4726562, 48.420311,
49.6845016, 51.2416191, 53.0514679, 55.0574455,
57.187603, 59.356739, 61.4695396, 63.424675,
65.1198349, 66.4573746, 67.3504486, 67.729126,
67.5461884, 66.7820969, 65.4486618, 63.5909958,
61.2873077, 58.6463623, 55.8024063, 52.9077072,
50.1229668, 47.6062126, 45.5008659, 43.923996,
42.9557343, 42.6309929, 42.9343758, 43.7990532,
45.1100044, 46.711586, 48.4189796, 50.0326614,
51.3545609, 52.2045021, 52.4352913, 51.9450874,
50.6857491, 48.6664925, 45.9524689, 42.6585007,
38.9386177, 34.9724808, 30.9500198, 27.0557327,
23.4541149, 20.2775459, 17.6176262, 15.5207052,
13.9877377, 12.9783249, 12.418232, 12.209404,
12.2412558, 12.401947, 12.5884552, 12.7145233,
12.7158709, 12.5524969, 12.2082186, 11.6879463,
11.0133543, 10.2176933, 9.34045506, 8.42250156,
7.50204515, 6.61176348, 5.77706861, 5.01546812,
4.3368206, 3.74425268, 3.23547411, 2.80425739,
2.4418931, 2.13847399, 1.88393486, 1.66880786,
1.48471224, 1.32460427, 1.18284678, 1.05514359,
0.938394129, 0.830503702, 0.730181158, 0.636742115,
0.549929857, 0.46975863, 0.396382481, 0.329989672,
0.270721495, 0.218615383, 0.173570439, 0.135333925,
0.103505999, 0.0775592849, 0.0568695553, 0.0407526605,
0.0285033733, 0.0194318648, 0.012894419, 0.00831620116,
0.00520504266, 0.00315654068, 0.00185168535, 0.00104891404,
0.000572720193, 0.000300850486, 0.000151740125, 7.33306879e-05,
3.38809587e-05, 1.49318385e-05, 6.26197652e-06,
/* Z=44 -> Ru */
0, 0.0323932245, 0.0355855227, 0.0390909836,
0.0429401062, 0.0471663214, 0.0518062785, 0.0569001362,
0.0624919087, 0.0686298013, 0.0753666312, 0.0827602297,
0.0908739269, 0.0997770429, 0.109545447, 0.120262168,
0.132018015, 0.144912317, 0.159053653, 0.174560741,
0.191563249, 0.210202873, 0.230634317, 0.253026426,
0.277563483, 0.304446429, 0.333894402, 0.366146207,
0.401461869, 0.440124601, 0.482442468, 0.528750539,
0.579412937, 0.634825289, 0.695416749, 0.761653125,
0.834039032, 0.913120985, 0.99949044, 1.09378672,
1.1967001, 1.30897558, 1.43141603, 1.56488526,
1.71031272, 1.86869526, 2.04110241, 2.2286787,
2.43264675, 2.6543119, 2.89506245, 3.15637445,
3.43981218, 3.74702954, 4.07977104, 4.43987083,
4.82925081, 5.24991894, 5.70396376, 6.19354868,
6.7209034, 7.28831339, 7.89810658, 8.5526371,
9.25426483, 10.0053349, 10.8081474, 11.6649246,
12.5777798, 13.5486717, 14.5793581, 15.6713419,
16.8258171, 18.0436058, 19.3250828, 20.6701088,
22.0779476, 23.5471821, 25.0756416, 26.6602993,
28.2971935, 29.9813519, 31.7067051, 33.4660263,
35.2508698, 37.0515404, 38.8570747, 40.6552391,
42.4326057, 44.1745872, 45.865612, 47.489254,
49.0284882, 50.4659729, 51.7843895, 52.9668617,
53.9974213, 54.8615341, 55.5466843, 56.042984,
56.3438034, 56.4464149, 56.3526039, 56.0692215,
55.6086502, 54.989151, 54.2350273, 53.3765793,
52.4498367, 51.4959564, 50.5603752, 49.6915817,
48.9395752, 48.3540497, 47.9822388, 47.8666077,
48.042408, 48.5351982, 49.3585167, 50.5117912,
51.9787407, 53.7263222, 55.7044868, 57.8467941,
60.0720901, 62.2871857, 64.3906174, 66.2773819,
67.8444901, 68.9970627, 69.6546707, 69.7575607,
69.2721786, 68.1956482, 66.5586624, 64.4263,
61.8965797, 59.0963554, 56.1747322, 53.294075,
50.6191521, 48.3050385, 46.4847374, 45.2575722,
44.6793861, 44.7557335, 45.4388351, 46.6289978,
48.1805725, 49.9122963, 51.6211929, 53.0989227,
54.1490631, 54.603775, 54.3381157, 53.280735,
51.4198074, 48.8036995, 45.5363235, 41.7676888,
37.6805649, 33.4746666, 29.3497791, 25.4895458,
22.0473042, 19.1353474, 16.8184223, 15.1119699,
13.9849873, 13.3670206, 13.1582546, 13.2414417,
13.4942656, 13.8007746, 14.0607624, 14.196331,
14.1553068, 13.9115753, 13.4628096, 12.8262644,
12.0334358, 11.1244125, 10.1425362, 9.12991714,
8.12407207, 7.1557765, 6.24806356, 5.41619921,
4.66836977, 4.00683594, 3.42929935, 2.93028378,
2.50239205, 2.13734078, 1.82674682, 1.56266344,
1.33789825, 1.14616024, 0.982081831, 0.84116596,
0.719690084, 0.614597917, 0.523392439, 0.444040537,
0.374891102, 0.314605147, 0.262096673, 0.216480896,
0.177028775, 0.143126637, 0.114241242, 0.0898911953,
0.0696248636, 0.0530057512, 0.0396049395, 0.0289999172,
0.020778507, 0.014546046, 0.0099339541, 0.00660796277,
0.00427452894, 0.00268455781, 0.00163413538, 0.000962449063,
0.000547465635, 0.000300200365, 0.000158377166, 8.02262657e-05,
3.89367233e-05, 1.80657298e-05, 7.99455302e-06,
/* Z=45 -> Rh */
0, 0.0355234817, 0.0390138514, 0.0428455621,
0.0470517427, 0.0516686998, 0.0567362309, 0.0622979105,
0.0684014931, 0.0750992596, 0.0824484825, 0.0905118212,
0.099357903, 0.1090618, 0.119705647, 0.131379306,
0.144181013, 0.15821816, 0.173608154, 0.190479234,
0.208971485, 0.229237854, 0.251445323, 0.275775969,
0.302428544, 0.331619561, 0.363585114, 0.39858222,
0.436890781, 0.478815347, 0.524687111, 0.574866056,
0.629743218, 0.689742982, 0.755325854, 0.826990843,
0.905278563, 0.990774035, 1.08410978, 1.18596911,
1.29708934, 1.41826534, 1.55035317, 1.69427335,
1.85101438, 2.02163672, 2.20727634, 2.40914726,
2.62854552, 2.86685205, 3.12553549, 3.40615296,
3.71035337, 4.03987741, 4.39655733, 4.78231573,
5.19916439, 5.64919949, 6.13459539, 6.65759897,
7.22051859, 7.82571268, 8.47557259, 9.17250824,
9.91892052, 10.7171803, 11.5695963, 12.4783792,
13.4456043, 14.4731617, 15.5627136, 16.7156296,
17.9329281, 19.21521, 20.5625858, 21.9745922,
23.4501228, 24.9873257, 26.5835266, 28.2351456,
29.9375992, 31.6852303, 33.4712257, 35.2875633,
37.124958, 38.9728317, 40.8193207, 42.6512947,
44.4544182, 46.2132683, 47.9114723, 49.531929,
51.0570564, 52.4691238, 53.7506447, 54.8848228,
55.8560524, 56.6505051, 57.2567177, 57.6662521,
57.8743248, 57.8804741, 57.6891365, 57.3101883,
56.7593422, 56.058445, 55.2355042, 54.3245621,
53.3652382, 52.4019928, 51.4830551, 50.6590271,
49.9811325, 49.4991913, 49.2593384, 49.301548,
49.6571045, 50.346138, 51.3753166, 52.7359657,
54.4026566, 56.3325653, 58.4656258, 60.7257233,
63.0229263, 65.2568283, 67.3209381, 69.1080017,
70.516037, 71.4548187, 71.8523636, 71.6610336,
70.8627548, 69.4727783, 67.5416489, 65.1547852,
62.4295692, 59.509716, 56.5570602, 53.7411613,
51.2272453, 49.1633835, 47.6679535, 46.81847,
46.6430016, 47.1151543, 48.1534424, 49.6254349,
51.3565941, 53.1433487, 54.7692604, 56.0229568,
56.7161293, 56.6998558, 55.877655, 54.2139587,
51.7371597, 48.5369568, 44.7562256, 40.5783119,
36.2109337, 31.8682976, 27.7532063, 24.0407715,
20.8653164, 18.3116341, 16.4112759, 15.1440163,
14.4441147, 14.2103968, 14.3188629, 14.6362629,
15.0330954, 15.3946686, 15.6292496, 15.672761,
15.4900188, 15.0728989, 14.4361467, 13.6117153,
12.6425314, 11.5764751, 10.461175, 9.34000111,
8.24939156, 7.21746683, 6.26376772, 5.39983559,
4.6303606, 3.95461941, 3.36797071, 2.86324811,
2.43193412, 2.06507683, 1.75393641, 1.49039626,
1.26718044, 1.07793009, 0.917188108, 0.780329943,
0.663472056, 0.563376248, 0.4773601, 0.40321669,
0.339145005, 0.283686906, 0.235670149, 0.194155037,
0.15838474, 0.127739415, 0.101695769, 0.0797933489,
0.0616082773, 0.0467356332, 0.0347797982, 0.0253520161,
0.0180734936, 0.012582045, 0.00854022522, 0.0056430758,
0.00362407649, 0.00225840951, 0.00136332528, 0.000795851171,
0.000448451086, 0.00024346383, 0.000127098465, 6.36716577e-05,
3.05439098e-05, 1.39992799e-05, 6.1160772e-06,
/* Z=46 -> Pd */
0, 0.038911555, 0.0427231491, 0.0469063073,
0.0514969751, 0.0565345287, 0.0620621033, 0.0681269318,
0.0747807473, 0.082080178, 0.0900872126, 0.0988696814,
0.108501822, 0.119064808, 0.130647451, 0.143346846,
0.15726909, 0.172530189, 0.189256817, 0.207587376,
0.227672905, 0.249678284, 0.273783416, 0.300184488,
0.329095334, 0.360749006, 0.395399392, 0.433322787,
0.474819928, 0.520217836, 0.569871962, 0.624168396,
0.683526397, 0.748400629, 0.819284081, 0.896710873,
0.981258988, 1.07355344, 1.1742698, 1.28413701,
1.40394127, 1.53452945, 1.67681229, 1.83176887,
2.00044942, 2.18397951, 2.3835628, 2.6004858,
2.83611894, 3.09192109, 3.36944151, 3.67032075,
3.99629307, 4.34918642, 4.73092079, 5.14350843,
5.58904886, 6.06972504, 6.58779573, 7.14558887,
7.74548674, 8.38991547, 9.08132553, 9.82217312,
10.6148911, 11.4618683, 12.3654079, 13.3276939,
14.3507481, 15.4363766, 16.5861225, 17.8012009,
19.0824261, 20.4301586, 21.8442097, 23.3237686,
24.8673153, 26.4725342, 28.1362228, 29.8542004,
31.6212368, 33.430954, 35.2757683, 37.146843,
39.0340195, 40.9258385, 42.8095284, 44.6710625,
46.4952316, 48.2657928, 49.9656448, 51.5770569,
53.0819893, 54.4624367, 55.7008667, 56.7807045,
57.6868935, 58.4064827, 58.9292755, 59.2484779,
59.3613815, 59.2699814, 58.9815674, 58.509201,
57.8720703, 57.0956726, 56.2117577, 55.2580414,
54.2775993, 53.3179512, 52.4297867, 51.6653786,
51.0766296, 50.7128716, 50.6184196, 50.8300133,
51.3742142, 52.2649689, 53.5014267, 55.0662498,
56.924511, 59.0234451, 61.2931175, 63.6481781,
65.9907074, 68.2142258, 70.2086487, 71.8662186,
73.0879364, 73.7902908, 73.9117661, 73.4187546,
72.310173, 70.6204758, 68.4203949, 65.8152695,
62.9405098, 59.9544144, 57.0284271, 54.335392,
52.0365868, 50.2684631, 49.1302948, 48.6739235,
48.8967361, 49.7388687, 51.085228, 52.7725334,
54.6010284, 56.3500557, 57.7961731, 58.7321396,
58.9850159, 58.4315453, 57.0092735, 54.7223129,
51.6410904, 47.8961372, 43.6665154, 39.1640244,
34.6147499, 30.2397461, 26.2367573, 22.7646999,
19.9323502, 17.7922916, 16.3404198, 15.5209093,
15.235734, 15.3575077, 15.7439747, 16.2524395,
16.7525692, 17.1363297, 17.3243046, 17.2682152,
16.9499168, 16.3776016, 15.5800924, 14.6002502,
13.4883652, 12.2962904, 11.0727329, 9.85997772,
8.69199753, 7.59381628, 6.58184862, 5.66491699,
4.84564734, 4.12199545, 3.48870969, 2.93859935,
2.46355581, 2.05529737, 1.70586574, 1.40791595,
1.15484226, 0.940799356, 0.760653436, 0.609903514,
0.484592825, 0.38122642, 0.296702176, 0.228257239,
0.173428267, 0.130023301, 0.0961013734, 0.0699568987,
0.0501061864, 0.0352743752, 0.0243814848, 0.0165270865,
0.0109735159, 0.0071278899, 0.0045234249, 0.00280067488,
0.00168933335, 0.000991205452, 0.000564825314, 0.000312061398,
0.00016687077, 8.62060115e-05, 4.29413885e-05, 2.05835622e-05,
9.4744637e-06, 4.17847286e-06, 1.76157675e-06, 7.08198684e-07,
2.70814212e-07, 9.82423387e-08, 3.37153949e-08,
/* Z=47 -> Ag */
0, 0.0425906554, 0.0467495658, 0.0513125695,
0.0563186295, 0.0618104078, 0.0678346083, 0.0744423792,
0.0816897079, 0.0896378532, 0.0983538553, 0.10791105,
0.118389659, 0.129877388, 0.142470136, 0.156272694,
0.171399593, 0.187975898, 0.206138223, 0.226035669,
0.247831002, 0.271701723, 0.29784146, 0.326461256,
0.357791096, 0.39208141, 0.429604888, 0.470658273,
0.515564203, 0.564673424, 0.618367016, 0.677058578,
0.74119699, 0.811268806, 0.88780117, 0.971364856,
1.06257701, 1.16210485, 1.27066875, 1.38904524,
1.51807153, 1.65864837, 1.81174409, 1.97839797,
2.15972447, 2.35691619, 2.57124758, 2.80407858,
3.05685687, 3.33112121, 3.62850285, 3.95072794,
4.29961729, 4.67708635, 5.085145, 5.52589369,
6.00152016, 6.51429272, 7.06655359, 7.66070652,
8.29920673, 8.98454285, 9.71921635, 10.505723,
11.3465223, 12.2440033, 13.2004547, 14.2180223,
15.2986517, 16.4440517, 17.6556206, 18.9343967,
20.2809696, 21.6954269, 23.1772499, 24.7252464,
26.3374577, 28.0110607, 29.7422905, 31.5263386,
33.3572807, 35.2279968, 37.1300964, 39.053894,
40.9883575, 42.9211197, 44.8384972, 46.7255783,
48.5662994, 50.3436356, 52.0397987, 53.6365204,
55.1153755, 56.4581985, 57.6475487, 58.6672325,
59.502903, 60.1426888, 60.5778542, 60.8034821,
60.8191376, 60.6294975, 60.2448921, 59.6817474,
58.9628525, 58.1174355, 57.181015, 56.1949196,
55.2055397, 54.2632103, 53.4207573, 52.7316628,
52.2479858, 52.0179253, 52.0832901, 52.4768181,
53.2195969, 54.3186455, 55.7649231, 57.5318642,
59.5746574, 61.8304253, 64.2194519, 66.6475296,
69.0094681, 71.1937103, 73.0879593, 74.5855484,
75.5922546, 76.0332031, 75.8592834, 75.0526428,
73.6306915, 71.6480408, 69.1960907, 66.3997192,
63.411274, 60.4016762, 57.5492287, 55.0266685,
52.9874496, 51.5523529, 50.7976418, 50.7460785,
51.3618393, 52.5502548, 54.1627121, 56.0067329,
57.8605461, 59.491024, 60.6734161, 61.2110252,
60.9528847, 59.8076477, 57.7522736, 54.8345451,
51.1691513, 46.9276505, 42.3233147, 37.5923004,
32.9730949, 28.6861286, 24.9156914, 21.7958355,
19.4015789, 17.7462082, 16.7846375, 16.4222603,
16.5279579, 16.9496346, 17.530302, 18.1229286,
18.6024647, 18.8740768, 18.8771267, 18.5850906,
18.0020733, 17.1568851, 16.0958118, 14.8751221,
13.5541773, 12.1897821, 10.8320684, 9.52198696,
8.29025459, 7.15750694, 6.13529062, 5.22757673,
4.43248463, 3.74398804, 3.15343571, 2.65080309,
2.22564268, 1.8677454, 1.56755853, 1.31640971,
1.10659516, 0.931379676, 0.784947336, 0.662328541,
0.559320867, 0.472410411, 0.398697615, 0.335825741,
0.281911105, 0.235474363, 0.195371807, 0.160728425,
0.130874246, 0.105286352, 0.0835390687, 0.0652638376,
0.050119888, 0.0377756916, 0.0279001966, 0.0201620497,
0.0142344711, 0.00980335381, 0.00657624472, 0.00429026829,
0.00271776784, 0.00166902004, 0.000991991372, 0.000569640368,
0.000315470272, 0.00016817663, 8.61329681e-05, 4.22938392e-05,
1.98679409e-05, 8.90871434e-06, 3.80393953e-06,
/* Z=48 -> Cd */
0, 0.0465783365, 0.0511120185, 0.0560847335,
0.061538659, 0.0675199553, 0.0740791708, 0.0812716037,
0.089157775, 0.0978038907, 0.107282378, 0.117672421,
0.129060626, 0.1415416, 0.15521881, 0.170205235,
0.186624303, 0.204610735, 0.22431168, 0.245887607,
0.269513607, 0.295380652, 0.323696792, 0.354688823,
0.388603687, 0.425710291, 0.466301113, 0.510694325,
0.559235752, 0.612301111, 0.670298338, 0.733669937,
0.802895844, 0.878495991, 0.961033404, 1.05111694,
1.14940524, 1.25660884, 1.37349498, 1.50089025,
1.6396842, 1.79083395, 1.95536721, 2.13438582,
2.32907009, 2.54068208, 2.77056885, 3.02016616,
3.29100013, 3.58469129, 3.90295482, 4.24760246,
4.620543, 5.0237813, 5.45941544, 5.92963409,
6.43671179, 6.98300171, 7.57092476, 8.20295906,
8.88162708, 9.60947227, 10.3890448, 11.222868,
12.1134138, 13.0630693, 14.07409, 15.1485624,
16.2883472, 17.4950275, 18.7698441, 20.1136246,
21.5267143, 23.0088921, 24.5592861, 26.1762886,
27.8574657, 29.5994568, 31.3978977, 33.2473145,
35.1410675, 37.0712471, 39.0286484, 41.0027046,
42.9814987, 44.9517441, 46.8988647, 48.8070641,
50.6594658, 52.4383011, 54.1251678, 55.7013245,
57.1480827, 58.4472351, 59.5815697, 60.5354424,
61.2954063, 61.8508492, 62.1947174, 62.3241692,
62.2412643, 61.9535484, 61.474575, 60.8242683,
60.0291214, 59.122139, 58.1425629, 57.1352272,
56.1496353, 55.2386398, 54.4567757, 53.8582573,
53.4946823, 53.4124603, 53.6501541, 54.2357597,
55.1841278, 56.4946785, 58.1495781, 60.1126137,
62.3288422, 64.725296, 67.2127991, 69.6889114,
72.0421219, 74.1571121, 75.9209137, 77.2297668,
77.9961853, 78.1559067, 77.6740799, 76.5502396,
74.821434, 72.5630646, 69.8869858, 66.9367142,
63.8796692, 60.8967094, 58.1695442, 55.8667984,
54.1298103, 53.0594292, 52.7051048, 53.0575256,
54.045887, 55.5404129, 57.360363, 59.2871704,
61.0817146, 62.5043716, 63.3359375, 63.3973885,
62.5665627, 60.7899361, 58.0882835, 54.5554924,
50.3506546, 45.6840744, 40.7985954, 35.9480743,
31.3751621, 27.2906094, 23.8561268, 21.1725845,
19.2745514, 18.1315994, 17.6559601, 17.7153683,
18.1493855, 18.7871113, 19.4641724, 20.0371361,
20.3939571, 20.4597931, 20.1981525, 19.6079273,
18.7173901, 17.5763092, 16.2474613, 14.7985926,
13.2955761, 11.7973061, 10.3523884, 8.99758053,
7.75768948, 6.64654922, 5.66870117, 4.82140303,
4.09668541, 3.48323488, 2.96799064, 2.53738952,
2.178267, 1.87845182, 1.6271069, 1.41488171,
1.23393011, 1.07784128, 0.941518128, 0.821025491,
0.713426292, 0.616612792, 0.529140592, 0.45007056,
0.37882176, 0.315041035, 0.258491933, 0.208966076,
0.166218713, 0.12992847, 0.0996793956, 0.0749626681,
0.0551930778, 0.0397356115, 0.0279367846, 0.0191560257,
0.0127932243, 0.00830983091, 0.00524215167, 0.00320680556,
0.00189929362, 0.00108729268, 0.000600591826, 0.000319519721,
0.000163406017, 8.01707938e-05, 3.76550342e-05, 1.68936513e-05,
7.22276945e-06, 2.93561288e-06, 1.13133365e-06,
/* Z=49 -> In */
0, 0.0508931205, 0.0558304451, 0.0612442531,
0.0671801493, 0.0736880228, 0.0808224976, 0.088643305,
0.097215794, 0.106611431, 0.116908342, 0.128191948,
0.140555605, 0.154101297, 0.16894047, 0.185194775,
0.202997074, 0.222492352, 0.243838802, 0.267208964,
0.292791009, 0.320789963, 0.351429254, 0.384952217,
0.421623677, 0.461731881, 0.5055902, 0.553539455,
0.605949581, 0.663222611, 0.725794554, 0.794138253,
0.868766069, 0.950232923, 1.03913915, 1.13613355,
1.24191737, 1.35724711, 1.48293805, 1.61986864,
1.76898324, 1.93129694, 2.10789847, 2.29995441,
2.50871301, 2.73550749, 2.98175955, 3.24898171,
3.53878069, 3.85285974, 4.19301939, 4.5611577,
4.95927238, 5.3894558, 5.85389566, 6.35486746,
6.89473057, 7.47591972, 8.10093212, 8.77231598,
9.49265385, 10.2645407, 11.0905619, 11.9732628,
12.9151192, 13.9184952, 14.9856033, 16.1184559,
17.3188038, 18.5880909, 19.9273701, 21.3372402,
22.8177681, 24.3684006, 25.9878788, 27.6741505,
29.4242687, 31.2343102, 33.0992699, 35.0129929,
36.9680672, 38.9557991, 40.9661255, 42.9876022,
45.0074005, 47.0113335, 48.9839325, 50.9085503,
52.7675323, 54.5424347, 56.2143097, 57.7640457,
59.1727982, 60.4224548, 61.4961929, 62.379097,
63.0587921, 63.5261497, 63.7759895, 63.8077621,
63.6262093, 63.2419395, 62.6718788, 61.9395599,
61.0752335, 60.1156845, 59.1037865, 58.0877113,
57.1198044, 56.2550583, 55.549263, 55.0567856,
54.8281097, 54.9071426, 55.3284416, 56.1144981,
57.2732048, 58.7957306, 60.6549568, 62.8046722,
65.1797333, 67.6972809, 70.2591553, 72.7555542,
75.0698242, 77.0843735, 78.6873398, 79.7797928,
80.2830429, 80.1454086, 79.3480835, 77.9094009,
75.8869247, 73.3770218, 70.5114136, 67.4507065,
64.3749771, 61.4717865, 58.9223328, 56.8867722,
55.4898834, 54.8084183, 54.8615227, 55.6054535,
56.9334717, 58.6814461, 60.6390419, 62.5658417,
64.2111282, 65.3356171, 65.7329712, 65.2491226,
63.7972145, 61.3666458, 58.0251579, 53.9135818,
49.2337036, 44.2303505, 39.1694832, 34.3144646,
29.9028778, 26.1263428, 23.1152878, 20.9302788,
19.5606384, 18.9302464, 18.9096394, 19.3326817,
20.0156631, 20.7764301, 21.4513741, 21.9084892,
22.0554848, 21.8426323, 21.2607861, 20.3355656,
19.1190128, 17.6801434, 16.0956116, 14.4415693,
12.7872448, 11.1906433, 9.69622231, 8.33437347,
7.12227869, 6.06569481, 5.16125917, 4.39894533,
3.76439285, 3.2409389, 2.81125712, 2.45858097,
2.16753888, 1.92465425, 1.71857929, 1.54012728,
1.38216376, 1.23940492, 1.10816097, 0.986054242,
0.871733069, 0.76459831, 0.664555252, 0.571799517,
0.486642241, 0.409377515, 0.340191364, 0.279108435,
0.225971714, 0.180447757, 0.14205049, 0.11017625,
0.0841434449, 0.0632320791, 0.046719145, 0.0339078307,
0.0241495185, 0.0168586355, 0.0115209911, 0.00769672729,
0.00501899654, 0.00318948762, 0.00197184901, 0.00118383672,
0.000688897911, 0.000387801381, 0.000210750528, 0.00011033527,
5.55258812e-05, 2.6799542e-05, 1.23762711e-05,
/* Z=50 -> Sn */
0, 0.0555638708, 0.0609360971, 0.0668249503,
0.0732796937, 0.0803542063, 0.0881074294, 0.0966038257,
0.10591387, 0.116114631, 0.127290294, 0.139532909,
0.152943, 0.16763036, 0.183714896, 0.201327473,
0.220610932, 0.241721079, 0.264827877, 0.290116578,
0.317789108, 0.348065466, 0.381185174, 0.417409062,
0.457020789, 0.500328958, 0.547668934, 0.59940511,
0.655933142, 0.717682302, 0.785118222, 0.858745396,
0.939110279, 1.02680409, 1.12246621, 1.22678733,
1.34051275, 1.46444666, 1.59945464, 1.74646866,
1.90648985, 2.08059311, 2.2699306, 2.47573543,
2.6993258, 2.94210744, 3.20557833, 3.49133039,
3.80105209, 4.1365304, 4.49965191, 4.89240265,
5.31686783, 5.77522945, 6.26976204, 6.80282784,
7.37686872, 7.99439764, 8.65798473, 9.37024403,
10.133812, 10.9513273, 11.8254013, 12.7585917,
13.7533646, 14.8120508, 15.936801, 17.1295357,
18.3918839, 19.7251148, 21.1300793, 22.6071186,
24.1559925, 25.7757893, 27.4648285, 29.2205811,
31.0395603, 32.9172363, 34.8479462, 36.8247986,
38.8396187, 40.8828697, 42.9436264, 45.0095482,
47.0669022, 49.1006012, 51.0943031, 53.0305405,
54.8909264, 56.6564102, 58.3075752, 59.8250504,
61.189949, 62.3844032, 63.3921471, 64.1991501,
64.7943192, 65.1702042, 65.3237076, 65.2567673,
64.9770126, 64.4982681, 63.8409729, 63.0323677,
62.1064796, 61.1038399, 60.0708427, 59.0587883,
58.1225586, 57.3188858, 56.7043037, 56.3327446,
56.2529221, 56.5055008, 57.1202965, 58.1135597,
59.4855423, 61.2185783, 63.2758255, 65.6008759,
68.1183853, 70.7359238, 73.3470001, 75.8353958,
78.0806046, 79.9643402, 81.3776398, 82.2284088,
82.4486771, 82.0012283, 80.884903, 79.1379852,
76.8391495, 74.1055298, 71.0877228, 67.9615631,
64.917038, 62.1449013, 59.8217888, 58.0950661,
57.0686722, 56.7914658, 57.2493629, 58.3624992,
59.9880753, 61.9291916, 63.9492683, 65.791008,
67.1983795, 67.9394913, 67.8282547, 66.7424698,
64.6364212, 61.5466003, 57.5896873, 52.9529381,
47.8777237, 42.6378326, 37.5147057, 32.7720947,
28.6327763, 25.2597828, 22.7440052, 21.0995693,
20.2671261, 20.1245461, 20.5034351, 21.2092667,
22.0425739, 22.8186169, 23.3833961, 23.6244888,
23.4760876, 22.9184437, 21.9725723, 20.6916485,
19.1505985, 17.4354305, 15.6334934, 13.8255987,
12.0803881, 10.451067, 8.97429276, 7.67081165,
6.54735184, 5.59928036, 4.81355906, 4.17166328,
3.65218902, 3.23301911, 2.89297438, 2.61295843,
2.3766489, 2.1708045, 1.98527586, 1.81279635,
1.64862955, 1.49013412, 1.33629715, 1.18727505,
1.04397225, 0.907678723, 0.779776275, 0.661519349,
0.553888142, 0.457506418, 0.372614473, 0.299084038,
0.236463308, 0.184039906, 0.140911639, 0.106057331,
0.0784016997, 0.056870956, 0.0404372253, 0.0281513613,
0.0191647373, 0.0127411308, 0.00826019887, 0.00521420268,
0.0031996374, 0.0019054357, 0.00109925715, 0.000613214972,
0.000330139301, 0.000171190884, 8.53207748e-05, 4.078247e-05,
1.86530888e-05, 8.14437863e-06, 3.3862716e-06,
/* Z=51 -> Sb */
0, 0.0606186949, 0.0664593354, 0.0728596225,
0.0798727125, 0.0875567272, 0.0959752202, 0.105197683,
0.115300037, 0.126365304, 0.138484135, 0.151755556,
0.16628772, 0.182198718, 0.199617416, 0.218684435,
0.239553168, 0.262390912, 0.28737995, 0.314719081,
0.344624728, 0.377332628, 0.413099349, 0.452204049,
0.494950265, 0.541667998, 0.592715681, 0.648482621,
0.709391177, 0.77589941, 0.848503828, 0.927742124,
1.01419616, 1.10849535, 1.21131957, 1.32340312,
1.44553745, 1.57857573, 1.72343624, 1.88110602,
2.05264497, 2.2391901, 2.44195867, 2.66225195,
2.90146017, 3.16106391, 3.4426384, 3.74785662,
4.07848978, 4.43641043, 4.82359219, 5.24210835,
5.6941328, 6.18193579, 6.70787811, 7.27440643,
7.88404322, 8.53937721, 9.24304581, 9.99772263,
10.8060913, 11.6708269, 12.5945597, 13.5798473,
14.6291304, 15.7446928, 16.9286098, 18.1826897,
19.5084133, 20.9068642, 22.3786564, 23.9238529,
25.5418758, 27.2314186, 28.9903603, 30.8156528,
32.7032394, 34.647953, 36.6434364, 38.682045,
40.7547989, 42.8513107, 44.9597702, 47.0669403,
49.1581726, 51.2174911, 53.2277107, 55.1705894,
57.0270576, 58.7775192, 60.402195, 61.8815536,
63.1968079, 64.3304749, 65.2670135, 65.9934692,
66.5002213, 66.7817001, 66.8370895, 66.6710205,
66.2941742, 65.7237625, 64.9838333, 64.1054001,
63.1262932, 62.0906982, 61.0483818, 60.0535202,
59.1631851, 58.4354134, 57.9269447, 57.6906548,
57.772789, 58.2100601, 59.0268059, 60.2323112,
61.8185654, 63.7585678, 66.0054092, 68.492363,
71.1340485, 73.8289185, 76.4629288, 78.9145355,
81.0608139, 82.7844391, 83.9812317, 84.5678406,
84.4889603, 83.7235794, 82.2895584, 80.2460175,
77.6929398, 74.7677155, 71.6383743, 68.4936676,
65.5304184, 62.9388084, 60.8867264, 59.5044365,
58.8710175, 59.0040588, 59.8539581, 61.3038254,
63.1755562, 65.2420197, 67.2445984, 68.9148331,
69.9981155, 70.2772903, 69.5936661, 67.8633118,
65.0866013, 61.3500519, 56.819828, 51.7275124,
46.3493729, 40.9811745, 35.9110985, 31.3935642,
27.6267414, 24.7361794, 22.7662277, 21.6801605,
21.3686733, 21.6655769, 22.3684654, 23.2617092,
24.1388454, 24.8217983, 25.1749306, 25.1128292,
24.6017227, 23.6551876, 22.3255901, 20.6928654,
18.8524303, 16.9037437, 14.9405832, 13.0438557,
11.2770615, 9.68434906, 8.29079914, 7.10435343,
6.11884212, 5.31755209, 4.67685556, 4.16956282,
3.76775956, 3.44501209, 3.17790914, 2.9469831,
2.73709369, 2.53738117, 2.34090209, 2.14405632,
1.94590414, 1.74745095, 1.5509665, 1.35937977,
1.1757791, 1.00303054, 0.84351486, 0.698974133,
0.570450664, 0.458301902, 0.362268656, 0.281578183,
0.215065077, 0.161295876, 0.118686892, 0.0856079236,
0.06046772, 0.0417790934, 0.0282038543, 0.0185789578,
0.0119263874, 0.00744980341, 0.00452133035, 0.00266178953,
0.00151750981, 0.000836311607, 0.000444707752, 0.000227722267,
0.000112066482, 5.28883793e-05, 2.38831653e-05, 1.02957802e-05,
4.22673111e-06, 1.64824439e-06, 6.08909602e-07,
/* Z=52 -> Te */
0, 0.0660882443, 0.0724332556, 0.0793839917,
0.0869977549, 0.0953371897, 0.10447076, 0.114473291,
0.125426516, 0.137419745, 0.150550485, 0.164925218,
0.180660173, 0.197882205, 0.216729671, 0.237353519,
0.259918332, 0.284603447, 0.311604381, 0.341134012,
0.373424113, 0.40872705, 0.447317302, 0.48949334,
0.535579622, 0.585928619, 0.640922964, 0.700978041,
0.766544342, 0.83810991, 0.916203678, 1.00139785,
1.09431159, 1.19561374, 1.3060267, 1.42632973,
1.55736244, 1.70002913, 1.85530221, 2.02422595,
2.20792127, 2.40758824, 2.62451172, 2.86006355,
3.11570692, 3.39299917, 3.69359517, 4.01924944,
4.37181759, 4.75325775, 5.16563129, 5.61110067,
6.09192657, 6.61046696, 7.169168, 7.77055788,
8.41723824, 9.111866, 9.85714436, 10.6557999,
11.5105572, 12.4241161, 13.3991175, 14.4381027,
15.5434809, 16.7174702, 17.9620495, 19.2788982,
20.6693287, 22.1342125, 23.6739044, 25.2881565,
26.9760284, 28.7357922, 30.5648422, 32.4595909,
34.4153786, 36.4263649, 38.4854698, 40.5842667,
42.7129478, 44.8602638, 47.0135002, 49.1585121,
51.2797585, 53.3603897, 55.3823967, 57.3268089,
59.1739464, 60.9037514, 62.49617, 63.9316368,
65.191597, 66.2591171, 67.1195374, 67.7611923,
68.1761093, 68.3608017, 68.3169479, 68.0520401,
67.5799942, 66.9215164, 66.1043777, 65.1634064,
64.1401749, 63.0824394, 62.0431328, 61.0790176,
60.2489738, 59.6118507, 59.2240219, 59.1366653,
59.3928604, 60.0246315, 61.0501022, 62.4709511,
64.2703171, 66.4114151, 68.837059, 71.470192,
74.2157135, 76.9635239, 79.5929565, 81.9784164,
83.9960709, 85.5313187, 86.4866714, 86.7894821,
86.398941, 85.311821, 83.5661697, 81.2425308,
78.4620667, 75.3814545, 72.1843262, 69.0696793,
66.2377167, 63.8740616, 62.1335678, 61.1251678,
60.8993149, 61.4394341, 62.6587372, 64.4032288,
66.4611435, 68.5785217, 70.4797745, 71.8916321,
72.5681152, 72.3141937, 71.0055466, 68.6022873,
65.1548843, 60.8015747, 55.7570648, 50.2935982,
44.7161331, 39.3341026, 34.4327087, 30.2468319,
26.9403534, 24.5932121, 23.1975479, 22.6632214,
22.8318367, 23.4972992, 24.4301453, 25.4025459,
26.2108822, 26.6934204, 26.7414398, 26.3032303,
25.3814259, 24.0248775, 22.3169022, 20.3618336,
18.2716808, 16.1544132, 14.1047802, 12.1982059,
10.4877462, 9.00378132, 7.75590181, 6.73630905,
5.92407131, 5.28961992, 4.79901361, 4.41761923,
4.11300516, 3.85697699, 3.62676859, 3.40549421,
3.18199492, 2.95024514, 2.70847321, 2.45814705,
2.20294118, 1.9477793, 1.69801366, 1.45877814,
1.23452377, 1.02872968, 0.843768835, 0.680899918,
0.540353894, 0.421483338, 0.322947204, 0.242907107,
0.17921716, 0.129594266, 0.0917608291, 0.0635556728,
0.0430129096, 0.0284102559, 0.0182906762, 0.0114623057,
0.00698192045, 0.0041273823, 0.0023641251, 0.00130986481,
0.000700757781, 0.000361313549, 0.0001791947, 8.53100501e-05,
3.89024608e-05, 1.69542964e-05, 7.04509512e-06, 2.78438301e-06,
1.04396725e-06, 3.70330866e-07, 1.23940467e-07,
/* Z=53 -> I */
0, 0.0720055401, 0.0788934827, 0.0864365026,
0.0946962982, 0.10374032, 0.11364226, 0.124482617,
0.136349291, 0.14933826, 0.163554341, 0.179111883,
0.196135685, 0.214761853, 0.235138848, 0.257428497,
0.281807214, 0.30846712, 0.337617517, 0.369486332,
0.404321462, 0.442392737, 0.4839935, 0.529442608,
0.579086304, 0.633300841, 0.692494273, 0.757109165,
0.827625394, 0.904562652, 0.988483548, 1.07999635,
1.17975914, 1.28848195, 1.40693104, 1.5359329,
1.67637682, 1.82922006, 1.99549115, 2.17629361,
2.37281084, 2.58630872, 2.81814098, 3.0697515,
3.34267879, 3.63855863, 3.95912623, 4.3062191,
4.68177891, 5.08785057, 5.52658224, 6.00022507,
6.51112747, 7.06173325, 7.65457201, 8.29225159,
8.97744656, 9.712883, 10.5013208, 11.3455315,
12.2482748, 13.212265, 14.2401419, 15.3344221,
16.4974613, 17.7313995, 19.0381031, 20.4190998,
21.8755093, 23.4079704, 25.0165482, 26.7006607,
28.4589729, 30.2893047, 32.1885338, 34.152504,
36.1759109, 38.2522278, 40.3736076, 42.5308304,
44.7132301, 46.9086723, 49.10355, 51.2828064,
53.4300041, 55.5274582, 57.5563736, 59.4971046,
61.3294182, 63.0328903, 64.5873032, 65.9731827,
67.1723557, 68.1685944, 68.9483109, 69.5012894,
69.8214417, 69.9075317, 69.7639236, 69.4011688,
68.8365479, 68.0943909, 67.2062531, 66.2107697,
65.1532135, 64.0847397, 63.0612259, 62.1416931,
61.3863907, 60.8544617, 60.6013222, 60.6757736,
61.1170197, 61.9516716, 63.1909561, 64.8283005,
66.8374939, 69.1716232, 71.7630768, 74.5246353,
77.3518524, 80.1268616, 82.7234421, 85.0132828,
86.873291, 88.1934357, 88.8848343, 88.8874359,
88.1766739, 86.7684937, 84.7220535, 82.1395569,
79.1628647, 75.9665604, 72.7476501, 69.7123489,
67.0605011, 64.9690094, 63.5753975, 62.9632492,
63.1509781, 64.0855179, 65.6419983, 67.630043,
69.8067703, 71.8956757, 73.6100082, 74.6785507,
74.8713989, 74.0229721, 72.0497894, 68.9609528,
64.8598785, 59.9367828, 54.4524002, 48.7144165,
43.0488358, 37.7693329, 33.147789, 29.3892918,
26.6143475, 24.8504219, 24.0335674, 24.0198631,
24.6049843, 25.5492649, 26.6049404, 27.5421143,
28.1703815, 28.3538532, 28.0184765, 27.1516209,
25.7950497, 24.0329895, 21.9774799, 19.7531414,
17.4831219, 15.2776909, 13.2261333, 11.392231,
9.81311989, 8.50094128, 7.44656944, 6.62461281,
5.9989109, 5.52788639, 5.16925669, 4.88378,
4.63789606, 4.40525198, 4.16722345, 3.91261888,
3.63678336, 3.34033442, 3.0277307, 2.70585585,
2.38273501, 2.06647158, 1.76444387, 1.48276627,
1.22599244, 0.997026861, 0.797194123, 0.626423657,
0.483500898, 0.366350144, 0.272316933, 0.198428646,
0.141618535, 0.0989050344, 0.0675239488, 0.0450151786,
0.0292688124, 0.0185371339, 0.0114203822, 0.00683426904,
0.00396655919, 0.00222918531, 0.00121101737, 0.000634824915,
0.000320509833, 0.000155547139, 7.24139027e-05, 3.22689266e-05,
1.37330881e-05, 5.5685814e-06, 2.1460321e-06, 7.83998132e-07,
2.70769249e-07, 8.81563054e-08, 2.69764371e-08,
/* Z=54 -> Xe */
0, 0.0784064084, 0.0858786702, 0.0940588042,
0.10301324, 0.112814508, 0.123541869, 0.135281831,
0.148128852, 0.162186012, 0.177565813, 0.194390997,
0.212795407, 0.232924968, 0.254938811, 0.279010266,
0.30532819, 0.334098279, 0.365544409, 0.399910212,
0.437460691, 0.478484035, 0.523293436, 0.572229028,
0.625660241, 0.683987975, 0.747646928, 0.817108393,
0.892882884, 0.975522995, 1.06562662, 1.16383994,
1.27086079, 1.38744271, 1.51439774, 1.65260065,
1.80299306, 1.96658635, 2.14446759, 2.33780098,
2.5478344, 2.77590179, 3.02342701, 3.29192853,
3.58302116, 3.89842033, 4.2399435, 4.60951328,
5.00915575, 5.44100428, 5.90729475, 6.41036558,
6.95265293, 7.53668404, 8.16506958, 8.84049511,
9.56570435, 10.3434849, 11.1766491, 12.0680075,
13.0203419, 14.036377, 15.1187344, 16.2698936,
17.4921436, 18.7875252, 20.1577759, 21.604248,
23.1278496, 24.7289543, 26.4073219, 28.1619968,
29.9912224, 31.8923378, 33.8616753, 35.8944702,
37.9847527, 40.1252632, 42.3073883, 44.5210686,
46.7547684, 48.9954681, 51.2286415, 53.4383392,
55.6072578, 57.716877, 59.7476807, 61.6793976,
63.4913368, 65.1627884, 66.6735001, 68.0042038,
69.1372757, 70.0573502, 70.7521057, 71.2129669,
71.4359055, 71.4221649, 71.1789551, 70.7200394,
70.0662155, 69.2455292, 68.2933502, 67.2520981,
66.1706467, 65.1033783, 64.1088104, 63.2478714,
62.5817108, 62.16922, 62.0642128, 62.3124428,
62.9485207, 63.9929352, 65.4493561, 67.3023758,
69.5159836, 72.0329208, 74.7751236, 77.6454239,
80.5306549, 83.3060303, 85.8409653, 88.0059509,
89.6803284, 90.7605133, 91.1681595, 90.8576355,
89.8222122, 88.0981903, 85.7664566, 82.9508209,
79.8129196, 76.5435028, 73.3503571, 70.4435043,
68.0185165, 66.2393112, 65.2218857, 65.0206757,
65.6191406, 66.9260406, 68.7782593, 70.9506989,
73.17276, 75.1504898, 76.5923691, 77.2365646,
76.8767319, 75.3837585, 72.7208405, 68.9500046,
64.229126, 58.7991486, 52.9627686, 47.0563354,
41.4180222, 36.3554802, 32.1166115, 28.8668022,
26.6751442, 25.5113792, 25.2537003, 25.7063427,
26.6244984, 27.7432671, 28.8067875, 29.5940056,
29.9381275, 29.7379456, 28.960556, 27.6360989,
25.8462563, 23.7087364, 21.3601532, 18.9395733,
16.5744362, 14.3700781, 12.4033003, 10.7200022,
9.33634567, 8.2426796, 7.40928364, 6.79297686,
6.34373522, 6.01063871, 5.74666357, 5.51208353,
5.27642059, 5.01907587, 4.72886801, 4.40278339,
4.04424238, 3.66118288, 3.26418185, 2.86479568,
2.47422004, 2.1023159, 1.75699866, 1.44394588,
1.16657102, 0.926194072, 0.722342134, 0.553120613,
0.415606558, 0.306226671, 0.221093416, 0.156284735,
0.108059399, 0.0730084404, 0.0481470376, 0.0309553891,
0.0193785131, 0.0117959473, 0.00697184261, 0.0039948686,
0.00221563689, 0.00118740648, 0.000613805256, 0.000305476977,
0.000146079372, 6.69831279e-05, 2.93878602e-05, 1.23086456e-05,
4.90973798e-06, 1.86049226e-06, 6.68009079e-07, 2.26637297e-07,
7.24482589e-08, 2.17554614e-08, 6.11771656e-09,
/* Z=55 -> Cs */
0, 0.0853344053, 0.0934358165, 0.102301657,
0.112003364, 0.122618876, 0.13423337, 0.14693974,
0.160839409, 0.176043004, 0.192671165, 0.210855514,
0.230739504, 0.252479464, 0.276245773, 0.302223951,
0.330616027, 0.361641943, 0.395540982, 0.432573378,
0.473022133, 0.517194748, 0.565425277, 0.618076324,
0.67554152, 0.738247693, 0.806657553, 0.881272256,
0.962634563, 1.0513314, 1.1479975, 1.25331843,
1.36803401, 1.49294245, 1.62890339, 1.77684236,
1.93775415, 2.11270738, 2.30284834, 2.50940514,
2.73369169, 2.9771111, 3.24116015, 3.52743292,
3.83762264, 4.17352581, 4.53704357, 4.93018341,
5.35505867, 5.81389046, 6.30900192, 6.84281921,
7.41786385, 8.03674507, 8.70215416, 9.41684723,
10.1836357, 11.0053635, 11.8848848, 12.8250446,
13.8286409, 14.8983889, 16.0368843, 17.2465572,
18.5296097, 19.8879719, 21.3232193, 22.8365211,
24.4285412, 26.0993671, 27.8484154, 29.6743374,
31.5749245, 33.5469971, 35.5863113, 37.6874695,
39.8437958, 42.047287, 44.2885094, 46.5565605,
48.8390236, 51.1219673, 53.3899612, 55.6261673,
57.8124199, 59.9294281, 61.9569817, 63.8742599,
65.6601868, 67.2938766, 68.7551498, 70.0251083,
71.0867996, 71.9259262, 72.5315857, 72.897049,
73.0205383, 72.9059525, 72.5635376, 72.0104218,
71.2710114, 70.3771515, 69.3680573, 68.2898636,
67.1949234, 66.1406174, 65.1878357, 64.3989792,
63.8356323, 63.5558472, 63.6112175, 64.0437622,
64.8828049, 66.1420517, 67.8169785, 69.8828659,
72.293541, 74.9812393, 77.8575516, 80.8157806,
83.7346725, 86.4835663, 88.9288025, 90.9412308,
92.4043884, 93.2230225, 93.3311539, 92.6992798,
91.3398819, 89.3105545, 86.7141953, 83.6957703,
80.4354095, 77.1378555, 74.0187073, 71.2881622,
69.1334076, 67.7011261, 67.0817413, 67.2971497,
68.2934952, 69.9403992, 72.0372391, 74.3266907,
76.5147705, 78.2959213, 79.3808975, 79.5247879,
78.55233, 76.3774796, 73.0151215, 68.5830231,
63.2935829, 57.4356308, 51.3480186, 45.3874931,
39.8942108, 35.1587372, 31.3941727, 28.7168179,
27.1375313, 26.5649719, 26.8200378, 27.6596375,
28.8064823, 29.980957, 30.9309559, 31.4560776,
31.4236355, 30.7752304, 29.5241337, 27.7448788,
25.5573368, 23.1079693, 20.5508633, 18.0308399,
15.670167, 13.5598831, 11.7558413, 10.2791586,
9.12022209, 8.24520016, 7.60389042, 7.13779354,
6.78750563, 6.49873638, 6.22658205, 5.93793726,
5.61217403, 5.24038601, 4.82359457, 4.37034321,
3.89406562, 3.41057229, 2.93586326, 2.48443198,
2.06810069, 1.69537675, 1.37127006, 1.09747493,
0.872815192, 0.693846822, 0.555525243, 0.451861143,
0.376508713, 0.323249787, 0.286357015, 0.260834724,
0.242548153, 0.228259966, 0.215594977, 0.202956125,
0.189410821, 0.174563527, 0.158426881, 0.141299039,
0.12365289, 0.106040247, 0.0890132934, 0.073064208,
0.0585834607, 0.0458366498, 0.0349580683, 0.0259587727,
0.0187456626, 0.0131475357, 0.00894395076, 0.00589299481,
0.00375498645, 0.00231021619, 0.00137004955,
/* Z=56 -> Ba */
0, 0.0928303152, 0.101608858, 0.11121235,
0.12171752, 0.133208126, 0.145775586, 0.159519613,
0.174548954, 0.190982282, 0.20894888, 0.228589743,
0.250058502, 0.273522466, 0.299163908, 0.32718125,
0.35779044, 0.391226411, 0.427744687, 0.467623025,
0.511163294, 0.558693349, 0.610569179, 0.667176962,
0.728935719, 0.796299398, 0.869760096, 0.949850261,
1.03714621, 1.13227081, 1.23589718, 1.3487519,
1.47161865, 1.60534179, 1.75083065, 1.90906274,
2.08108878, 2.26803589, 2.47111249, 2.69161081,
2.93091369, 3.19049525, 3.47192693, 3.77687979,
4.10712719, 4.46454811, 4.8511281, 5.26896048,
5.72024679, 6.20729446, 6.73251581, 7.29842234,
7.907619, 8.56279659, 9.26672173, 10.0222187,
10.83216, 11.69944, 12.6269522, 13.6175623,
14.6740713, 15.79918, 16.9954433, 18.2652206,
19.6106186, 21.0334263, 22.5350533, 24.1164455,
25.7780037, 27.5195045, 29.3399944, 31.2377014,
33.2099266, 35.2529488, 37.3619194, 39.5307617,
41.7520866, 44.0170937, 46.3155327, 48.6356201,
50.9640541, 53.2859802, 55.585083, 57.8436241,
60.0426369, 62.1620712, 64.1810913, 66.0783997,
67.832634, 69.4228363, 70.8290253, 72.0328217,
73.0181198, 73.7718353, 74.2846985, 74.5520172,
74.5744324, 74.3587036, 73.9182587, 73.2737198,
72.4532242, 71.4924545, 70.434433, 69.3289642,
68.2316895, 67.2027588, 66.3050461, 65.6020279,
65.1551666, 65.0211105, 65.2485504, 65.8750992,
66.9240952, 68.4017944, 70.2949448, 72.5690155,
75.1674576, 78.0119247, 81.0038834, 84.0276108,
86.9545975, 89.6494217, 91.9767761, 93.8095093,
95.0372086, 95.5747757, 95.37043, 94.4123764,
92.7335205, 90.4133911, 87.5768967, 84.3893509,
81.0477066, 77.7682114, 74.7709885, 72.2625351,
70.4174652, 69.3610382, 69.1543274, 69.7837067,
71.1562881, 73.1023407, 75.3852921, 77.7190094,
79.7912064, 81.2911987, 81.9393845, 81.5154343,
79.8822632, 77.0028305, 72.9476166, 67.8915405,
62.0999832, 55.9051476, 49.6747513, 43.7763863,
38.5413094, 34.2318344, 31.0160656, 28.9532108,
27.9911118, 27.9764309, 28.6759911, 29.8063755,
31.0677929, 32.1777115, 32.8999748, 33.0660439,
32.5863419, 31.4511814, 29.7223797, 27.5176086,
24.9904137, 22.3088551, 19.6355629, 17.1113377,
14.8436747, 12.9007902, 11.3109245, 10.0662003,
9.12978077, 8.44501114, 7.94510365, 7.56217098,
7.2346859, 6.91278267, 6.56121063, 6.16005087,
5.70357609, 5.19776344, 4.65703154, 4.10073519,
3.54986501, 3.02427053, 2.54059768, 2.11100459,
1.74262881, 1.43768883, 1.19408071, 1.00629425,
0.866483867, 0.765551448, 0.694122314, 0.643342674,
0.605454981, 0.574147284, 0.54469496, 0.513931632,
0.480094701, 0.442590594, 0.401720911, 0.358403414,
0.313911945, 0.269651771, 0.226979703, 0.187072143,
0.150840476, 0.118890047, 0.0915163681, 0.0687311888,
0.0503098927, 0.0358512774, 0.0248415619, 0.016715169,
0.0109068146, 0.00689128879, 0.00420959434, 0.00248199003,
0.00141001039, 0.000770384911, 0.000404030259,
/* Z=57 -> La */
0, 0.100932971, 0.110439457, 0.120835572,
0.132203683, 0.14463371, 0.158223674, 0.173080504,
0.189320803, 0.207071632, 0.226471484, 0.247671276,
0.27083534, 0.296142638, 0.323787987, 0.353983372,
0.386959404, 0.422966868, 0.462278306, 0.505189955,
0.55202347, 0.603128076, 0.658882737, 0.71969837,
0.786020458, 0.858331621, 0.937154293, 1.02305377,
1.1166414, 1.21857762, 1.32957518, 1.45040345,
1.58189154, 1.72493184, 1.88048482, 2.04958248,
2.23333263, 2.4329226, 2.64962459, 2.88479781,
3.13989472, 3.41646266, 3.71614885, 4.0407033,
4.39198017, 4.77194214, 5.18265963, 5.62631369,
6.10519218, 6.62169027, 7.17830658, 7.77763748,
8.42237091, 9.11527443, 9.85918522, 10.6569948,
11.5116282, 12.4260244, 13.4031048, 14.4457493,
15.5567513, 16.7387829, 17.9943447, 19.3257084,
20.7348652, 22.2234516, 23.7926769, 25.4432468,
27.1752758, 28.9881973, 30.880661, 32.850441,
34.8943214, 37.0080032, 39.1860046, 41.4215469,
43.7064857, 46.0312195, 48.3846436, 50.7540932,
53.1253624, 55.4826889, 57.8088531, 60.0852776,
62.2921944, 64.4088669, 66.4138947, 68.2855835,
70.0023727, 71.5433731, 72.8889313, 74.0213394,
74.9254913, 75.5897293, 76.0065765, 76.1735458,
76.0939331, 75.7774734, 75.2409439, 74.5085831,
73.6123199, 72.5916748, 71.493454, 70.3709717,
69.2829666, 68.2920303, 67.462677, 66.8589172,
66.5415878, 66.5652618, 66.9750977, 67.8035812,
69.0674362, 70.7648621, 72.8733597, 75.3482971,
78.1225586, 81.1073532, 84.1944275, 87.2597122,
90.1684799, 92.7818298, 94.9643936, 96.5928116,
97.5645523, 97.8065567, 97.2829285, 96.0009537,
94.0148315, 91.4263153, 88.3817978, 85.0655594,
81.6891556, 78.4772415, 75.6507034, 73.4081421,
71.9072266, 71.2476883, 71.4578171, 72.4861603,
74.1999054, 76.3908997, 78.7894211, 81.0851288,
82.9536667, 84.0866089, 84.2218628, 83.1713562,
80.8428268, 77.253067, 72.530571, 66.9068451,
60.69664, 54.2688866, 48.0110474, 42.2907677,
37.4190292, 33.6191826, 31.0056, 29.5747204,
29.2095699, 29.6971931, 30.7566395, 32.0736465,
33.337368, 34.2742996, 34.6752014, 34.4121017,
33.444046, 31.8119564, 29.6244659, 27.0375595,
24.2313061, 21.3869381, 18.6669693, 16.2003765,
14.0737619, 12.3287373, 10.9648209, 9.94668674,
9.21417236, 8.69341469, 8.30757809, 7.98594284,
7.67055607, 7.32008505, 6.9109478, 6.43612719,
5.90228939, 5.32591248, 4.72910452, 4.13568497,
3.56792355, 3.04418349, 2.57753348, 2.17526722,
1.83918154, 1.56640184, 1.35053766, 1.18295729,
1.05401254, 0.954086244, 0.874394178, 0.807511926,
0.74764353, 0.690669298, 0.634026706, 0.576482177,
0.517844915, 0.45866558, 0.399951488, 0.342918396,
0.288789958, 0.238648713, 0.193337798, 0.153408483,
0.119107358, 0.0903953463, 0.0669896901, 0.0484208241,
0.0340954289, 0.0233585313, 0.0155486688, 0.0100419549,
0.00628297077, 0.00380226155, 0.00222187932, 0.00125150639,
0.000678222626, 0.000352929899, 0.000175989961,
/* Z=58 -> Ce */
0, 0.109678723, 0.119966492, 0.131212875,
0.143506274, 0.156943038, 0.171628267, 0.187676474,
0.205212533, 0.224372461, 0.245304406, 0.268169761,
0.293144137, 0.320418805, 0.350201726, 0.382719219,
0.418217301, 0.456963301, 0.499247789, 0.545386255,
0.595721066, 0.650623977, 0.710497797, 0.775779486,
0.846942067, 0.924497962, 1.00900149, 1.10105193,
1.20129704, 1.31043613, 1.42922366, 1.55847287,
1.69905984, 1.85192692, 2.01808715, 2.1986289,
2.39471817, 2.60760498, 2.83862615, 3.08921027,
3.3608799, 3.65525794, 3.97406816, 4.31914043,
4.69241095, 5.09592676, 5.53184462, 6.00243044,
6.51006031, 7.05721521, 7.64647961, 8.28053284,
8.96214008, 9.69414425, 10.4794502, 11.3210068,
12.2217894, 13.1847687, 14.2128916, 15.3090353,
16.4759769, 17.7163448, 19.0325661, 20.4268169,
21.9009457, 23.4564114, 25.0942097, 26.8147793,
28.6179218, 30.5026951, 32.4673271, 34.5091095,
36.6242752, 38.8079262, 41.0539055, 43.3547134,
45.7014236, 48.0836143, 50.4893036, 52.9049377,
55.3153954, 57.7040215, 60.0527115, 62.3420601,
64.5515518, 66.6598129, 68.6449585, 70.4849701,
72.1582108, 73.6439667, 74.9230576, 75.9785767,
76.7966232, 77.3670959, 77.684494, 77.7487335,
77.5658722, 77.1488113, 76.5177612, 75.7006607,
74.7332306, 73.6588211, 72.5278854, 71.3970795,
70.3279572, 69.3852158, 68.6345367, 68.1399918,
67.9611511, 68.1499329, 68.7472839, 69.7799377,
71.2574005, 73.1693268, 75.4836197, 78.1453476,
81.0769196, 84.1793976, 87.3353882, 90.4133987,
93.2736435, 95.7751923, 97.7842255, 99.182869,
99.8781891, 99.8107071, 98.9616394, 97.3581543,
95.0759354, 92.2384033, 89.0121078, 85.5981598,
82.2198029, 79.1066437, 76.4765396, 74.5163727,
73.3635025, 73.0896072, 73.6889572, 75.0727005,
77.0704498, 79.4399567, 81.8845139, 84.07724,
85.6901703, 86.4256287, 86.0466156, 84.4029388,
81.4500198, 77.2577591, 72.0080109, 65.9803772,
59.5271301, 53.039753, 46.9104652, 41.4929085,
37.0665665, 33.8092155, 31.7807598, 30.9206505,
31.0590878, 31.9405136, 33.2561569, 34.6811523,
35.9112549, 36.6944122, 36.8535461, 36.2982712,
35.0251999, 33.1079826, 30.6796093, 27.9101257,
24.9831676, 22.0743465, 19.3337364, 16.8740406,
14.7647972, 13.0323839, 11.6648521, 10.6201773,
9.83639431, 9.24208355, 8.76591492, 8.3443222,
7.92676401, 7.47844076, 6.98067713, 6.42941236,
5.83238173, 5.20559454, 4.56966448, 3.94643211,
3.35618496, 2.8156445, 2.33675981, 1.92625558,
1.5858134, 1.31272805, 1.10086644, 0.941763461,
0.825715899, 0.74276334, 0.683486164, 0.639583051,
0.604224622, 0.572202146, 0.53990835, 0.505191922,
0.467131615, 0.425768346, 0.381828636, 0.336463332,
0.29101783, 0.246843785, 0.205156475, 0.166937575,
0.132881284, 0.103378028, 0.0785297081, 0.0581884049,
0.042010501, 0.0295179337, 0.0201591961, 0.0133639984,
0.00858728494, 0.00534041505, 0.00320921722, 0.00186034909,
0.00103845296, 0.000557134685, 0.000286717783,
/* Z=59 -> Pr */
0, 0.119143568, 0.130272105, 0.142433077,
0.155721217, 0.170239791, 0.186101347, 0.203428507,
0.222354844, 0.243025884, 0.265599996, 0.290249646,
0.317162484, 0.346542567, 0.378611922, 0.413611889,
0.451804698, 0.493475258, 0.538932979, 0.588513553,
0.642581344, 0.70153147, 0.765792012, 0.835826993,
0.912138462, 0.995269954, 1.08580899, 1.18439054,
1.29170036, 1.40847814, 1.53552163, 1.67368984,
1.82390749, 1.98716891, 2.16454172, 2.35717154,
2.56628585, 2.79319835, 3.03931332, 3.3061285,
3.59524107, 3.9083488, 4.24725485, 4.61386967,
5.01021338, 5.43841791, 5.90072536, 6.39948988,
6.93717337, 7.51634312, 8.13966751, 8.80990505,
9.5298996, 10.3025627, 11.1308641, 12.0178041,
12.9663992, 13.9796495, 15.0605097, 16.2118511,
17.4364204, 18.7367859, 20.1152878, 21.5739822,
23.114563, 24.7382927, 26.4459209, 28.2375984,
30.1127834, 32.0701408, 34.1074371, 36.2214508,
38.4078407, 40.6610718, 42.9742889, 45.339241,
47.7461967, 50.1838837, 52.6394424, 55.0984116,
57.5447655, 59.9609413, 62.3279877, 64.6257019,
66.8328629, 68.9275208, 70.8873825, 72.6902084,
74.3143997, 75.7395401, 76.9470825, 77.9210968,
78.6490326, 79.1225586, 79.3383255, 79.2988358,
79.0131073, 78.4973221, 77.7752914, 76.8787079,
75.8471527, 74.7277527, 73.5745239, 72.4472885,
71.4101562, 70.5295715, 69.871933, 69.5008621,
69.4740829, 69.8401794, 70.635231, 71.87957,
73.5748444, 75.7016296, 78.2178116, 81.0579681,
84.1339798, 87.3370438, 90.5411682, 93.6082611,
96.3946304, 98.7587357, 100.569908, 101.71756,
102.120163, 101.733528, 100.55751, 98.6402359,
96.0794678, 93.0201874, 89.648262, 86.1799393,
82.847702, 79.8829269, 77.4967117, 75.8602524,
75.0866394, 75.2159729, 76.2057648, 77.9281464,
80.1750031, 82.6713867, 85.0966415, 87.1118088,
88.3909836, 88.6535721, 87.6941528, 85.4064102,
81.7982712, 76.9959106, 71.2356567, 64.8439331,
58.2069626, 51.7331848, 45.8123894, 40.7761612,
36.864399, 34.2019806, 32.7885666, 32.5029335,
33.1211777, 34.3462334, 35.8447113, 37.2859383,
38.3780441, 38.8966484, 38.7028961, 37.7496338,
36.0760193, 33.7926865, 31.0604286, 28.0659885,
24.9982986, 22.0280228, 19.2923145, 16.8858223,
14.8579226, 13.2155094, 11.9300251, 10.9471903,
10.197793, 9.60808563, 9.10865021, 8.64099026,
8.16154003, 7.64315081, 7.07442236, 6.45741892,
5.80438375, 5.13405132, 4.46805191, 3.82779574,
3.2320478, 2.69531107, 2.22699857, 1.83130097,
1.50761271, 1.25134754, 1.05497491, 0.909125924,
0.803642869, 0.728483081, 0.674422204, 0.633535206,
0.599462211, 0.567486048, 0.534459531, 0.498626709,
0.45937866, 0.416981578, 0.372304857, 0.326570183,
0.281135887, 0.237323165, 0.196287602, 0.158935085,
0.125878707, 0.0974314436, 0.073627606, 0.0542657562,
0.0389646105, 0.0272242147, 0.0184853226, 0.0121813631,
0.00777922291, 0.00480712252, 0.0028697364, 0.00165221572,
0.000915754063, 0.00048770319, 0.000249075121,
/* Z=60 -> Nd */
0, 0.129378513, 0.141410962, 0.15455471,
0.168911234, 0.184591115, 0.201714784, 0.220413461,
0.240829974, 0.263119817, 0.287452281, 0.314011425,
0.342997521, 0.374628365, 0.409140646, 0.44679153,
0.487860352, 0.532650471, 0.581491053, 0.634739161,
0.692782044, 0.756039441, 0.824965954, 0.90005368,
0.981835246, 1.07088649, 1.16782975, 1.27333713,
1.38813365, 1.51300144, 1.64878285, 1.79638457,
1.95678186, 2.13102245, 2.32023025, 2.52561069,
2.74845386, 2.99013901, 3.25213933, 3.53602481,
3.84346676, 4.17624092, 4.53623009, 4.92542696,
5.34593678, 5.79997587, 6.2898736, 6.81806993,
7.38711309, 7.9996562, 8.65844727, 9.36632633,
10.1262074, 10.9410696, 11.81394, 12.7478647,
13.7458973, 14.8110542, 15.946291, 17.1544571,
18.4382553, 19.8001823, 21.2424755, 22.7670498,
24.3754215, 26.0686359, 27.8471756, 29.7108746,
31.6588211, 33.6892548, 35.7994576, 37.9856606,
40.2429199, 42.565033, 44.9444199, 47.3720512,
49.8373756, 52.3282394, 54.8308983, 57.3299828,
59.8085556, 62.2481766, 64.6290588, 66.9302368,
69.1298523, 71.2054443, 73.1343765, 74.8943253,
76.4638214, 77.8228989, 78.9537888, 79.8417053,
80.4756317, 80.8491669, 80.961319, 80.817337,
80.4293442, 79.8169708, 79.0077057, 78.0370483,
76.9484406, 75.7927322, 74.6273499, 73.5150681,
72.5222244, 71.7166138, 71.1649017, 70.9296646,
71.0661926, 71.6190872, 72.6189041, 74.0789185,
75.9923859, 78.3303375, 81.0403671, 84.0464325,
87.250061, 90.5329895, 93.7613678, 96.7914963,
99.4770584, 101.677422, 103.266792, 104.14357,
104.239372, 103.52684, 102.02562, 99.805542,
96.9865189, 93.7344589, 90.253067, 86.7715378,
83.5286026, 80.7539062, 78.6479721, 77.3624802,
76.982811, 77.5148392, 78.8778076, 80.9047852,
83.3515472, 85.913765, 88.2517014, 90.0204239,
90.9029007, 90.6425171, 89.0716171, 86.1325836,
81.8886032, 76.5223541, 70.3220215, 63.6555939,
56.9356194, 50.5782776, 44.9610634, 40.3841705,
37.040184, 34.996048, 34.1894836, 34.4405098,
35.4763641, 36.9663506, 38.5618362, 39.9359207,
40.817627, 41.0165977, 40.4358215, 39.071949,
37.0045547, 34.3769455, 31.3721581, 28.1876717,
25.0122051, 22.0070992, 19.2937317, 16.9475231,
14.9981031, 13.4345541, 12.2142401, 11.2735205,
10.5387478, 9.93622684, 9.40014648, 8.87800503,
8.33338642, 7.74634457, 7.11186171, 6.43699217,
5.73729849, 5.03314638, 4.34629393, 3.69707942,
3.10237026, 2.57431555, 2.11984968, 1.74082518,
1.43462634, 1.19509184, 1.01359022, 0.880104661,
0.784225166, 0.715968847, 0.666391969, 0.627983153,
0.594853759, 0.562754989, 0.528963923, 0.492078841,
0.451764375, 0.408478409, 0.363206953, 0.317224354,
0.271890849, 0.22849232, 0.18812488, 0.15162231,
0.119522683, 0.0920686424, 0.0692344233, 0.050772015,
0.0362683944, 0.0252063051, 0.0170218702, 0.0111539168,
0.00708170794, 0.0043498138, 0.00258058822, 0.00147617003,
0.000812712766, 0.000429825159, 0.000217935289,
/* Z=61 -> Pm */
0, 0.140446872, 0.153451085, 0.167650819,
0.183154732, 0.20008114, 0.218558863, 0.238728195,
0.26074174, 0.284765601, 0.310980469, 0.339582801,
0.37078616, 0.404822737, 0.441944659, 0.482425869,
0.526563644, 0.574680686, 0.627126992, 0.684282005,
0.746556997, 0.814397454, 0.888285577, 0.968743145,
1.0563345, 1.15166938, 1.25540614, 1.36825573,
1.49098408, 1.62441719, 1.76944387, 1.92702031,
2.09817386, 2.28400731, 2.48570299, 2.70452785,
2.94183612, 3.19907475, 3.47778726, 3.77961731,
4.10631227, 4.45972681, 4.84182549, 5.25468397,
5.70049143, 6.18155098, 6.70027828, 7.25919962,
7.86094856, 8.50826073, 9.20396519, 9.95097542,
10.7522764, 11.6109066, 12.5299473, 13.5124846,
14.561595, 15.6803074, 16.8715649, 18.1381836,
19.4828072, 20.9078445, 22.4154129, 24.0072651,
25.6847248, 27.4485874, 29.2990494, 31.2355995,
33.2569275, 35.3608208, 37.5440483, 39.8022614,
42.1298866, 44.5200195, 46.9643326, 49.4529953,
51.9746017, 54.5161285, 57.0629196, 59.5986977,
62.1056213, 64.5643921, 66.954422, 69.2540283,
71.4407654, 73.4917297, 75.3840714, 77.0954514,
78.6046829, 79.8923798, 80.9417114, 81.7392044,
82.2755508, 82.546463, 82.5534897, 82.3047791,
81.8157349, 81.10952, 80.2173843, 79.1787109,
78.0407257, 76.8579254, 75.6909866, 74.6053467,
73.6692581, 72.9514389, 72.5182877, 72.4307861,
72.7411499, 73.489357, 74.6997833, 76.3780594,
78.508522, 81.052269, 83.9463806, 87.1042099,
90.4171753, 93.7580948, 96.9860535, 99.9529037,
102.511047, 104.522369, 105.867622, 106.455971,
106.233803, 105.191994, 103.370972, 100.86274,
97.8091507, 94.3960876, 90.8433533, 87.3905487,
84.2795029, 81.7344818, 79.9416122, 79.0294037,
79.0524063, 79.9800644, 81.6924515, 83.9842377,
86.5773773, 89.1421509, 91.325119, 92.7817993,
93.2108383, 92.3861923, 90.1835785, 86.5979538,
81.7493591, 75.8759079, 69.3138504, 62.4663315,
55.7638855, 49.6208878, 44.3929329, 40.3402596,
37.6017532, 36.1830063, 35.9598923, 36.6972427,
38.079998, 39.7524376, 41.3601379, 42.5889626,
43.1962128, 43.0304832, 42.0386162, 40.2602959,
37.8123016, 34.8657951, 31.6203995, 28.2787762,
25.0246754, 22.0066662, 19.3284473, 17.0458736,
15.1698189, 13.6735411, 12.5028467, 11.5873642,
10.8513756, 10.2230644, 9.64138031, 9.06027508,
8.45032215, 7.79814577, 7.10418653, 6.37944746,
5.64179802, 4.91236782, 4.21237707, 3.56066346,
2.97198844, 2.45612788, 2.01766062, 1.65631831,
1.3677386, 1.14445627, 0.976986051, 0.854870677,
0.767603695, 0.705366671, 0.659555197, 0.62309283,
0.59055531, 0.558138549, 0.523510516, 0.48558861,
0.444277614, 0.400198758, 0.354432523, 0.308290273,
0.263124287, 0.220180437, 0.180494636, 0.144830823,
0.113656253, 0.0871485993, 0.0652276427, 0.0476041064,
0.0338378474, 0.0233978648, 0.0157180876, 0.0102440687,
0.00646781549, 0.00394985452, 0.00232932949, 0.00132420578,
0.000724373269, 0.000380554528, 0.000191619431,
/* Z=62 -> Sm */
0, 0.152417436, 0.166466266, 0.181800589,
0.198536649, 0.216800973, 0.236731291, 0.25847742,
0.282202363, 0.308083415, 0.336313337, 0.36710161,
0.400675893, 0.437283427, 0.47719276, 0.520695329,
0.568107426, 0.619771898, 0.676060736, 0.737376809,
0.804156542, 0.876872361, 0.956035495, 1.04219866,
1.13595915, 1.23796201, 1.34890354, 1.46953452,
1.6006639, 1.74316299, 1.89796889, 2.06608868,
2.24860382, 2.44667411, 2.66154242, 2.89453769,
3.14708138, 3.42068911, 3.71697688, 4.03766298,
4.38457298, 4.75964165, 5.16491461, 5.60255337,
6.07483101, 6.58413792, 7.1329751, 7.72395468,
8.35979366, 9.04331017, 9.7774086, 10.5650749,
11.4093599, 12.3133602, 13.2801971, 14.312993,
15.4148407, 16.5887661, 17.8376923, 19.1643906,
20.5714264, 22.0611038, 23.6354008, 25.2958927,
27.0436783, 28.8792934, 30.8026104, 32.8127518,
34.9079819, 37.0856018, 39.3418388, 41.6717377,
44.0690613, 46.5261803, 49.0339966, 51.5818481,
54.1574707, 56.7469368, 59.3346863, 61.9035339,
64.4347534, 66.9082031, 69.3025284, 71.5953903,
73.7638092, 75.7845459, 77.6345978, 79.2917557,
80.7352295, 81.9463806, 82.9094696, 83.6124954,
84.0480576, 84.2141495, 84.1150284, 83.7619019,
83.173584, 82.3768921, 81.4069061, 80.3068542,
79.1277542, 77.9275818, 76.7700653, 75.7230377,
74.8562622, 74.2389297, 73.9366531, 74.0082245,
74.5021362, 75.4531174, 76.8787231, 78.7763901,
81.1210403, 83.8635406, 86.9303055, 90.2241898,
93.6268692, 97.002861, 100.205162, 103.082352,
105.487038, 107.28521, 108.365921, 108.650803,
108.102539, 106.731483, 104.599663, 101.821442,
98.5601349, 95.0203094, 91.4358521, 88.0539627,
85.1162262, 82.8378296, 81.3867264, 80.8648148,
81.2930832, 82.6028748, 84.6347961, 87.1464615,
89.82901, 92.331871, 94.2937241, 95.3771133,
95.3031235, 93.8824081, 91.0389252, 86.8230515,
81.4121323, 75.0973969, 68.2581635, 61.3254547,
54.7388649, 48.9013939, 44.1376076, 40.6602402,
38.5495071, 37.7479286, 38.071312, 39.2343292,
40.8871994, 42.6582031, 44.1963577, 45.2084694,
45.4862518, 44.9207039, 43.5031548, 41.3143234,
38.5042305, 35.2667122, 31.8124981, 28.3443794,
25.0371418, 22.023983, 19.3898411, 17.1713181,
15.3619499, 13.921298, 12.7860374, 11.8813963,
11.1315374, 10.4678907, 9.83490658, 9.1931057,
8.51967716, 7.80709505, 7.06035709, 6.29347849,
5.52578878, 4.7784934, 4.0717907, 3.42273712,
2.8438921, 2.34271169, 1.92157984, 1.57832909,
1.30709553, 1.09934795, 0.944956422, 0.83319056,
0.753569186, 0.69651562, 0.653803527, 0.618800104,
0.586533248, 0.553618073, 0.5180825, 0.479130745,
0.436878413, 0.392085463, 0.345907807, 0.299680263,
0.254738599, 0.212284625, 0.173293263, 0.138460413,
0.108185999, 0.0825871229, 0.0615337789, 0.0446999185,
0.0316220745, 0.0217584893, 0.0145429103, 0.00942870695,
0.00592091726, 0.0035956935, 0.00210821885, 0.00119132712,
0.000647635607, 0.000338044687, 0.000169073595,
/* Z=63 -> Eu */
0, 0.16536583, 0.180537641, 0.197091043,
0.215150326, 0.234850675, 0.256339252, 0.279775977,
0.305334866, 0.333205014, 0.363591909, 0.39671877,
0.432828128, 0.472183138, 0.515069544, 0.561797261,
0.61270231, 0.668149173, 0.728532493, 0.794279814,
0.865853965, 0.943755567, 1.02852607, 1.12075055,
1.22106063, 1.33013844, 1.44871938, 1.57759595,
1.71762168, 1.86971486, 2.03486228, 2.2141242,
2.408638, 2.61962199, 2.84838057, 3.09630847,
3.36489415, 3.65572476, 3.97048974, 4.31098413,
4.67911196, 5.07688951, 5.50644588, 5.97002649,
6.46999168, 7.00881577, 7.58908701, 8.21350193,
8.88485909, 9.60605526, 10.3800697, 11.2099581,
12.0988283, 13.0498276, 14.0661192, 15.1508455,
16.3071098, 17.5379238, 18.8461761, 20.2345772,
21.7056007, 23.2614326, 24.9038868, 26.6343422,
28.4536514, 30.3620567, 32.3590927, 34.4434776,
36.6130295, 38.8645287, 41.193634, 43.5947533,
46.0609627, 48.5838737, 51.1535912, 53.7586136,
56.3857841, 59.0202827, 61.6456299, 64.2437363,
66.7950211, 69.2785187, 71.6721573, 73.9529877,
76.0975723, 78.0824203, 79.8845062, 81.4818497,
82.8542023, 83.9838257, 84.8562317, 85.4610901,
85.7930527, 85.8525925, 85.6468201, 85.1901855,
84.5050049, 83.6218643, 82.5796814, 81.42556,
80.2141876, 79.0068817, 77.8701935, 76.8740158,
76.0892334, 75.585022, 75.4256516, 75.6671143,
76.353569, 77.5138092, 79.1580048, 81.2748337,
83.829422, 86.7621231, 89.9886703, 93.4015732,
96.8732376, 100.260674, 103.411751, 106.173126,
108.399117, 109.961502, 110.759331, 110.728363,
109.848991, 108.152161, 105.722076, 102.695442,
99.2562103, 95.6261368, 92.0508194, 88.7821121,
86.0578308, 84.0803375, 82.9957733, 82.8761978,
83.7066498, 85.3791733, 87.6952286, 90.3772659,
93.0891876, 95.4645462, 97.1402588, 97.792511,
97.1713028, 95.1296921, 91.6439362, 86.821846,
80.8974304, 74.2117691, 67.1814041, 60.2573967,
53.8792877, 48.4293976, 44.1928177, 41.3283272,
39.8537903, 39.6483498, 40.4707489, 41.9914703,
43.8340225, 45.6196709, 47.00951, 47.7385826,
47.6380539, 46.6437225, 44.7911758, 42.1996841,
39.0484161, 35.5489807, 31.9182301, 28.3547077,
25.0208855, 22.0325241, 19.4550323, 17.306097,
15.5631132, 14.1736364, 13.0670652, 12.1659622,
11.3957653, 10.6921043, 10.0054045, 9.30281544,
8.56787014, 7.79841089, 7.00341129, 6.19932127,
5.40642166, 4.6456008, 3.9357748, 3.2920835,
2.72486067, 2.23930407, 1.8357197, 1.51019144,
1.25551331, 1.06223989, 0.919730365, 0.817089617,
0.743942976, 0.691010892, 0.650477588, 0.616167665,
0.583560884, 0.549681306, 0.512900233, 0.47268945,
0.429354697, 0.383774847, 0.337162971, 0.290861249,
0.246175826, 0.204253614, 0.166000694, 0.132039353,
0.102698877, 0.078034237, 0.0578655154, 0.0418307222,
0.0294445027, 0.0201560203, 0.0134004913, 0.00864052866,
0.00539530301, 0.00325733447, 0.00189826428, 0.00106594805,
0.000575700367, 0.000298463507, 0.000148227424,
/* Z=64 -> Gd */
0, 0.179383636, 0.195763588, 0.213627815,
0.233109131, 0.254351944, 0.277513355, 0.302764058,
0.330289602, 0.36029163, 0.392989039, 0.428619623,
0.467441499, 0.509734631, 0.555802822, 0.605975509,
0.660609603, 0.720091879, 0.78484112, 0.855310678,
0.931990921, 1.01541209, 1.10614717, 1.20481515,
1.31208348, 1.42867279, 1.55535924, 1.69297886,
1.84243119, 2.00468349, 2.18077421, 2.37181854,
2.57901096, 2.80363107, 3.04704642, 3.31071877,
3.59620619, 3.90516853, 4.23937035, 4.60068464,
4.99109602, 5.41270304, 5.8677187, 6.35847378,
6.88741446, 7.45710087, 8.07020664, 8.72951126,
9.43789387, 10.1983271, 11.0138626, 11.8876181,
12.8227577, 13.8224726, 14.8899565, 16.028368,
17.2408047, 18.5302582, 19.8995686, 21.3513699,
22.8880272, 24.5115871, 26.2236843, 28.0254726,
29.9175415, 31.8998127, 33.9714508, 36.1307564,
38.3750534, 40.7005844, 43.1024055, 45.5742607,
48.1084976, 50.6959686, 53.3259468, 55.9860573,
58.6622581, 61.3388214, 63.9983559, 66.6218796,
69.1889572, 71.6778564, 74.0658188, 76.3293686,
78.4446869, 80.3881149, 82.1367188, 83.6688766,
84.9650497, 86.0085297, 86.7862778, 87.2897949,
87.5159683, 87.4679413, 87.1558456, 86.597496,
85.8188629, 84.8543472, 83.7467804, 82.5470657,
81.3134918, 80.1105499, 79.0073395, 78.0754623,
77.386528, 77.0091629, 77.0057297, 77.4288025,
78.3175354, 79.694191, 81.5609207, 83.8971481,
86.6577759, 89.7724609, 93.1462097, 96.6614685,
100.181892, 103.557739, 106.632957, 109.253593,
111.277237, 112.583191, 113.082283, 112.726044,
111.514061, 109.498901, 106.787521, 103.538811,
99.9565887, 96.2780762, 92.7581787, 89.6502457,
87.1847, 85.5471649, 84.8581161, 85.1563492,
86.3883286, 88.4053802, 90.9697723, 93.7703857,
96.4470978, 98.6223145, 99.9369736, 100.08741,
98.8591156, 96.1534653, 92.0037231, 86.577919,
80.1673126, 73.1608658, 66.0079651, 59.1731682,
53.087925, 48.1050453, 44.4615288, 42.2546349,
41.4342957, 41.8131332, 43.0924988, 44.9010277,
46.8401718, 48.5305061, 49.6525269, 49.9770012,
49.3816719, 47.8534126, 45.47715, 42.4145126,
38.8762741, 35.0929108, 31.2871895, 27.6519203,
24.3346252, 21.4299583, 18.9793472, 16.9766674,
15.3782101, 14.1149321, 13.1051426, 12.2660294,
11.5229006, 10.8155451, 10.1015434, 9.35682392,
8.57401276, 7.75924063, 6.92815542, 6.10176134,
5.30260086, 4.55162764, 3.86595178, 3.25750351,
2.73254919, 2.29191113, 1.93171132, 1.64444089,
1.42016995, 1.24774134, 1.11583078, 1.01379788,
0.932291806, 0.863611758, 0.801846981, 0.742837608,
0.684005439, 0.624101877, 0.562916994, 0.500983417,
0.439299554, 0.379088908, 0.321604013, 0.267977923,
0.219122663, 0.175670937, 0.137955576, 0.106020309,
0.0796543583, 0.0584432371, 0.0418280885, 0.0291665737,
0.0197892711, 0.0130470507, 0.00834662933, 0.00517332554,
0.00310167833, 0.00179582275, 0.00100231241, 0.000538280583,
0.000277607614, 0.000137207666, 6.48501591e-05,
/* Z=65 -> Tb */
0, 0.19452709, 0.212203711, 0.231474027,
0.252479881, 0.275375426, 0.300328255, 0.3275204,
0.357149661, 0.389430761, 0.424596876, 0.462900996,
0.504617631, 0.550044537, 0.599504411, 0.653346956,
0.711951196, 0.775727153, 0.845118999, 0.920606792,
1.00270987, 1.09198928, 1.18905091, 1.29454875,
1.40918791, 1.5337286, 1.66898954, 1.81585169,
1.97526228, 2.14823914, 2.33587432, 2.53933859,
2.75988626, 2.99885893, 3.25768995, 3.53790855,
3.84114456, 4.16913128, 4.52371025, 4.90683317,
5.32056618, 5.76709032, 6.248703, 6.76782036,
7.32697392, 7.92880917, 8.57608318, 9.27165604,
10.018486, 10.8196173, 11.6781693, 12.5973158,
13.5802736, 14.6302681, 15.750514, 16.9441795,
18.2143459, 19.5639668, 20.9958172, 22.5124435,
24.1160908, 25.8086338, 27.5915127, 29.4656372,
31.4313011, 33.4880867, 35.6347618, 37.8691673,
40.188118, 42.5872917, 45.0611, 47.6026039,
50.2034073, 52.8535576, 55.5414848, 58.2539406,
60.975975, 63.6909447, 66.3805618, 69.0249634,
71.6028976, 74.0918961, 76.4685822, 78.708992,
80.7890396, 82.6849976, 84.374115, 85.8352966,
87.0498199, 88.0021896, 88.6809616, 89.0796356,
89.1975098, 89.0405197, 88.6219788, 87.9631805,
87.0938034, 86.0521088, 84.8847885, 83.6464844,
82.3989105, 81.2094803, 80.1495209, 79.2919769,
78.7086639, 78.4671478, 78.6272888, 79.2376251,
80.3317184, 81.9247131, 84.0102615, 86.5581512,
89.5128937, 92.7934113, 96.2942505, 99.8882828,
103.43119, 106.76757, 109.738701, 112.19149,
113.98848, 115.018044, 115.204308, 114.515823,
112.972237, 110.648041, 107.672623, 104.22599,
100.529953, 96.8346863, 93.401268, 90.4810791,
88.2935944, 87.0044785, 86.7060547, 87.4025116,
89.0018921, 91.3166428, 94.0735855, 96.9334335,
99.5188065, 101.448517, 102.375122, 102.021797,
100.214478, 96.9051208, 92.1830139, 86.2718506,
79.5120773, 72.3295898, 65.19384, 58.5696754,
52.8685303, 48.4048042, 45.3629951, 43.7799606,
43.5446167, 44.4152451, 46.0518799, 48.0591812,
50.0338173, 51.6098061, 52.4959526, 52.5010796,
51.5447273, 49.6535606, 46.9454842, 43.6051102,
39.8549232, 35.9262924, 32.0339737, 28.3567066,
25.0250778, 22.1169224, 19.6593933, 17.6362038,
15.9982376, 14.6756001, 13.5894527, 12.662303,
11.8258944, 11.0263224, 10.2264156, 9.40573215,
8.55872059, 7.6916914, 6.81919622, 5.96037006,
5.13561535, 4.36390352, 3.66082239, 3.03739619,
2.49960995, 2.04852772, 1.68085885, 1.38981819,
1.16613626, 0.999093235, 0.877476335, 0.79039216,
0.727892935, 0.681402743, 0.64395237, 0.610245824,
0.576592624, 0.540742278, 0.501656532, 0.459252387,
0.414140016, 0.367376179, 0.320245385, 0.274077624,
0.230105981, 0.189365134, 0.152629048, 0.120384119,
0.0928328484, 0.069921717, 0.0513862744, 0.0368062332,
0.0256635267, 0.0173972063, 0.0114504881, 0.00730680767,
0.0045136963, 0.00269489922, 0.00155247445, 0.000861399167,
0.000459480711, 0.000235155225, 0.000115229261,
/* Z=66 -> Dy */
0, 0.210925415, 0.229997009, 0.250779212,
0.273423374, 0.298094004, 0.324969828, 0.354244858,
0.386129797, 0.420853257, 0.458663404, 0.499829322,
0.544642806, 0.593420208, 0.646504164, 0.704265893,
0.767107308, 0.835463107, 0.909803748, 0.99063766,
1.07851422, 1.17402673, 1.27781534, 1.39057076,
1.5130372, 1.64601636, 1.79037082, 1.9470284,
2.1169858, 2.30131292, 2.50115728, 2.71774769,
2.95239949, 3.20651865, 3.48160529, 3.77925873,
4.10118151, 4.44918251, 4.82518101, 5.23120975,
5.66941595, 6.14206457, 6.65153933, 7.20033979,
7.79108381, 8.42650127, 9.10942936, 9.84281063,
10.6296768, 11.4731417, 12.3763876, 13.3426418,
14.3751621, 15.4772043, 16.6519966, 17.9027004,
19.2323723, 20.6439171, 22.1400337, 23.7231579,
25.3953876, 27.1584244, 29.0134811, 30.9612007,
33.0015564, 35.1337662, 37.3561707, 39.6661263,
42.0599136, 44.5325966, 47.0779381, 49.6882782,
52.3544426, 55.0656586, 57.8094978, 60.5718155,
63.3367577, 66.0867615, 68.8026428, 71.4636917,
74.0478592, 76.5320053, 78.8921661, 81.1040039,
83.143219, 84.9861374, 86.6103439, 87.995369,
89.1234894, 89.9805908, 90.5569839, 90.8483582,
90.8565979, 90.5906067, 90.067009, 89.3106995,
88.3551636, 87.2425613, 86.0234299, 84.7560654,
83.505455, 82.3417053, 81.3380508, 80.5683594,
80.1041946, 80.0114899, 80.3470306, 81.1546707,
82.4617691, 84.2757187, 86.5811691, 89.3378677,
92.4796448, 95.9146652, 99.5271835, 103.180946,
106.724388, 109.99749, 112.84008, 115.101501,
116.650818, 117.38726, 117.249847, 116.225639,
114.355461, 111.736389, 108.520264, 104.907547,
101.136642, 97.468483, 94.1674347, 91.4795151,
89.6095581, 88.6995926, 88.8104401, 89.9090347,
91.8634567, 94.4470291, 97.3523636, 100.214828,
102.643951, 104.260239, 104.733833, 103.820778,
101.392906, 97.4571381, 92.1614304, 85.7857361,
78.7180099, 71.4172287, 64.3671722, 58.0259705,
52.7774086, 48.8900986, 46.4896622, 45.5478935,
45.8901253, 47.2200241, 49.1581078, 51.2886238,
53.2081604, 54.5694809, 55.1151009, 54.6969566,
53.2809906, 50.9376373, 47.8211975, 44.1421623,
40.1370316, 36.0397224, 32.0578423, 28.3559017,
25.0462437, 22.1874065, 19.7886791, 17.8191833,
16.2195187, 14.9141016, 13.8226585, 12.8697147,
11.9914417, 11.139678, 10.2832994, 9.4074173,
8.51098824, 7.6034894, 6.70123148, 5.82381058,
4.99101639, 4.22042322, 3.52574205, 2.91591549,
2.39487791, 1.96184647, 1.6120038, 1.33741331,
1.12803841, 0.972747147, 0.860216677, 0.779677927,
0.721470654, 0.677403212, 0.640930057, 0.607172847,
0.572820961, 0.535945594, 0.495763063, 0.452375859,
0.406515449, 0.359303296, 0.312042534, 0.266046017,
0.222504839, 0.182396367, 0.146430552, 0.115030169,
0.0883399695, 0.0662583262, 0.0484844856, 0.0345743224,
0.0239976868, 0.0161916986, 0.0106054926, 0.0067337607,
0.00413818331, 0.00245746016, 0.00140782644, 0.000776638044,
0.000411788846, 0.000209436752, 0.000101963349,
/* Z=67 -> Ho */
0, 0.228673086, 0.249244317, 0.27165091,
0.296054363, 0.322630078, 0.35156855, 0.383076429,
0.417378038, 0.454716742, 0.495356351, 0.539582968,
0.587706625, 0.640063107, 0.69701612, 0.758959413,
0.8263188, 0.899555027, 0.979165971, 1.06568968,
1.15970695, 1.26184475, 1.37277913, 1.49323893,
1.62400866, 1.76593351, 1.91992164, 2.08694911,
2.26806402, 2.46439028, 2.67713213, 2.90757871,
3.15710831, 3.42719173, 3.71939874, 4.03540039,
4.37697268, 4.74600172, 5.14448643, 5.57454014,
6.03839302, 6.5383954, 7.07701445, 7.65683603,
8.28056145, 8.95100403, 9.67108345, 10.4438162,
11.2723074, 12.1597347, 13.1093397, 14.1243973,
15.2081976, 16.3640213, 17.5950966, 18.9045696,
20.2954617, 21.7706108, 23.3326225, 24.9838047,
26.7260971, 28.5609989, 30.4894753, 32.511879,
34.6278381, 36.836174, 39.1347733, 41.5204849,
43.9890137, 46.5348015, 49.1509132, 51.828949,
54.5589333, 57.3292618, 60.1266174, 62.935955,
65.7405014, 68.5217972, 71.2597733, 73.9328842,
76.5183411, 78.9923477, 81.3304749, 83.5080414,
85.5006638, 87.2848434, 88.8385849, 90.1422424,
91.1792221, 91.9369507, 92.4076996, 92.5894775,
92.4869461, 92.112114, 91.4850693, 90.6343994,
89.5974579, 88.4202957, 87.1572495, 85.8701706,
84.6270905, 83.5005417, 82.5653152, 81.8957672,
81.5626755, 81.6298218, 82.1502457, 83.1625443,
84.6872253, 86.7234268, 89.2463074, 92.2052536,
95.5233002, 99.0979156, 102.803383, 106.494949,
110.014687, 113.199059, 115.887917, 117.93454,
119.216202, 119.644577, 119.17514, 117.814651,
115.625893, 112.728798, 109.297203, 105.550888,
101.742867, 98.1422424, 95.0134811, 92.5936661,
91.0694427, 90.5558701, 91.0796356, 92.5688553,
94.851326, 97.6625671, 100.663872, 103.46962,
105.681839, 106.929024, 106.905228, 105.40519,
102.351059, 97.8071594, 91.9801865, 85.2037354,
77.9081345, 70.578186, 63.7033157, 57.7258224,
52.9934425, 49.722332, 47.9752312, 47.6580467,
48.5350647, 50.2607956, 52.423893, 54.5968742,
56.3847847, 57.4664154, 57.6231003, 56.752449,
54.866703, 52.0777321, 48.5722427, 44.5817566,
40.3518639, 36.1146812, 32.0673256, 28.3580551,
25.0802326, 22.273489, 19.9305019, 18.0075665,
16.4369278, 15.1391201, 14.0339012, 13.0488214,
12.1250029, 11.2201004, 10.3087597, 9.38113308,
8.44005108, 7.49750996, 6.57099962, 5.68010855,
4.84368563, 4.0777216, 3.39398646, 2.7993803,
2.29589605, 1.88105953, 1.54869676, 1.28988755,
1.09397805, 0.949547112, 0.845253229, 0.770512223,
0.715984941, 0.673874974, 0.638054609, 0.604046702,
0.568897545, 0.530975521, 0.489727706, 0.44542101,
0.398890644, 0.351309568, 0.303989798, 0.258221358,
0.215150192, 0.175695851, 0.140505522, 0.109940849,
0.0840920061, 0.0628127009, 0.0457692482, 0.0324965976,
0.0224549007, 0.015081034, 0.00983107835, 0.00621139724,
0.00379776093, 0.00224342081, 0.00127818808, 0.000701125304,
0.000369562156, 0.000186810314, 9.03692198e-05,
/* Z=68 -> Er */
0, 0.247885138, 0.270068645, 0.294220626,
0.320513338, 0.34913373, 0.380284667, 0.414186209,
0.451077074, 0.491216034, 0.534883559, 0.582383573,
0.634045243, 0.690224946, 0.751308382, 0.817712843,
0.889889479, 0.968326032, 1.05354917, 1.14612806,
1.24667585, 1.35585523, 1.47437906, 1.60301614,
1.74259317, 1.89399993, 2.05819201, 2.2361958,
2.42911196, 2.63812065, 2.86448479, 3.10955477,
3.3747735, 3.66167998, 3.97191358, 4.30721855,
4.66944695, 5.06056309, 5.48264551, 5.93789005,
6.42861128, 6.95724249, 7.52633667, 8.13856411,
8.79671001, 9.50366974, 10.2624388, 11.0761089,
11.947855, 12.8809156, 13.878582, 14.94417,
16.0809975, 17.2923565, 18.5814705, 19.9514599,
21.4052868, 22.945715, 24.5752392, 26.2960224,
28.1098232, 30.0179157, 32.0209961, 34.1191025,
36.3114891, 38.5965538, 40.9717026, 43.4332504,
45.9762917, 48.5946121, 51.280571, 54.0249825,
56.8170624, 59.6443405, 62.4926109, 65.3459167,
68.1865692, 70.9952087, 73.7508926, 76.4313049,
79.0129318, 81.471405, 83.7818604, 85.9194031,
87.8596573, 89.5793915, 91.0572357, 92.274437,
93.2157516, 93.8702927, 94.2324448, 94.3027496,
94.088768, 93.6057968, 92.8774567, 91.9361496,
90.8231125, 89.588295, 88.2897644, 86.9927292,
85.7680969, 84.6904907, 83.8358688, 83.2786102,
83.0881958, 83.3256302, 84.03965, 85.2629471,
87.0085983, 89.2669678, 92.0033264, 95.1564331,
98.6384735, 102.336372, 106.114899, 109.82148,
113.292809, 116.363098, 118.873619, 120.683212,
121.679024, 121.786774, 120.979752, 119.285522,
116.789429, 113.634239, 110.015099, 106.169647,
102.363358, 98.8706131, 95.9526901, 93.8341904,
92.6800308, 92.5752563, 93.5101776, 95.3729477,
97.951416, 100.945183, 103.987663, 106.677094,
108.613876, 109.440826, 108.882103, 106.776329,
103.09967, 97.9754181, 91.6679535, 84.5608902,
77.1208954, 69.850708, 63.2365303, 57.6959839,
53.5330124, 50.905735, 49.8113556, 50.0905151,
51.4502449, 53.5023613, 55.8117828, 57.9479752,
59.5324745, 60.2764397, 60.0040359, 58.6599274,
56.3015747, 53.079174, 49.2074814, 44.9341583,
40.5092125, 36.1590805, 32.0676537, 28.3654728,
25.1266823, 22.3727589, 20.0812244, 18.19734,
16.6468334, 15.3479767, 14.2217922, 13.1996336,
12.2278948, 11.2699728, 10.3059244, 9.33039761,
8.34949017, 7.3771286, 6.4314723, 5.53171396,
4.69550705, 3.9371295, 3.26639199, 2.68821645,
2.20277762, 1.80606163, 1.49069953, 1.24694085,
1.0636462, 0.929210782, 0.832350791, 0.76271534,
0.711310506, 0.670740247, 0.635285735, 0.600853443,
0.56482482, 0.525842369, 0.483561814, 0.438395709,
0.391267449, 0.343389571, 0.296074867, 0.250585109,
0.208018869, 0.169237435, 0.134826481, 0.105088808,
0.0800629705, 0.0595611595, 0.0432197452, 0.0305554178,
0.0210207235, 0.014053788, 0.00911851227, 0.00573327579,
0.00348784449, 0.00204963633, 0.00116148335, 0.000633543765,
0.000331998803, 0.000166808371, 8.01862261e-05,
/* Z=69 -> Tm */
0, 0.26868698, 0.29260397, 0.3186315,
0.346953183, 0.377768129, 0.411292344, 0.447760016,
0.487425029, 0.530562401, 0.577470183, 0.628471017,
0.683914244, 0.744177759, 0.809670389, 0.880834222,
0.958146811, 1.04212415, 1.13332331, 1.2323451,
1.33983791, 1.45650005, 1.58308375, 1.7203989,
1.86931646, 2.03077197, 2.20577049, 2.39539003,
2.60078645, 2.82319713, 3.06394529, 3.32444501,
3.60620546, 3.91083455, 4.24004412, 4.5956521,
4.97958851, 5.39389658, 5.84073591, 6.32238531,
6.84124327, 7.39982796, 8.00077629, 8.64684391,
9.34089661, 10.0859089, 10.8849554, 11.7411947,
12.6578674, 13.6382666, 14.6857309, 15.8036098,
16.9952393, 18.2639122, 19.6128368, 21.0450878,
22.5635681, 24.1709423, 25.8695793, 27.661478,
29.5481949, 31.5307522, 33.6095581, 35.7843056,
38.0538559, 40.4161491, 42.8680878, 45.405407,
48.022583, 50.7127151, 53.4674072, 56.2766953,
59.1289444, 62.0108109, 64.9071808, 67.8011856,
70.6742325, 73.5060577, 76.2749023, 78.9576645,
81.5301895, 83.9675903, 86.2446594, 88.3363647,
90.2184601, 91.8681183, 93.2647018, 94.3905563,
95.2318954, 95.7797318, 96.0307083, 95.9880829,
95.6624603, 95.0725479, 94.2456436, 93.2179871,
92.0347519, 90.7497253, 89.4246063, 88.1278076,
86.9328079, 85.9160385, 85.1541824, 84.7211533,
84.6845932, 85.1021423, 86.017601, 87.4571609,
89.4259109, 91.9049683, 94.8493423, 98.1870117,
101.81929, 105.622871, 109.453491, 113.151588,
116.549553, 119.480621, 121.789032, 123.34079,
124.034523, 123.811562, 122.664307, 120.642021,
117.852982, 114.462547, 110.686211, 106.777763,
103.012703, 99.6676865, 96.9973679, 95.2103348,
94.4464111, 94.7578659, 96.096756, 98.3106842,
101.14846, 104.276199, 107.303459, 109.817574,
111.42337, 111.784264, 110.660347, 107.938828,
103.652748, 97.984848, 91.2551727, 83.892746,
76.3937759, 69.2706146, 62.9973297, 57.9584198,
54.4071732, 52.4392624, 51.9850502, 52.8218842,
54.6044998, 56.909214, 59.2856445, 61.3086548,
62.6236115, 62.9794159, 62.245945, 60.4152222,
57.587944, 53.9489937, 49.7365532, 45.2096519,
40.6183739, 36.1800804, 32.0632782, 28.3798542,
25.1849194, 22.4828434, 20.2375565, 18.3850765,
16.8463192, 15.5387192, 14.385581, 13.3226328,
12.3016949, 11.2917233, 10.2777634, 9.25841713,
8.24247169, 7.24525118, 6.28514433, 5.38063002,
4.54797173, 3.79965496, 3.14354515, 2.58267069,
2.11551547, 1.73667502, 1.43773735, 1.20825922,
1.03673339, 0.911461413, 0.821280301, 0.756110966,
0.707321525, 0.667916536, 0.632575512, 0.597570121,
0.56059581, 0.52054745, 0.47726965, 0.431303084,
0.383645415, 0.335538208, 0.288287699, 0.243123055,
0.201093271, 0.163001314, 0.129372582, 0.100453302,
0.0762331113, 0.0564856417, 0.0408200845, 0.0287372842,
0.0196840856, 0.0131011894, 0.00846108329, 0.00529443799,
0.0032049031, 0.00187368365, 0.00105611281, 0.000572878867,
0.00029848158, 0.000149071348, 7.12141773e-05,
/* Z=70 -> Yb */
0, 0.291215748, 0.316996723, 0.345039815,
0.375540614, 0.408711165, 0.444781303, 0.484000146,
0.526637495, 0.572985709, 0.623360991, 0.67810595,
0.737590909, 0.802216589, 0.872416019, 0.948657155,
1.03144526, 1.12132597, 1.21888769, 1.32476532,
1.43964243, 1.56425583, 1.69939816, 1.84592211,
2.00474405, 2.1768477, 2.36328912, 2.56519961,
2.78379178, 3.0203619, 3.2762959, 3.55307293,
3.85226989, 4.17556572, 4.52474499, 4.90170288,
5.30844641, 5.7470994, 6.21990395, 6.72922182,
7.27753544, 7.86744833, 8.50168133, 9.18307114,
9.91456699, 10.6992178, 11.5401716, 12.4406567,
13.4039688, 14.4334555, 15.5324898, 16.7044487,
17.9526806, 19.2804642, 20.6909828, 22.1872559,
23.7721024, 25.4480801, 27.2174072, 29.0819035,
31.0428944, 33.1011391, 35.2567253, 37.5089722,
39.8563194, 42.2962303, 44.8250656, 47.4379616,
50.1287422, 52.889782, 55.7119293, 58.5843925,
61.4946861, 64.428566, 67.3700104, 70.301239,
73.2027435, 76.0534058, 78.8306427, 81.510643,
84.0686569, 86.4793243, 88.7172012, 90.7572327,
92.575386, 94.1493912, 95.4594803, 96.4892654,
97.2265854, 97.6644974, 97.802124, 97.6455383,
97.20858, 96.5134659, 95.5912704, 94.4821243,
93.2351303, 91.9078751, 90.5655289, 89.2795029,
88.1256027, 87.1816406, 86.5246353, 86.2275085,
86.355484, 86.9622574, 88.0860748, 89.7460403,
91.938736, 94.6355667, 97.7810135, 101.292137,
105.05954, 108.949951, 112.810783, 116.476334,
119.775841, 122.542999, 124.626534, 125.901222,
126.278816, 125.71769, 124.230499, 121.888924,
118.824371, 115.224274, 111.323242, 107.389236,
103.70517, 100.546799, 98.1586838, 96.729866,
96.3719711, 97.1019974, 98.8323441, 101.370018,
104.426247, 107.636703, 110.59153, 112.872742,
114.095741, 113.950691, 112.239052, 108.900612,
104.027222, 97.8606339, 90.7734985, 83.2347717,
75.762764, 68.8708344, 63.0121422, 58.5302277,
55.6218033, 54.3169594, 54.4792366, 55.8259277,
57.9653816, 60.4462013, 62.8111801, 64.6486206,
65.6342697, 65.5590973, 64.3404922, 62.0171585,
58.7303276, 54.6954842, 50.1695328, 45.4182587,
40.6879196, 36.1839409, 32.0577927, 28.4022598,
25.2539482, 22.6013641, 20.3964958, 18.5678291,
17.0330429, 15.7099609, 14.524991, 13.4186268,
12.3481302, 11.2877493, 10.227066, 9.16810036,
8.12178707, 7.10437298, 6.13410282, 5.2284832,
4.40224504, 3.66604018, 3.0258286, 2.48284197,
2.03400445, 1.6726644, 1.38950658, 1.17352092,
1.01293409, 0.896031916, 0.81182456, 0.750533879,
0.703901172, 0.665328562, 0.629880846, 0.594177008,
0.556205809, 0.51509434, 0.470857531, 0.42414856,
0.37602675, 0.327753395, 0.280621678, 0.235824406,
0.194359347, 0.156971171, 0.124126367, 0.0960166901,
0.0725855231, 0.0535705909, 0.0385565162, 0.0270304903,
0.0184353702, 0.0122156125, 0.00785296038, 0.00489058346,
0.00294587901, 0.00171347032, 0.000960698759, 0.000518260116,
0.000268482981, 0.00013329339, 6.32836382e-05,
/* Z=71 -> Lu */
0, 0.315639436, 0.343426526, 0.373637587,
0.406480938, 0.442182213, 0.48098594, 0.523156881,
0.568981826, 0.618771136, 0.672860444, 0.731613159,
0.795421839, 0.864710987, 0.939939141, 1.02160132,
1.11023188, 1.20640755, 1.31074953, 1.42392766,
1.54666328, 1.67973268, 1.82397056, 1.98027432,
2.14960718, 2.33300328, 2.53157091, 2.74649739,
2.97905278, 3.23059511, 3.50257421, 3.79653597,
4.11412716, 4.45709848, 4.82731056, 5.22673464,
5.65745831, 6.12168646, 6.62174368, 7.16007566,
7.73924971, 8.36195183, 9.03098869, 9.74927711,
10.5198441, 11.3458157, 12.2304068, 13.1769104,
14.1886749, 15.2690926, 16.4215698, 17.6494999,
18.9562283, 20.3450184, 21.819006, 23.3811474,
25.0341644, 26.7804832, 28.6221581, 30.5608006,
32.597496, 34.7327003, 36.9661674, 39.2968102,
41.7226257, 44.2405624, 46.8464127, 49.534687,
52.2985229, 55.1295586, 58.0178413, 60.9517479,
63.9179115, 66.9011841, 69.8846283, 72.8495483,
75.7755432, 78.6406479, 81.4215012, 84.0936203,
86.6317139, 89.0100555, 91.2030334, 93.1856613,
94.9342957, 96.4273224, 97.6460114, 98.5753937,
99.2051315, 99.5304794, 99.5531998, 99.2823792,
98.7352066, 97.937561, 96.9243546, 95.7396698,
94.4365234, 93.0762024, 91.7272263, 90.4637909,
89.3636932, 88.5057831, 87.9669113, 87.8185043,
88.1227875, 88.9288788, 90.2688675, 92.1541595,
94.5723038, 97.4845734, 100.824638, 104.498573,
108.38633, 112.345169, 116.214767, 119.824272,
123.000977, 125.580437, 127.41748, 128.397354,
128.446533, 127.541931, 125.717644, 123.068481,
119.749184, 115.968719, 111.979553, 108.061821,
104.503098, 101.575043, 99.5084915, 98.4693298,
98.53759, 99.6923294, 101.804588, 104.640343,
107.874268, 111.114227, 113.93499, 115.918411,
116.696404, 115.991989, 113.653587, 109.678078,
104.218964, 97.5776825, 90.1778488, 82.5243759,
75.1517105, 68.5668106, 63.1938133, 59.3273506,
57.1007118, 56.4733124, 57.2391586, 59.0552483,
61.4857941, 64.0559082, 66.307251, 67.8479919,
68.3908081, 67.7749023, 65.9705048, 63.0674019,
59.2506714, 54.7686691, 49.8982697, 44.9122009,
40.0520935, 35.5096397, 31.4165344, 27.8429279,
24.8028183, 22.2644882, 20.1637325, 18.4177742,
16.9381561, 15.6413288, 14.4562769, 13.3289671,
12.2238798, 11.1231127, 10.0237589, 8.9342432,
7.87029219, 6.85104322, 5.89569187, 5.02089453,
4.23902893, 3.55728388, 2.97748804, 2.496526,
2.10716867, 1.79914939, 1.560323, 1.37778175,
1.23882985, 1.13175476, 1.04636884, 0.97432375,
0.909217775, 0.846535802, 0.783465147, 0.718630672,
0.651791036, 0.583527088, 0.514948726, 0.447436363,
0.382426739, 0.321247786, 0.265001923, 0.214495316,
0.170207649, 0.132296324, 0.10062743, 0.0748258457,
0.0543366186, 0.0384901278, 0.0265645254, 0.0178402215,
0.0116429236, 0.00737349736, 0.00452467892, 0.00268611009,
0.00154015969, 0.000851454271, 0.000453023385, 0.000231533966,
0.000113442118, 5.31726437e-05, 2.37904005e-05,
/* Z=72 -> Hf */
0, 0.342106819, 0.372051656, 0.404593199,
0.439953089, 0.478371471, 0.520108223, 0.565444827,
0.614685714, 0.668160319, 0.72622484, 0.789264262,
0.857694745, 0.931965649, 1.01256216, 1.10000765,
1.19486725, 1.29774952, 1.40931046, 1.53025651,
1.66134775, 1.80340159, 1.95729685, 2.12397671,
2.30445409, 2.49981403, 2.71121955, 2.93991494,
3.18723059, 3.45458746, 3.74350071, 4.05558538,
4.39255857, 4.75624609, 5.14858389, 5.57162237,
6.02752876, 6.51859045, 7.04721546, 7.61593342,
8.22739601, 8.88437176, 9.58975029, 10.3465281,
11.1578083, 12.0267878, 12.956749, 13.9510403,
15.0130606, 16.1462402, 17.3540058, 18.6397591,
20.0068378, 21.4584713, 22.9977417, 24.6275196,
26.3504143, 28.1687031, 30.0842552, 32.0984573,
34.2121201, 36.4253883, 38.7376366, 41.1473618,
43.6520767, 46.248188, 48.9308968, 51.6940575,
54.5300903, 57.4298706, 60.3826332, 63.3758888,
66.3953857, 69.4250565, 72.447052, 75.4417572,
78.3879013, 81.2626877, 84.0420456, 86.7008514,
89.2133408, 91.5535126, 93.6956635, 95.6150284,
97.2884445, 98.6951218, 99.8175278, 100.64225,
101.160957, 101.371277, 101.277771, 100.892693,
100.23671, 99.3394547, 98.2397461, 96.9856339,
95.6339798, 94.2496948, 92.9044571, 91.6749649,
90.6406784, 89.8810577, 89.4723053, 89.4838028,
89.9741745, 90.9873657, 92.5487061, 94.6613617,
97.3033829, 100.425583, 103.950661, 107.773697,
111.764381, 115.770973, 119.626266, 123.15535,
126.184914, 128.553909, 130.124847, 130.795151,
130.507523, 129.258636, 127.104988, 124.164879,
120.616013, 116.687897, 112.649078, 108.789352,
105.39785, 102.738579, 101.024986, 100.396362,
100.898239, 102.469749, 104.939903, 108.034477,
111.394096, 114.602814, 117.225304, 118.849518,
119.130386, 117.829857, 114.848282, 110.242767,
104.229317, 97.1672516, 89.5266647, 81.8416977,
74.6544647, 68.4563522, 63.6335602, 60.4243774,
58.8935623, 58.9278412, 60.2529526, 62.4700203,
65.1060028, 67.6709671, 69.7143021, 70.8721924,
70.9008179, 69.6919556, 67.2706604, 63.7774239,
59.4389725, 54.5329742, 49.3520203, 44.1714478,
39.2242775, 34.6851997, 30.6637878, 27.2061577,
24.3032341, 21.9033966, 19.9271393, 18.2816887,
16.8738422, 15.6199789, 14.4526777, 13.3239813,
12.2056732, 11.0872526, 9.97238541, 8.87457275,
7.81274891, 6.80730057, 5.87685299, 5.03600168,
4.29401922, 3.6544385, 3.11536598, 2.67032003,
2.30938411, 2.02048302, 1.79061985, 1.60695696,
1.45766306, 1.33249843, 1.22313964, 1.12327647,
1.02852345, 0.936204195, 0.845054686, 0.754894674,
0.666300356, 0.580305398, 0.498144716, 0.421050519,
0.350100815, 0.286119401, 0.229621574, 0.180799127,
0.139537036, 0.105454028, 0.0779587403, 0.0563139804,
0.0397019461, 0.0272845943, 0.0182544924, 0.0118733821,
0.00749731483, 0.00458886102, 0.00271818554, 0.00155560672,
0.000858619926, 0.000456223468, 0.000232907667, 0.00011400666,
5.33927923e-05, 2.38704215e-05, 1.01632049e-05,
/* Z=73 -> Ta */
0, 0.370798081, 0.403064162, 0.438111186,
0.47617504, 0.517510951, 0.562395215, 0.611126721,
0.664028645, 0.721450508, 0.783769965, 0.851394951,
0.924766064, 1.00435889, 1.09068656, 1.18430245,
1.28580296, 1.39583087, 1.51507783, 1.64428854,
1.78426349, 1.93586326, 2.10001159, 2.27770019,
2.46999216, 2.67802644, 2.90302181, 3.14628172,
3.40919828, 3.69325709, 4.00004101, 4.33123446,
4.6886282, 5.07412291, 5.48973179, 5.93758488,
6.41993141, 6.93914032, 7.49770403, 8.09823608,
8.74347115, 9.43626118, 10.179575, 10.9764872,
11.8301754, 12.7439032, 13.721015, 14.7649107,
15.879034, 17.0668411, 18.3317757, 19.6772385,
21.1065426, 22.6228733, 24.2292442, 25.9284248,
27.7228928, 29.6147594, 31.6056881, 33.6968155,
35.8886604, 38.181015, 40.5728645, 43.062252,
45.6461754, 48.320488, 51.0797501, 53.9171448,
56.8243446, 59.7914391, 62.8068161, 65.8571243,
68.9271927, 72.0000458, 75.0569153, 78.0772858,
81.0390244, 83.9185638, 86.691124, 89.3310242,
91.8121033, 94.1081619, 96.1935425, 98.0437775,
99.6363373, 100.951424, 101.972832, 102.688889,
103.09343, 103.186638, 102.976021, 102.477127,
101.714256, 100.720871, 99.5397263, 98.2228317,
96.8308563, 95.4321518, 94.1013565, 92.9173965,
91.9610291, 91.3118515, 91.0449371, 91.2270279,
91.9125824, 93.1397476, 94.9265213, 97.2673111,
100.130249, 103.455406, 107.154411, 111.111519,
115.186462, 119.219193, 123.036552, 126.460716,
129.319183, 131.455887, 132.742645, 133.090622,
132.460236, 130.86911, 128.396744, 125.185097,
121.434311, 117.39315, 113.34417, 109.584084,
106.400337, 104.04567, 102.712563, 102.510361,
103.447571, 105.421898, 108.220169, 111.529427,
114.959251, 118.074417, 120.435303, 121.642281,
121.37973, 119.454277, 115.822571, 110.604263,
104.077629, 96.6570206, 88.8535843, 81.2230682,
74.3063583, 68.5699158, 64.353508, 61.8323364,
60.9986458, 61.6657448, 63.4937439, 66.0335464,
68.7827225, 71.2453308, 72.9874725, 73.6813049,
73.1325226, 71.2890701, 68.2319336, 64.1511688,
59.3121376, 54.017662, 48.5713272, 43.2463799,
38.2630005, 33.7754784, 29.8688526, 26.5638332,
23.8278618, 21.5897884, 19.7558022, 18.2244473,
16.8992043, 15.6976576, 14.5569592, 13.4357576,
12.3132029, 11.1858025, 10.0630217, 8.96245384,
7.90519571, 6.91195774, 6.00014448, 5.18203449,
4.4639883, 3.84652948, 3.32508039, 2.89111018,
2.53347039, 2.23972011, 1.99729955, 1.79446208,
1.6209234, 1.46823204, 1.3298912, 1.20128703,
1.07947695, 0.962898791, 0.851045012, 0.744142294,
0.642860591, 0.548067451, 0.460634798, 0.381297737,
0.310563475, 0.248663232, 0.195541084, 0.150871426,
0.11409805, 0.0844872296, 0.0611873493, 0.0432893857,
0.029882418, 0.0201002937, 0.0131568136, 0.00836835802,
0.00516439183, 0.00308747427, 0.00178514805, 0.000996500603,
0.000536069623, 0.000277378887, 0.000137771945, 6.55489785e-05,
2.98074829e-05, 1.29249129e-05, 5.33101593e-06,
/* Z=74 -> W */
0, 0.401910275, 0.43667385, 0.474414945,
0.515384376, 0.559853435, 0.608115673, 0.660488367,
0.717314482, 0.77896452, 0.845838726, 0.918369114,
0.997022092, 1.08230054, 1.17474711, 1.27494597,
1.38352704, 1.50116813, 1.62859845, 1.76660216,
1.9160223, 2.0777638, 2.25279737, 2.4421649,
2.64698124, 2.8684411, 3.10782099, 3.36648488,
3.64588881, 3.94758439, 4.2732234, 4.62456274,
5.00346661, 5.41191244, 5.85199213, 6.32591581,
6.83601522, 7.38474226, 7.97467279, 8.6085043,
9.28905296, 10.0192537, 10.8021526, 11.6409006,
12.538744, 13.499012, 14.5251036, 15.6204681,
16.7885799, 18.0329189, 19.3569355, 20.7640152,
22.2574387, 23.8403339, 25.5156231, 27.2859669,
29.1536884, 31.1207142, 33.1884766, 35.3578415,
37.6290054, 40.0014, 42.4735718, 45.043087,
47.7064171, 50.4588013, 53.2941628, 56.2049599,
59.1821098, 62.2148819, 65.2908096, 68.3956451,
71.5133133, 74.6259079, 77.7137451, 80.7554398,
83.7280121, 86.6071548, 89.3674469, 91.9827042,
94.4264526, 96.6723862, 98.6949997, 100.470268,
101.976418, 103.194794, 104.11068, 104.714348,
105.001923, 104.976318, 104.648148, 104.036423,
103.169121, 102.083611, 100.82666, 99.4541702,
98.0305176, 96.6273727, 95.3220596, 94.1954117,
93.3290787, 92.8023758, 92.6886597, 93.0514908,
93.9405518, 95.3875885, 97.4027176, 99.9710999,
103.050568, 106.570251, 110.430687, 114.505508,
118.644958, 122.68145, 126.436852, 129.731705,
132.395782, 134.279541, 135.265823, 135.281036,
134.304657, 132.376266, 129.598892, 126.138031,
122.215446, 118.097603, 114.078773, 110.459648,
107.522591, 105.50544, 104.57618, 104.81118,
106.179672, 108.536919, 111.627998, 115.103241,
118.544807, 121.503258, 123.540642, 124.276283,
123.430267, 120.859238, 116.579773, 110.775452,
103.78566, 96.0758438, 88.1918182, 80.7026825,
74.1388092, 68.9325104, 65.3690643, 63.5547867,
63.4066238, 64.6651077, 66.9286957, 69.7048416,
72.4703827, 74.7327499, 76.0837479, 76.2389755,
75.0589371, 72.5505219, 68.8508224, 64.1973953,
58.8905678, 53.2535782, 47.5958519, 42.1835861,
37.2198334, 32.8350868, 29.0875473, 25.9713192,
23.4301357, 21.3739338, 19.6957569, 18.2869396,
17.0491467, 15.9024916, 14.7896729, 13.676487,
12.5495396, 11.4120607, 10.2787828, 9.17074299,
8.11062717, 7.1190958, 6.21227026, 5.40040255,
4.68757582, 4.0722146, 3.5481391, 3.10589862,
2.73416018, 2.42097521, 2.15481377, 1.92531025,
1.72371852, 1.54310036, 1.37830675, 1.22580636,
1.08342516, 0.950045168, 0.825301707, 0.709308445,
0.602423251, 0.505062997, 0.41756767, 0.3401106,
0.27264896, 0.214907661, 0.166390285, 0.126409784,
0.0941327214, 0.0686305389, 0.0489326194, 0.0340758637,
0.0231473017, 0.0153168663, 0.00985912606, 0.00616395287,
0.00373727456, 0.00219389284, 0.00124478969, 0.000681421894,
0.0003592172, 0.000181995347, 8.84349793e-05, 4.11247674e-05,
1.82602253e-05, 7.72309886e-06, 3.10361497e-06,
/* Z=75 -> Re */
0, 0.435660452, 0.473111749, 0.513750196,
0.557842493, 0.605676949, 0.657565176, 0.713843822,
0.774876654, 0.841056347, 0.912806869, 0.990585566,
1.07488585, 1.16623914, 1.26521885, 1.37244165,
1.48857236, 1.61432505, 1.75046849, 1.89782798,
2.05729032, 2.22980642, 2.41639662, 2.61815357,
2.83624673, 3.07192731, 3.32653189, 3.60148692,
3.89831376, 4.21863174, 4.56416321, 4.93673849,
5.33829737, 5.77089453, 6.23670197, 6.73801184,
7.27723694, 7.85691309, 8.47969913, 9.14837551,
9.86584187, 10.6351099, 11.4593039, 12.3416471,
13.28545, 14.2941036, 15.3710585, 16.5197983,
17.7438316, 19.0466461, 20.4316921, 21.9023266,
23.4617844, 25.1131191, 26.8591537, 28.7024136,
30.6450539, 32.6887894, 34.8348045, 37.0836678,
39.4352303, 41.8885193, 44.4416389, 47.0916443,
49.8344383, 52.6646385, 55.5754776, 58.5586815,
61.6043777, 64.7009964, 67.8352051, 70.9918365,
74.1539001, 77.3025742, 80.4172745, 83.4757233,
86.4541779, 89.3276062, 92.0699921, 94.654747,
97.0551453, 99.2448883, 101.198738, 102.89325,
104.307549, 105.424271, 106.23037, 106.718201,
106.886368, 106.740692, 106.295013, 105.571907,
104.60318, 103.430153, 102.103561, 100.683197,
99.2370071, 97.8397598, 96.5712433, 95.5138245,
94.7496414, 94.3572006, 94.4076233, 94.9606934,
96.0606995, 97.7324371, 99.9775696, 102.771568,
106.061653, 109.765862, 113.773682, 117.948418,
122.131439, 126.148392, 129.817307, 132.95842,
135.405273, 137.016479, 137.687515, 137.361526,
136.038345, 133.780289, 130.714279, 127.029022,
122.966843, 118.810081, 114.862244, 111.424896,
108.771828, 107.122353, 106.616562, 107.295067,
109.085983, 111.801537, 115.146042, 118.735649,
122.129272, 124.868584, 126.523521, 126.738838,
125.276299, 122.04731, 117.131241, 110.776161,
103.380318, 95.4554214, 87.5748215, 80.3122253,
74.1781235, 69.5617905, 66.6867218, 65.5856476,
66.0987701, 67.8958282, 70.5188675, 73.4396133,
76.1233902, 78.0905457, 78.9671707, 78.519165,
76.6661911, 73.4757385, 69.1401443, 63.941494,
58.2105255, 52.2855072, 46.4761696, 41.0364838,
36.1480064, 31.9141979, 28.3643684, 25.4652061,
23.1370144, 21.2719421, 19.7515945, 18.4620705,
17.3051758, 16.2052593, 15.1118431, 13.9986591,
12.8600683, 11.7059135, 10.5558186, 9.43377686,
8.36359978, 7.36559296, 6.4545188, 5.63877344,
4.92055464, 4.29673433, 3.7601409, 3.30098653,
2.90822816, 2.57071996, 2.27808094, 2.02125978,
1.79281831, 1.58698773, 1.39955497, 1.22764504,
1.06945014, 0.923950672, 0.79065454, 0.669373274,
0.560042262, 0.46258688, 0.376831502, 0.302445233,
0.238920018, 0.185573503, 0.141571254, 0.105962329,
0.0777227655, 0.0558017157, 0.039166037, 0.0268392954,
0.0179326218, 0.0116657643, 0.00737797702, 0.00452944404,
0.00269484683, 0.00155120948, 0.000862353307, 0.000462139898,
0.000238282417, 0.000117966047, 5.59554646e-05, 2.53733433e-05,
1.09734747e-05, 4.51518599e-06, 1.76300284e-06,
/* Z=76 -> Os */
0, 0.472284257, 0.512628317, 0.556383252,
0.603832424, 0.655281961, 0.71106267, 0.771531701,
0.837074578, 0.908107281, 0.985078752, 1.06847274,
1.15881097, 1.25665522, 1.36261046, 1.47732794,
1.60150802, 1.73590374, 1.88132393, 2.0386374,
2.208776, 2.39273882, 2.59159684, 2.8064959,
3.03866148, 3.28940344, 3.56011987, 3.8523016,
4.16753674, 4.507514, 4.87402821, 5.26898432,
5.6943984, 6.15240479, 6.64525509, 7.17532349,
7.74510622, 8.3572216, 9.01441193, 9.71953964,
10.4755831, 11.285634, 12.1528893, 13.0806398,
14.0722599, 15.1311951, 16.2609367, 17.4650059,
18.7469273, 20.1101952, 21.5582371, 23.0943813,
24.7217941, 26.443449, 28.262043, 30.1799507,
32.1991386, 34.3210907, 36.5467148, 38.8762627,
41.3092079, 43.8441582, 46.4787331, 49.2094498,
52.0316162, 54.9391937, 57.9247093, 60.979126,
64.0917587, 67.2501678, 70.4401398, 73.6455917,
76.8486099, 80.0294571, 83.1666489, 86.2370758,
89.2162323, 92.0784073, 94.7970886, 97.3453217,
99.6962509, 101.823677, 103.702766, 105.310768,
106.627876, 107.638161, 108.330437, 108.699287,
108.745987, 108.479378, 107.91671, 107.084221,
106.017609, 104.762192, 103.372681, 101.912651,
100.453484, 99.0728455, 97.8526535, 96.8764725,
96.2264557, 95.9797974, 96.2048264, 96.956955,
98.2744827, 100.174667, 102.650238, 105.666557,
109.159981, 113.037361, 117.177299, 121.433182,
125.638107, 129.611923, 133.169983, 136.133636,
138.341751, 139.662704, 140.006165, 139.333527,
137.665924, 135.089233, 131.754257, 127.872337,
123.705048, 119.548523, 115.712738, 112.496902,
110.162582, 108.907051, 108.839302, 109.961647,
112.159714, 115.202682, 118.755669, 122.403816,
125.687439, 128.145096, 129.361115, 129.011993,
126.90686, 123.016037, 117.48381, 110.622177,
102.88504, 94.8245392, 87.0336227, 80.0814438,
74.4491196, 70.4743805, 68.312439, 67.9188309,
69.0568542, 71.328804, 74.2266769, 77.1950836,
79.697525, 81.2767334, 81.6014023, 80.493782,
77.9361877, 74.057457, 69.1034012, 63.3968887,
57.2940025, 51.142334, 45.2462425, 39.8423691,
35.0866203, 31.0524673, 27.7386913, 25.0841007,
22.9861641, 21.3205986, 19.9593716, 18.7852993,
17.7021332, 16.6399307, 15.5560427, 14.4326782,
13.2720747, 12.0905342, 10.9122734, 9.76396561,
8.67042351, 7.6516819, 6.72146606, 5.88684177,
5.14877558, 4.50327826, 3.94281864, 3.4577632,
3.03765655, 2.6722374, 2.35214877, 2.0693543,
1.8173033, 1.59090614, 1.38638151, 1.20103586,
1.03301597, 0.881070793, 0.744339824, 0.622179031,
0.514026701, 0.419307739, 0.337372065, 0.267462283,
0.208704874, 0.160120383, 0.120647117, 0.0891741961,
0.0645788237, 0.04576426, 0.0316944607, 0.0214226581,
0.0141118784, 0.00904649962, 0.00563503336, 0.0034051782,
0.00199290877, 0.00112767436, 0.000615799625, 0.000323913235,
0.000163789955, 7.94530788e-05, 3.68936489e-05, 1.63612931e-05,
6.91303558e-06, 2.77597883e-06, 1.05661775e-06,
/* Z=77 -> Ir */
0, 0.512041748, 0.555499911, 0.602607548,
0.653665662, 0.708999336, 0.768959403, 0.833924472,
0.904303193, 0.980536044, 1.06309795, 1.15250075,
1.24929535, 1.35407543, 1.46747935, 1.59019375,
1.7229569, 1.86656165, 2.02185917, 2.18976283,
2.37125206, 2.56737542, 2.77925611, 3.00809479,
3.25517559, 3.52186823, 3.80963421, 4.12002993,
4.45471239, 4.81544161, 5.20408583, 5.62262535,
6.07315493, 6.55788803, 7.07915831, 7.63942099,
8.24125576, 8.88736439, 9.58057117, 10.3238182,
11.1201639, 11.9727736, 12.8849154, 13.8599453,
14.9012947, 16.0124569, 17.1969624, 18.4583569,
19.8001728, 21.2259007, 22.7389374, 24.3425617,
26.0398674, 27.8337154, 29.726675, 31.7209435,
33.8182755, 36.0199051, 38.3264389, 40.7377815,
43.2530098, 45.8702736, 48.586689, 51.398201,
54.2994957, 57.2838516, 60.3430595, 63.4672928,
66.6450195, 69.8629532, 73.1059494, 76.3570099,
79.5973053, 82.8061676, 85.9612579, 89.0386581,
92.0131149, 94.8583374, 97.5473404, 100.052933,
102.348183, 104.407127, 106.20546, 107.721268,
108.935989, 109.835258, 110.409927, 110.656998,
110.580544, 110.192596, 109.513939, 108.574577,
107.414192, 106.082069, 104.636871, 103.145866,
101.683708, 100.330688, 99.1705627, 98.2876587,
97.7636871, 97.673996, 98.0835648, 99.0428162,
100.583481, 102.714752, 105.419899, 108.65387,
112.341927, 116.379753, 120.635277, 124.952454,
129.156876, 133.063583, 136.486557, 139.24968,
141.19873, 142.213486, 142.21936, 141.197205,
139.190598, 136.309235, 132.727829, 128.679428,
124.44326, 120.326973, 116.644058, 113.687927,
111.704376, 110.865143, 111.245071, 112.806122,
115.390419, 118.724701, 122.436974, 126.085129,
129.195923, 131.311005, 132.035446, 131.083817,
128.317795, 123.770103, 117.651077, 110.33519,
102.327759, 94.2146378, 86.5998764, 80.0385513,
74.9731369, 71.6818619, 70.2460861, 70.5418243,
72.2566376, 74.9300079, 78.0113449, 80.9274368,
83.1498871, 84.2531815, 83.9562836, 82.1430817,
78.8610001, 74.2999649, 68.7565689, 62.5899315,
56.1758118, 49.8650627, 43.9508133, 38.6472816,
34.0807686, 30.2921028, 27.2482586, 24.860157,
23.0034275, 21.5390759, 20.3315468, 19.2625256,
18.2396584, 17.2002468, 16.1105442, 14.9618168,
13.7643957, 12.5409946, 11.3202877, 10.1315212,
9.00051975, 7.9472332, 6.98467922, 6.11903,
5.35049248, 4.67463827, 4.08388758, 3.56891561,
3.11983395, 2.72708201, 2.38200855, 2.0771842,
1.80649626, 1.56508744, 1.34920168, 1.15598524,
0.983276308, 0.829411745, 0.693059206, 0.573082864,
0.468441665, 0.378117651, 0.301070571, 0.236214757,
0.182414308, 0.138492405, 0.103251107, 0.0754979253,
0.0540752448, 0.0378893912, 0.0259360895, 0.0173200611,
0.0112672942, 0.00712947734, 0.00438106898, 0.00261020847,
0.00150522531, 0.000838659762, 0.00045063076, 0.000233057566,
0.00011577941, 5.51319026e-05, 2.5108011e-05, 1.09106177e-05,
4.51289225e-06, 1.77223546e-06, 6.59003774e-07,
/* Z=78 -> Pt */
0, 0.555177689, 0.601985514, 0.652697086,
0.707631946, 0.767135024, 0.831578434, 0.901363373,
0.976922512, 1.05872214, 1.14726448, 1.24309051,
1.34678233, 1.45896626, 1.58031559, 1.71155417,
1.85345936, 2.00686574, 2.17266822, 2.35182643,
2.54536867, 2.75439525, 2.98008323, 3.22369051,
3.48655963, 3.770123, 4.07590723, 4.4055357,
4.76073551, 5.14333916, 5.55529022, 5.99864531,
6.47557831, 6.98838282, 7.53947401, 8.13138962,
8.76679134, 9.44846439, 10.1793118, 10.9623556,
11.8007317, 12.6976757, 13.6565237, 14.6806898,
15.7736597, 16.9389668, 18.1801739, 19.5008392,
20.9044991, 22.3946209, 23.9745655, 25.6475449,
27.4165592, 29.2843533, 31.253336, 33.3255081,
35.5024033, 37.7849655, 40.1734886, 42.6674957,
45.2656403, 47.9655914, 50.7639236, 53.6559944,
56.6358299, 59.6960068, 62.8275414, 66.0198059,
69.2604218, 72.5351868, 75.8280563, 79.1211166,
82.3946075, 85.6269684, 88.7950058, 91.8740311,
94.8381195, 97.6604309, 100.313622, 102.770287,
105.003609, 106.987938, 108.699631, 110.117783,
111.225182, 112.009262, 112.463043, 112.586067,
112.385429, 111.87648, 111.083611, 110.040703,
108.791412, 107.389053, 105.896133, 104.383453,
102.928719, 101.614616, 100.526299, 99.7484818,
99.361908, 99.4395294, 100.042374, 101.215302,
102.982918, 105.345802, 108.27742, 111.722,
115.593628, 119.776962, 124.129646, 128.486816,
132.667526, 136.483185, 139.747757, 142.289276,
143.962051, 144.658875, 144.322327, 142.953918,
140.620316, 137.455307, 133.656784, 129.478287,
125.21463, 121.182137, 117.694489, 115.035591,
113.431732, 113.02565, 113.8554, 115.840881,
118.780533, 122.360008, 126.173317, 129.755768,
132.626511, 134.336823, 134.519394, 132.932922,
129.496155, 124.306808, 117.641121, 109.933022,
101.733551, 93.6543884, 86.3012924, 80.2056198,
75.7623901, 73.1835556, 72.4728394, 73.4264374,
75.6595154, 78.6551285, 81.8287125, 84.5988464,
86.4544907, 87.0096664, 86.0389709, 83.4905014,
79.4766159, 74.2457199, 68.1409912, 61.5527878,
54.8716164, 48.4473801, 42.5590096, 37.3967781,
33.0572739, 29.549736, 26.8110809, 24.7263012,
23.1508579, 21.9319706, 20.9264545, 20.0136127,
19.1026878, 18.1351147, 17.0825195, 15.9417381,
14.7281723, 13.468791, 12.1956797, 10.9408369,
9.7324543, 8.59275532, 7.5371418, 6.57438898,
5.70751047, 4.93498421, 4.25206757, 3.65201712,
3.12709999, 2.66935635, 2.27111197, 1.92527878,
1.6254921, 1.36613345, 1.14228725, 0.94966203,
0.784502804, 0.643508136, 0.523757637, 0.422652811,
0.33787024, 0.267323971, 0.209135845, 0.161612287,
0.123225428, 0.0925985277, 0.0684947148, 0.0498088822,
0.0355612263, 0.0248924717, 0.0170592293, 0.0114289857,
0.00747389579, 0.0047630854, 0.00295337732, 0.00177868886,
0.0010386405, 0.000586976879, 0.000320435734, 0.000168642684,
8.53901001e-05, 4.15078503e-05, 1.93270116e-05, 8.60000455e-06,
3.64816219e-06, 1.47159074e-06, 5.62967443e-07,
/* Z=79 -> Au */
0, 0.602082193, 0.652500808, 0.707094669,
0.766202986, 0.830191493, 0.899454713, 0.974417686,
1.05553854, 1.14331043, 1.23826444, 1.34097195,
1.45204759, 1.57215226, 1.70199573, 1.84234035,
1.99400461, 2.157866, 2.33486581, 2.52601147,
2.73238158, 2.95513034, 3.19549036, 3.45477819,
3.73439789, 4.03584576, 4.36071491, 4.71069813,
5.08759403, 5.49330902, 5.9298625, 6.39938974,
6.90414429, 7.44650126, 8.02895641, 8.65413189,
9.32477093, 10.0437384, 10.8140192, 11.6387119,
12.5210238, 13.4642639, 14.4718285, 15.5471859,
16.6938705, 17.9154472, 19.2155037, 20.5976067,
22.065279, 23.6219578, 25.2709503, 27.0153904,
28.8581696, 30.8018913, 32.8487854, 35.0006523,
37.2587509, 39.6237373, 42.0955505, 44.6733093,
47.3552208, 50.1384354, 53.0189629, 55.991539,
59.0494995, 62.1846924, 65.387352, 68.6459961,
71.9473724, 75.2763977, 78.6160812, 81.9475861,
85.2502289, 88.5015869, 91.6776352, 94.7529373,
97.7009506, 100.494362, 103.105499, 105.506927,
107.671982, 109.575478, 111.19455, 112.509483,
113.50457, 114.169197, 114.498711, 114.495438,
114.169548, 113.539886, 112.634598, 111.491501,
110.158272, 108.692207, 107.159622, 105.63472,
104.198059, 102.934357, 101.929878, 101.269241,
101.031738, 101.287369, 102.092628, 103.486229,
105.485062, 108.080597, 111.236076, 114.88472,
118.929359, 123.243683, 127.67543, 132.051514,
136.185303, 139.885681, 142.967957, 145.265732,
146.643433, 147.008408, 146.321793, 144.606903,
141.954163, 138.521561, 134.529816, 130.251724,
125.995781, 122.084518, 118.828743, 116.499512,
115.30024, 115.341621, 116.622482, 119.019257,
122.286652, 126.07058, 129.933945, 133.393829,
135.967163, 137.221008, 136.821716, 134.577469,
130.468277, 124.658791, 117.490761, 109.454536,
101.141312, 93.1808319, 86.1715546, 80.6117172,
76.8403015, 74.9962845, 75.0018997, 76.5730438,
79.2555618, 82.4824448, 85.6439514, 88.160675,
89.5494003, 89.4731827, 87.7698288, 84.4566879,
79.7130737, 73.8450165, 67.2386932, 60.309967,
53.4567032, 47.0196152, 41.2550163, 36.3213272,
32.2786369, 29.0994415, 26.6874275, 24.9006214,
23.5753708, 22.5480499, 21.6722889, 20.8305187,
19.9396038, 18.9512005, 17.8479996, 16.6373444,
15.3436489, 14.0009184, 12.6462107, 11.3146381,
10.0360317, 8.83320141, 7.72150183, 6.70934534,
5.79929972, 4.98943233, 4.27467108, 3.64801121,
3.1014874, 2.62689066, 2.21624494, 1.8620882,
1.55760753, 1.29667664, 1.0738349, 0.884237289,
0.723593891, 0.58810997, 0.474430948, 0.379593521,
0.300982535, 0.236292213, 0.183491185, 0.140790984,
0.106617957, 0.0795888156, 0.0584899113, 0.0422602072,
0.0299774166, 0.0208466426, 0.0141906943, 0.00944109168,
0.00612909719, 0.00387623371, 0.00238409918, 0.00142356567,
0.000823724258, 0.000461024669, 0.000249092293, 0.000129663109,
6.48909845e-05, 3.11543954e-05, 1.43165189e-05, 6.28222915e-06,
2.62590174e-06, 1.04283492e-06, 3.92427381e-07,
/* Z=80 -> Hg */
0, 0.653117001, 0.707429707, 0.766207516,
0.829810381, 0.898626328, 0.973073184, 1.05360126,
1.14069533, 1.23487687, 1.33670723, 1.44678974,
1.56577325, 1.69435441, 1.83328116, 1.98335671,
2.14544177, 2.32045889, 2.50939703, 2.71331358,
2.93333983, 3.17068505, 3.42663956, 3.70258069,
3.99997544, 4.32038641, 4.66547394, 5.03700256,
5.43684387, 5.86698008, 6.32950783, 6.82664156,
7.36071491, 7.93418503, 8.54963112, 9.2097559,
9.91738415, 10.6754627, 11.4870539, 12.3553324,
13.2835741, 14.2751541, 15.3335257, 16.4622116,
17.6647816, 18.9448318, 20.3059597, 21.75173,
23.2856445, 24.9110947, 26.6313248, 28.4493675,
30.3679924, 32.3896446, 34.5163574, 36.7496872,
39.0906181, 41.5394821, 44.0958405, 46.7583809,
49.5248184, 52.3917809, 55.3546638, 58.4075546,
61.5430832, 64.752327, 68.0246964, 71.3478699,
74.707695, 78.0881577, 81.4713516, 84.8375092,
88.1650314, 91.4306335, 94.6095047, 97.6755066,
100.601517, 103.359833, 105.922569, 108.262299,
110.352654, 112.169052, 113.68956, 114.895767,
115.773689, 116.314789, 116.516953, 116.385399,
115.933594, 115.18396, 114.16851, 112.929077,
111.517387, 109.99472, 108.431038, 106.903816,
105.496223, 104.294724, 103.386269, 102.854927,
102.778023, 103.222038, 104.238342, 105.858887,
108.092323, 110.920509, 114.296059, 118.140968,
122.346741, 126.776299, 131.267853, 135.640808,
139.703735, 143.264221, 146.140244, 148.172562,
149.237244, 149.257736, 148.215042, 146.155273,
143.193222, 139.511093, 135.351761, 131.005936,
126.793747, 123.041206, 120.053131, 118.084343,
117.312027, 117.811951, 119.541489, 122.332619,
125.8965, 129.841171, 133.701782, 136.981812,
139.201721, 139.9505, 138.934189, 136.015625,
131.239594, 124.839058, 117.220131, 108.925636,
100.58049, 92.824173, 86.2383575, 81.278656,
78.2196884, 77.1213989, 77.8216248, 79.9567795,
83.0078049, 86.3652878, 89.4043121, 91.558609,
92.3837738, 91.6014786, 89.120018, 85.030098,
79.5788269, 73.1273346, 66.0993652, 58.9284744,
52.0105629, 45.6671562, 40.122261, 35.4938774,
31.7989502, 28.9690418, 26.8731709, 25.3437366,
24.201807, 23.2787304, 22.4321041, 21.5552082,
20.5801258, 19.4755611, 18.2408733, 16.8979912,
15.4827757, 14.037096, 12.6023617, 11.2149696,
9.9036293, 8.68836308, 7.58077049, 6.585145,
5.70001888, 4.91981459, 4.23637438, 3.64023876,
3.12161422, 2.67103839, 2.27978587, 1.94006729,
1.64508784, 1.38900959, 1.1668644, 0.974441111,
0.80816859, 0.665002763, 0.542325199, 0.437853307,
0.34956491, 0.27563706, 0.214398846, 0.164298162,
0.123881347, 0.0917840898, 0.0667314455, 0.0475440696,
0.0331476778, 0.0225826465, 0.0150113637, 0.00972143374,
0.00612388831, 0.00374637847, 0.00222208258, 0.00127562671,
0.000707495841, 0.000378400407, 0.000194788663, 9.6312011e-05,
4.56438647e-05, 2.06875557e-05, 8.94653203e-06, 3.68270366e-06,
1.43927195e-06, 5.32633464e-07, 1.86129313e-07,
/* Z=81 -> Tl */
0, 0.708591223, 0.767097771, 0.830378532,
0.898815334, 0.972819388, 1.05283344, 1.13933384,
1.23283362, 1.33388412, 1.44307792, 1.56105232,
1.68849123, 1.82612908, 1.97475386, 2.13521051,
2.30840421, 2.49530458, 2.69694901, 2.91444731,
3.14898539, 3.40182853, 3.67432761, 3.9679215,
4.28414249, 4.62462044, 4.99108505, 5.38537407,
5.80943346, 6.26532078, 6.75521278, 7.28140259,
7.84630537, 8.45246029, 9.10252762, 9.79929256,
10.54566, 11.344656, 12.199419, 13.1131945,
14.0893269, 15.1312513, 16.2424755, 17.4265614,
18.6871166, 20.0277538, 21.4520721, 22.9636269,
24.5658836, 26.2621746, 28.0556622, 29.9492683,
31.9456177, 34.0469704, 36.2551498, 38.5714493,
40.9965553, 43.5304298, 46.1722412, 48.9202194,
51.7715645, 54.7223358, 57.7673073, 60.8998756,
64.1119308, 67.3937683, 70.733963, 74.1193085,
77.5347519, 80.963356, 84.3862686, 87.7828064,
91.1304855, 94.4051895, 97.581337, 100.632156,
103.530037, 106.246918, 108.754822, 111.026428,
113.035812, 114.759117, 116.175522, 117.268059,
118.02462, 118.438942, 118.511589, 118.250847,
117.673607, 116.806023, 115.683998, 114.353439,
112.870117, 111.299179, 109.714157, 108.195557,
106.828842, 105.701859, 104.90184, 104.511757,
104.606407, 105.248169, 106.482658, 108.334518,
110.803589, 113.861702, 117.450562, 121.480766,
125.832642, 130.358643, 134.888092, 139.233704,
143.200455, 146.595947, 149.242447, 150.989426,
151.726303, 151.394073, 149.994873, 147.598419,
144.344147, 140.438095, 136.144135, 131.769012,
127.641907, 124.089142, 121.405899, 119.827171,
119.500488, 120.463837, 122.631439, 125.790283,
129.609161, 133.66098, 137.457504, 140.494263,
142.301727, 142.497421, 140.833176, 137.231247,
131.803833, 124.852402, 116.844597, 108.370247,
100.080063, 92.6137619, 86.5262604, 82.2212906,
79.9018097, 79.5444031, 80.9019012, 83.5344086,
86.8647385, 90.2504196, 93.0621872, 94.7577896,
94.9412155, 93.4000168, 90.1170502, 85.2572021,
79.1329651, 72.1555405, 64.7792969, 57.4475975,
50.5464325, 44.3709526, 39.107048, 34.8283997,
31.5069218, 29.0333805, 27.2439957, 25.9486713,
24.9570637, 24.0995502, 23.2414398, 22.2899361,
21.1945705, 19.9424343, 18.5500946, 17.0540257,
15.501112, 13.9405022, 12.4173698, 10.9689121,
9.62237549, 8.39478588, 7.29388046, 6.3197546,
5.4668107, 4.72567272, 4.08487177, 3.53219151,
3.0556426, 2.64410472, 2.28768229, 1.97785199,
1.70745575, 1.47060394, 1.26252389, 1.07938707,
0.918132663, 0.776301861, 0.651890218, 0.543221176,
0.448844343, 0.36745742, 0.297850847, 0.238873079,
0.189412564, 0.148392946, 0.114776947, 0.0875757039,
0.0658596382, 0.048768919, 0.0355216749, 0.0254192613,
0.0178483054, 0.0122798849, 0.00826626644, 0.00543569494,
0.00348582701, 0.0021762203, 0.00132024661, 0.000776861503,
0.000442508841, 0.000243509989, 0.000129189561, 6.59362922e-05,
3.2303371e-05, 1.51566601e-05, 6.7945557e-06,
/* Z=82 -> Pb */
0, 0.768951714, 0.831978738, 0.900109828,
0.973749697, 1.05333412, 1.1393317, 1.23224688,
1.33262157, 1.44103873, 1.55812395, 1.68454945,
1.82103634, 1.96835828, 2.12734485, 2.29888439,
2.48392868, 2.68349576, 2.89867401, 3.13062692,
3.38059616, 3.6499064, 3.93996978, 4.25228882,
4.58846235, 4.95018911, 5.33927155, 5.75761938,
6.20725441, 6.69031382, 7.20905113, 7.76584101,
8.36318111, 9.00368977, 9.69011116, 10.4253111,
11.2122717, 12.0540981, 12.9540005, 13.9152937,
14.9413862, 16.0357666, 17.201992, 18.4436626,
19.7644043, 21.1678448, 22.6575775, 24.2371254,
25.9099121, 27.6791992, 29.5480442, 31.5192413,
33.595253, 35.7781372, 38.0694809, 40.4702873,
42.9809074, 45.6009407, 48.3291054, 51.1631584,
54.0997543, 57.1343422, 60.261055, 63.4725723,
66.760025, 70.1128769, 73.5188675, 76.9638824,
80.4319534, 83.9052048, 87.3638687, 90.7863388,
94.1492615, 97.4277115, 100.595413, 103.624992,
106.488411, 109.157349, 111.603844, 113.800819,
115.72287, 117.347061, 118.653793, 119.627724,
120.258797, 120.543198, 120.484322, 120.093681,
119.391708, 118.408386, 117.183617, 115.767403,
114.21949, 112.608833, 111.01236, 109.513359,
108.19931, 107.159058, 106.479607, 106.242371,
106.51902, 107.367233, 108.826286, 110.912933,
113.617706, 116.902023, 120.696404, 124.900032,
129.382126, 133.985153, 138.530136, 142.824127,
146.669601, 149.875671, 152.27034, 153.713501,
154.109467, 153.418167, 151.664017, 148.941025,
145.413315, 141.310196, 136.915253, 132.54921,
128.547546, 125.23365, 122.889587, 121.726891,
121.86026, 123.287453, 125.878082, 129.374207,
133.403793, 137.507843, 141.179398, 143.911865,
145.252213, 144.852966, 142.517395, 138.231232,
132.176117, 124.721184, 116.392097, 107.819366,
99.6710739, 92.5774689, 87.0567627, 83.4520187,
81.8879776, 82.2546234, 84.2202682, 87.2731171,
90.7855911, 94.0923996, 96.5712509, 97.7149734,
97.1854095, 94.8427582, 90.747963, 85.1399994,
78.3933334, 70.9630356, 63.3259583, 55.9260864,
49.1303291, 43.1992035, 38.2739754, 34.3797302,
31.4416809, 29.3106785, 27.7932796, 26.6817837,
25.7803898, 24.9248009, 23.9939938, 22.9142017,
21.6562424, 20.2280445, 18.6644211, 17.0161514,
15.3398867, 13.6900082, 12.112915, 10.6438036,
9.30561924, 8.10967922, 7.05740261, 6.14260006,
5.35388231, 4.67688799, 4.096138, 3.59643579,
3.16382527, 2.78614497, 2.45326853, 2.15710473,
1.89143717, 1.65166974, 1.43452656, 1.23774445,
1.05978346, 0.899573565, 0.756305814, 0.629271746,
0.517750442, 0.420939028, 0.337920159, 0.267658383,
0.209017664, 0.160792246, 0.121743686, 0.0906392708,
0.0662873685, 0.0475674234, 0.0334530808, 0.0230280012,
0.0154945804, 0.0101760952, 0.00651329523, 0.00405645231,
0.00245411089, 0.00143975718, 0.000817609252, 0.000448586885,
0.000237324144, 0.000120822639, 5.90671807e-05, 2.76680057e-05,
1.23892378e-05, 5.29059207e-06, 2.14915758e-06,
/* Z=83 -> Bi */
0, 0.834659696, 0.902560532, 0.975917161,
1.05515862, 1.14074636, 1.23317659, 1.33298254,
1.44073713, 1.55705595, 1.68259919, 1.81807578,
1.9642458, 2.12192369, 2.29198194, 2.47535491,
2.67304182, 2.88611126, 3.11570477, 3.36304092,
3.6294198, 3.91622591, 4.22493505, 4.55711555,
4.91443443, 5.29866028, 5.71166897, 6.1554451,
6.63208771, 7.1438117, 7.6929512, 8.28196144,
8.91342163, 9.59003258, 10.3146172, 11.0901213,
11.9196072, 12.8062496, 13.7533331, 14.7642345,
15.8424244, 16.9914398, 18.2148762, 19.5163631,
20.8995476, 22.3680534, 23.9254532, 25.5752373,
27.3207626, 29.1652031, 31.1115036, 33.1623077,
35.3198891, 37.5860939, 39.9622307, 42.4490013,
45.0464058, 47.7536201, 50.5689163, 53.4895248,
56.5115356, 59.6297684, 62.8376656, 66.1271744,
69.4886246, 72.9106598, 76.3801193, 79.8820038,
83.3994064, 86.9135056, 90.4036102, 93.8472214,
97.2201462, 100.496689, 103.649902, 106.651894,
109.474251, 112.088547, 114.466873, 116.582527,
118.41082, 119.92981, 121.121323, 121.971817,
122.473442, 122.624992, 122.432854, 121.911919,
121.086304, 119.989891, 118.666649, 117.170647,
115.565628, 113.924202, 112.326508, 110.858383,
109.60894, 108.667641, 108.120796, 108.047699,
108.516342, 109.579086, 111.268311, 113.592308,
116.531853, 120.037582, 124.028641, 128.392807,
132.988434, 137.648453, 142.186356, 146.404526,
150.104233, 153.097443, 155.219559, 156.342438,
156.386795, 155.332855, 153.228226, 150.191666,
146.41188, 142.140671, 137.679688, 133.361435,
129.524826, 126.486954, 124.513237, 123.788338,
124.391197, 126.277229, 129.270584, 133.068863,
137.261398, 141.360947, 144.846863, 147.216599,
148.039902, 147.010513, 143.988174, 139.025497,
132.37442, 124.470062, 115.891479, 107.302856,
99.3807602, 92.7362289, 87.8413773, 84.9707108,
84.1655045, 85.2273712, 87.7421799, 91.1319656,
94.7274551, 97.8510895, 99.8986435, 100.408279,
99.1078796, 95.9355087, 91.0319824, 84.7087936,
77.3977356, 69.5907593, 61.7787781, 54.3975372,
47.7864647, 42.1644211, 37.6229706, 34.1359482,
31.5816536, 29.7730942, 28.4910851, 27.5154591,
26.6506233, 25.7431316, 24.6904469, 23.4415455,
21.9909782, 20.3686352, 18.6275444, 16.8318062,
15.0461512, 13.3280897, 11.7229414, 10.2616034,
8.96056747, 7.82355976, 6.84414721, 6.00870609,
5.2993288, 4.69635773, 4.1803813, 3.73364663,
3.3409214, 2.98988771, 2.67116642, 2.37808347,
2.10627484, 1.85321128, 1.61770749, 1.39946342,
1.19866586, 1.01566935, 0.85075897, 0.703995764,
0.575130582, 0.463578522, 0.368436754, 0.288532734,
0.222490266, 0.168802604, 0.125904724, 0.0922389627,
0.0663105547, 0.0467309169, 0.0322484411, 0.0217669662,
0.0143531393, 0.00923430733, 0.00578886038, 0.00353109487,
0.0020927703, 0.00120328926, 0.000670136011, 0.000360891077,
0.000187606522, 9.39672682e-05, 4.5260218e-05, 2.09206464e-05,
9.25993299e-06, 3.91576259e-06, 1.57813565e-06,
/* Z=84 -> Po */
0, 0.90622884, 0.979385972, 1.05837417,
1.14364815, 1.23569608, 1.33504331, 1.44225335,
1.55793178, 1.68272805, 1.81733894, 1.96251142,
2.11904621, 2.28780007, 2.4696908, 2.6657002,
2.87687683, 3.10434175, 3.34929109, 3.61300063,
3.89683008, 4.20222712, 4.53073168, 4.88397932,
5.26370764, 5.67175674, 6.11007643, 6.58072805,
7.08588839, 7.62785101, 8.20903111, 8.83196545,
9.49931335, 10.2138557, 10.9784985, 11.7962608,
12.6702843, 13.6038141, 14.6001997, 15.6628819,
16.7953815, 18.0012798, 19.2842064, 20.6478157,
22.0957527, 23.6316338, 25.2590046, 26.9812984,
28.8017998, 30.7235756, 32.7494354, 34.8818512,
37.1229019, 39.4741745, 41.9366951, 44.5108337,
47.1961937, 49.9915314, 52.8946152, 55.9021378,
59.0095787, 62.2111092, 65.4994583, 68.8657913,
72.2996445, 75.7887878, 79.3191681, 82.8748627,
86.4380264, 89.9889069, 93.5059052, 96.9656219,
100.343071, 103.611809, 106.744293, 109.712173,
112.486771, 115.039589, 117.342941, 119.370628,
121.098778, 122.506638, 123.577599, 124.30011,
124.668663, 124.684837, 124.3582, 123.707138,
122.75956, 121.553329, 120.136543, 118.567299,
116.913261, 115.250549, 113.662323, 112.236649,
111.06398, 110.233879, 109.831497, 109.933441,
110.603432, 111.887939, 113.811836, 116.374451,
119.546349, 123.267113, 127.444359, 131.954529,
136.645477, 141.341095, 145.848282, 149.965759,
153.494965, 156.252258, 158.081985, 158.869583,
158.553665, 157.135925, 154.687988, 151.353683,
147.345963, 142.938019, 138.447861, 134.217194,
130.585297, 127.859558, 126.285156, 126.016579,
127.094231, 129.429413, 132.800323, 136.861145,
141.165222, 145.201233, 148.44043, 150.390427,
150.650375, 148.961105, 145.243607, 139.619904,
132.412476, 124.119637, 115.368446, 106.8489,
99.2366486, 93.1135559, 88.8964005, 86.7838287,
86.7294388, 88.4458923, 91.4400024, 95.0746307,
98.6485748, 101.483269, 103.003983, 102.80426,
100.685631, 96.6683121, 90.9736557, 83.9826965,
76.178566, 68.0818558, 60.1880341, 52.9149208,
46.5656929, 41.3105278, 37.1867409, 34.1151428,
31.9281883, 30.4045982, 29.3049259, 28.4031525,
27.5108261, 26.491806, 25.2674179, 23.8132553,
22.1497822, 20.3293877, 18.4223576, 16.5039864,
14.6441135, 12.8999252, 11.312048, 9.90360069,
8.68151665, 7.63938332, 6.76103401, 6.02427816,
5.4043045, 4.87646437, 4.41831207, 4.01089144,
3.6393435, 3.29296684, 2.96487331, 2.65138793,
2.3513217, 2.06521797, 1.79465115, 1.54163218,
1.30813909, 1.09578598, 0.905621111, 0.738034129,
0.592753649, 0.468908787, 0.365132064, 0.279683918,
0.210582927, 0.155729294, 0.113013938, 0.0804081783,
0.0560319647, 0.0382004417, 0.0254505128, 0.0165496375,
0.0104901353, 0.00647261739, 0.00388203259, 0.0022597427,
0.00127462868, 0.000695509836, 0.000366475899, 0.000186122881,
9.09306764e-05, 4.26456863e-05, 1.91576637e-05, 8.22450693e-06,
3.3660524e-06, 1.30997705e-06, 4.83469023e-07,
/* Z=85 -> At */
0, 0.984225869, 1.06305373, 1.14811301,
1.23988509, 1.33888698, 1.44567406, 1.56084204,
1.6850301, 1.81892383, 1.96325767, 2.11881876,
2.28644991, 2.46705222, 2.66159081, 2.87109566,
3.09666777, 3.33948159, 3.6007905, 3.88192892,
4.18431807, 4.50947046, 4.85899162, 5.23458672,
5.63806391, 6.07133818, 6.53643322, 7.03548861,
7.5707593, 8.14461899, 8.75956345, 9.41821003,
10.1232977, 10.8776913, 11.68437, 12.5464344,
13.4670935, 14.4496632, 15.4975557, 16.6142654,
17.8033638, 19.0684662, 20.4132328, 21.8413219,
23.3563805, 24.9619999, 26.6616821, 28.4587955,
30.3565273, 32.3578262, 34.4653473, 36.6813736,
39.0077515, 41.4458008, 43.9962349, 46.6590576,
49.4334679, 52.3177414, 55.3091393, 58.4037781,
61.5965042, 64.8807983, 68.248642, 71.6904221,
75.1948242, 78.7487488, 82.3372192, 85.9433899,
89.5484695, 93.1317825, 96.6708145, 100.141319,
103.517517, 106.772324, 109.877586, 112.804642,
115.524582, 118.00898, 120.230476, 122.163528,
123.785187, 125.076103, 126.021362, 126.611549,
126.843727, 126.722412, 126.260468, 125.479927,
124.41259, 123.100388, 121.59552, 119.960129,
118.265663, 116.591629, 115.023918, 113.652573,
112.568901, 111.86219, 111.61586, 111.903267,
112.78331, 114.295921, 116.457916, 119.259171,
122.659653, 126.587608, 130.939117, 135.579407,
140.346207, 145.055115, 149.507294, 153.499069,
156.833374, 159.33252, 160.851425, 161.290665,
160.608124, 158.828125, 156.046967, 152.433624,
148.224731, 143.713547, 139.232391, 135.129532,
131.741333, 129.361984, 128.212891, 128.415146,
129.968155, 132.737762, 136.456116, 140.735626,
145.096756, 149.008835, 151.940735, 153.416718,
153.071793, 150.699509, 146.286087, 140.024963,
132.308304, 123.694023, 114.850769, 106.485847,
99.2642212, 93.7286835, 90.231926, 88.8903351,
89.5667648, 91.8857956, 95.2799759, 99.0611572,
102.506828, 104.94912, 105.854012, 104.879921,
101.908569, 97.0453186, 90.5911865, 82.9923935,
74.7761078, 66.4823074, 58.6008606, 51.5218391,
45.5036888, 40.6616821, 36.9755211, 34.3126755,
32.4623833, 31.1741505, 30.1949959, 29.3005619,
28.3169041, 27.1316147, 25.6947727, 24.0116158,
22.1295986, 20.1228638, 18.0767002, 16.0742054,
14.1862497, 12.4653568, 10.9432611, 9.63157463,
8.524683, 7.60394621, 6.84237289, 6.20909309,
5.67315626, 5.20641041, 4.78536463, 4.39211369,
4.0144558, 3.64541721, 3.28238034, 2.92602038,
2.5792017, 2.24596262, 1.93065727, 1.63730383,
1.36914062, 1.12837505, 0.916097224, 0.732320607,
0.576110244, 0.445764333, 0.339019328, 0.253254324,
0.185679793, 0.133498564, 0.0940346569, 0.0648276657,
0.0436940379, 0.0287586078, 0.0184611604, 0.0115431398,
0.00702031422, 0.00414682785, 0.00237534591, 0.00131727161,
0.000706003455, 0.000365032145, 0.000181722426, 8.69283685e-05,
3.98714983e-05, 1.74958623e-05, 7.32744365e-06, 2.92168647e-06,
1.10622625e-06, 3.96636182e-07, 1.34285784e-07,
/* Z=86 -> Rn */
0, 1.06927836, 1.15422595, 1.24583185,
1.34460616, 1.45109558, 1.56588721, 1.68961024,
1.82293975, 1.96659827, 2.1213603, 2.2880547,
2.46756768, 2.66084766, 2.86890697, 3.0928278,
3.3337636, 3.59294581, 3.87168527, 4.17137766,
4.49350786, 4.83965349, 5.2114892, 5.61079025,
6.03943777, 6.49942017, 6.99283981, 7.52191305,
8.088974, 8.69647694, 9.34699821, 10.0432348,
10.7880087, 11.5842609, 12.4350471, 13.3435411,
14.3130226, 15.3468723, 16.4485588, 17.6216278,
18.8696899, 20.1963921, 21.6054096, 23.1004047,
24.6850052, 26.3627701, 28.1371422, 30.0114098,
31.9886475, 34.0716667, 36.2629395, 38.5645485,
40.9780769, 43.5045586, 46.1443634, 48.8971024,
51.7615318, 54.7354431, 57.8155403, 60.9973259,
64.2749939, 67.6413116, 71.0874863, 74.6030884,
78.1759338, 81.7920303, 85.4354858, 89.0884933,
92.7313461, 96.3424301, 99.8983459, 103.374031,
106.74295, 109.977386, 113.048759, 115.928032,
118.586273, 120.995201, 123.127899, 124.959602,
126.468513, 127.636757, 128.45134, 128.905167,
128.998001, 128.737457, 128.139877, 127.231018,
126.046677, 124.632896, 123.045998, 121.352112,
119.626328, 117.951347, 116.415558, 115.11058,
114.12822, 113.556953, 113.477959, 113.960762,
115.058777, 116.804893, 119.207291, 122.245911,
125.869789, 129.995667, 134.508057, 139.261246,
144.083328, 148.782364, 153.1548, 156.995789,
160.111267, 162.331055, 163.522247, 163.602112,
162.549118, 160.411194, 157.309769, 153.438858,
149.057999, 144.478958, 140.046127, 136.111343,
133.004837, 131.003922, 130.302765, 130.98613,
133.010254, 136.194489, 140.225494, 144.675903,
149.037048, 152.763962, 155.329254, 156.280396,
155.294434, 152.222885, 147.120697, 140.253723,
132.082062, 123.218597, 114.366463, 106.24115,
99.4869156, 94.5977859, 91.8542175, 91.284996,
92.6604538, 95.5193329, 99.2260666, 103.050827,
106.261078, 108.211517, 108.419769, 106.617813,
102.772881, 97.0770569, 89.9086685, 81.7732697,
73.2335739, 64.8387833, 57.0626373, 50.2576942,
44.6297913, 40.2341461, 36.9908485, 34.7153664,
33.1579437, 32.045372, 31.1189728, 30.1641884,
29.0290527, 27.6309204, 25.9526958, 24.0311203,
21.9403591, 19.7741222, 17.6290722, 15.5915098,
13.7283268, 12.0824633, 10.6723776, 9.4946909,
8.52888393, 7.74297428, 7.09924841, 6.55932999,
6.0881505, 5.65661097, 5.24296236, 4.83305693,
4.41973686, 4.00164223, 3.58172297, 3.1657002,
2.76063871, 2.37376881, 2.01159739, 1.67932582,
1.38054621, 1.11716759, 0.889516115, 0.696551442,
0.536149144, 0.405405462, 0.300933331, 0.219128102,
0.156389594, 0.109294593, 0.0747195184, 0.049916286,
0.0325474106, 0.0206878241, 0.0128014954, 0.00770090753,
0.0044968687, 0.00254495698, 0.00139357068, 0.000737042748,
0.000375808566, 0.000184375487, 8.68578645e-05, 3.92052971e-05,
1.69169125e-05, 6.9614357e-06, 2.72512216e-06, 1.01213072e-06,
3.55671176e-07, 1.17913743e-07, 3.67676982e-08,
/* Z=87 -> Fr */
0, 1.16211104, 1.25366747, 1.35233819,
1.45866275, 1.57321954, 1.69662869, 1.82955515,
1.97271049, 2.12685728, 2.29281068, 2.47144318,
2.66368723, 2.87053871, 3.09306121, 3.33238912,
3.58973193, 3.86637807, 4.16369915, 4.48315382,
4.82629156, 5.19475794, 5.59029675, 6.01475668,
6.47009134, 6.95836687, 7.48176146, 8.04257107,
8.6432085, 9.28621101, 9.97423267, 10.7100534,
11.4965706, 12.3368034, 13.2338829, 14.1910543,
15.2116613, 16.2991447, 17.4570255, 18.6888962,
19.9983978, 21.3892002, 22.8649864, 24.4294071,
26.0860653, 27.8384686, 29.6899891, 31.6438141,
33.7028923, 35.8698692, 38.1470337, 40.5362167,
43.0387344, 45.6553001, 48.3859138, 51.229763,
54.1851425, 57.2493095, 60.4183922, 63.6872559,
67.049408, 70.4968491, 74.0200119, 77.6076202,
81.2465973, 84.9220428, 88.6171341, 92.3131104,
95.9893188, 99.6232529, 103.190643, 106.665619,
110.020981, 113.228409, 116.258919, 119.08329,
121.672592, 123.998817, 126.03566, 127.759262,
129.149109, 130.188995, 130.868027, 131.181534,
131.132217, 130.730911, 129.997559, 128.961823,
127.663513, 126.15284, 124.490196, 122.745651,
120.997803, 119.332314, 117.839767, 116.612999,
115.743896, 115.319618, 115.418518, 116.105743,
117.428627, 119.412407, 122.056137, 125.329422,
129.170059, 133.483124, 138.141693, 142.989426,
147.845367, 152.510864, 156.778763, 160.444412,
163.318207, 165.23909, 166.087952, 165.800171,
164.376053, 161.887924, 158.482697, 154.379013,
149.858276, 145.248947, 140.904922, 137.178665,
134.390594, 132.797668, 132.563416, 133.733414,
136.218918, 139.792252, 144.095581, 148.664444,
152.965256, 156.444321, 158.584412, 158.962875,
157.304947, 153.524994, 147.749466, 140.316864,
131.752502, 122.718643, 113.94471, 106.14463,
99.9315414, 95.7409973, 93.7735825, 93.966011,
95.9956207, 99.3191223, 103.240471, 106.998848,
109.864082, 111.225891, 110.664558, 107.993668,
103.270302, 96.7731018, 88.9534607, 80.3683472,
71.6054382, 63.2113037, 55.6318626, 49.1720009,
43.9775963, 40.0400887, 37.2202835, 35.2858009,
33.9553032, 32.9423714, 31.9929371, 30.9119873,
29.5775051, 27.941906, 26.0230427, 23.8880653,
21.6338081, 19.3672581, 17.1887016, 15.1793966,
13.3944159, 11.8605051, 10.5781069, 9.52636719,
8.66976643, 7.9651556, 7.36818743, 6.83847141,
6.34309435, 5.8584466, 5.37054205, 4.87414122,
4.37108421, 3.86821628, 3.37525392, 2.90284252,
2.46098089, 2.05789185, 1.69935215, 1.38843095,
1.12557006, 0.908909321, 0.734765351, 0.598181844,
0.493479878, 0.414757639, 0.35630542, 0.31291908,
0.280107528, 0.254202247, 0.232382044, 0.212631524,
0.193652064, 0.174743474, 0.155671984, 0.136537582,
0.117650278, 0.0994221792, 0.0822797343, 0.066598244,
0.0526587293, 0.040626213, 0.0305462852, 0.022356322,
0.0159068704, 0.0109884767, 0.00735960389, 0.00477197999,
0.00299086864, 0.00180900819, 0.00105409417,
/* Z=88 -> Ra */
0, 1.2634877, 1.36218297, 1.46847892,
1.58294618, 1.70619655, 1.83888495, 1.98171318,
2.135432, 2.30084443, 2.4788096, 2.67024469,
2.8761301, 3.09751153, 3.33550525, 3.59130025,
3.86616302, 4.16144228, 4.47857141, 4.8190732,
5.18456459, 5.57676029, 5.9974761, 6.44863224,
6.93225956, 7.45050001, 8.00561047, 8.59996605,
9.23606014, 9.91650963, 10.6440487, 11.4215374,
12.2519484, 13.1383762, 14.0840263, 15.092206,
16.1663265, 17.3098793, 18.5264359, 19.819622,
21.1931057, 22.6505718, 24.1956921, 25.8321056,
27.5633698, 29.392931, 31.32407, 33.3598595,
35.5030975, 37.7562523, 40.1213875, 42.6000824,
45.1933517, 47.9015503, 50.7242889, 53.6603127,
56.7074013, 59.8622665, 63.1204147, 66.476059,
69.9219666, 73.449379, 77.047905, 80.7053909,
84.4078674, 88.1395035, 91.8825226, 95.6172333,
99.3220444, 102.973549, 106.546638, 110.014702,
113.349869, 116.523354, 119.505821, 122.267937,
124.780891, 127.017113, 128.950989, 130.559753,
131.824326, 132.730377, 133.269196, 133.438812,
133.244934, 132.701859, 131.833206, 130.672607,
129.264023, 127.661812, 125.93042, 124.143707,
122.383636, 120.738602, 119.301048, 118.16465,
117.42086, 117.155029, 117.442131, 118.3423,
119.896233, 122.120949, 125.005882, 128.509872,
132.559265, 137.04747, 141.836212, 146.758957,
151.626343, 156.234009, 160.372345, 163.838287,
166.448257, 168.051895, 168.545456, 167.883865,
166.090363, 163.262344, 159.572235, 155.262833,
150.636017, 146.034958, 141.820404, 138.342056,
135.90712, 134.748535, 134.996033, 136.653442,
139.585648, 143.517883, 148.049347, 152.681656,
156.860977, 160.030807, 161.690598, 161.454086,
159.100494, 154.611191, 148.186111, 140.235611,
131.346466, 122.223808, 113.614601, 106.2211,
100.615112, 97.1646729, 95.9839783, 96.9146652,
99.5422134, 103.246567, 107.280159, 110.86264,
113.278702, 113.965103, 112.574631, 109.009041,
103.41761, 96.1636734, 87.7656784, 78.8227921,
69.9364319, 61.6387215, 54.3367424, 48.278965,
43.5458183, 40.0634079, 37.6356354, 35.9882278,
34.8167648, 33.83144, 32.7925491, 31.5329876,
29.9666557, 28.0839691, 25.9374599, 23.6214619,
21.2499447, 18.9361362, 16.7763863, 14.8398218,
13.163909, 11.7553682, 10.595109, 9.64569187,
8.85966682, 8.18750095, 7.58407307, 7.01318979,
6.44994068, 5.8810792, 5.30381823, 4.72356796,
4.15114164, 3.59991813, 3.08331442, 2.61282229,
2.19670725, 1.8393805, 1.54136729, 1.2997371,
1.10884643, 0.961239219, 0.848568201, 0.762429595,
0.695038617, 0.639707386, 0.591119826, 0.545419097,
0.500143647, 0.45405212, 0.406881899, 0.359078974,
0.311532408, 0.265336424, 0.221594453, 0.181273445,
0.145108804, 0.113556817, 0.0867876485, 0.0647103414,
0.0470197536, 0.0332558155, 0.0228661299, 0.0152643546,
0.00987898558, 0.00618935144, 0.00374791608, 0.00218988117,
0.00123245502, 0.000666857988, 0.000346223096,
/* Z=89 -> Ac */
0, 1.37422657, 1.48063254, 1.59515774,
1.7184062, 1.85102391, 1.99370289, 2.14718318,
2.3122561, 2.48976779, 2.6806221, 2.88578391,
3.10628271, 3.34321618, 3.59775496, 3.87114453,
4.16471052, 4.47986317, 4.81809998, 5.18100977,
5.57027817, 5.98769045, 6.43513441, 6.91460657,
7.42821312, 7.97817326, 8.56682301, 9.19661808,
9.87013054, 10.5900574, 11.3592119, 12.1805305,
13.057065, 13.9919777, 14.9885454, 16.0501385,
17.1802216, 18.3823395, 19.6601028, 21.0171642,
22.4572124, 23.9839287, 25.6009789, 27.3119583,
29.1203747, 31.0295925, 33.0427895, 35.1629028,
37.3925629, 39.7340279, 42.1891251, 44.7591476,
47.4447823, 50.2460098, 53.1620102, 56.1910515,
59.3303833, 62.5761299, 65.9231567, 69.364975,
72.8936005, 76.4994888, 80.1713791, 83.8962402,
87.6591949, 91.4434509, 95.2303009, 98.9990921,
102.727333, 106.390732, 109.963379, 113.417953,
116.725998, 119.858292, 122.785271, 125.477577,
127.906662, 130.045486, 131.869308, 133.356598,
134.489883, 135.256821, 135.651154, 135.673721,
135.333435, 134.648132, 133.645294, 132.362564,
130.848099, 129.1604, 127.367912, 125.548141,
123.786232, 122.172989, 120.802406, 119.768539,
119.161942, 119.06559, 119.550499, 120.671188,
122.461159, 124.928642, 128.053024, 131.782059,
136.030487, 140.680008, 145.581375, 150.558304,
155.41391, 159.939072, 163.92308, 167.165894,
169.491592, 170.762131, 170.89064, 169.852905,
167.696045, 164.542892, 160.591293, 156.107269,
151.411545, 146.859604, 142.816055, 139.624405,
137.574966, 136.873138, 137.611786, 139.750916,
143.108017, 147.361862, 152.070908, 156.706757,
160.700653, 163.499573, 164.626434, 163.737854,
160.672318, 155.481674, 148.440247, 140.028305,
130.889114, 121.763046, 113.405098, 106.495422,
101.554489, 98.8746948, 98.4786224, 100.111504,
103.26992, 107.264038, 111.304932, 114.604752,
116.475456, 116.411797, 114.147324, 109.676361,
103.240593, 95.2840424, 86.384697, 77.173996,
68.2560959, 60.1379585, 53.1788864, 47.5647812,
43.3079224, 40.2699852, 38.2021942, 36.7949677,
35.7287064, 34.7181473, 33.5447121, 32.0739517,
30.2579231, 28.1247406, 25.7591381, 23.2786503,
20.8096848, 18.4671688, 16.3398972, 14.4826536,
12.9148092, 11.6242771, 10.5751228, 9.71698475,
8.99453545, 8.35564232, 7.75733614, 7.16921568,
6.57437515, 5.96828794, 5.35624361, 4.75005531,
4.16462994, 3.61491132, 3.11352015, 2.66924095,
2.28636265, 1.96475232, 1.70049012, 1.48684847,
1.31541324, 1.17717147, 1.06344068, 0.966560423,
0.880323827, 0.800157785, 0.723094165, 0.647587061,
0.573233783, 0.500454366, 0.430174053, 0.363538861,
0.301685333, 0.245572329, 0.195875674, 0.152939707,
0.11677672, 0.0871025845, 0.0633964837, 0.0449731275,
0.0310570225, 0.0208506193, 0.0135903647, 0.00858742371,
0.00525224721, 0.00310436171, 0.00177011138, 0.000971955771,
0.00051296223, 0.000259686552, 0.000125842023,
/* Z=90 -> Th */
0, 1.49529815, 1.61003745, 1.73344958,
1.86617279, 2.00888968, 2.16233039, 2.32727575,
2.50455928, 2.69507194, 2.8997643, 3.11965013,
3.35581088, 3.60939789, 3.88163757, 4.17383432,
4.48737526, 4.82373285, 5.18447018, 5.57124519,
5.98581314, 6.43003082, 6.90586042, 7.41537428,
7.96075535, 8.54430199, 9.16842937, 9.83567047,
10.5486813, 11.3102341, 12.1232214, 12.9906549,
13.915658, 14.9014664, 15.951416, 17.0689392,
18.2575531, 19.5208435, 20.8624516, 22.2860565,
23.7953453, 25.3939991, 27.0856495, 28.8738499,
30.7620335, 32.7534714, 34.8512154, 37.0580444,
39.3764038, 41.8083267, 44.3553658, 47.0185051,
49.7980804, 52.6936646, 55.7039795, 58.8267899,
62.0587769, 65.3954468, 68.8309937, 72.3582001,
75.9683075, 79.6509323, 83.3939514, 87.1834259,
91.0035477, 94.8365707, 98.6628342, 102.46077,
106.206947, 109.876259, 113.442009, 116.876228,
120.14994, 123.233566, 126.097412, 128.712204,
131.049744, 133.08371, 134.790375, 136.149582,
137.145645, 137.768417, 138.014236, 137.886917,
137.398727, 136.571167, 135.435699, 134.034103,
132.418671, 130.652054, 128.806625, 126.963371,
125.210373, 123.640572, 122.349091, 121.429939,
120.972267, 121.056099, 121.747917, 123.096039,
125.126137, 127.837219, 131.198135, 135.145355,
139.581802, 144.37767, 149.373001, 154.382446,
159.202347, 163.620056, 167.425064, 170.421906,
172.443863, 173.366837, 173.122314, 171.708115,
169.19603, 165.73465, 161.546829, 156.920715,
152.194046, 147.732117, 143.900177, 141.032104,
139.397675, 139.171387, 140.406403, 143.017075,
146.773071, 151.307678, 156.141357, 160.719971,
164.465485, 166.834793, 167.380966, 165.809616,
162.023331, 156.147156, 148.529922, 139.718872,
130.40802, 121.364738, 113.342133, 106.9879,
102.761627, 100.87262, 101.247772, 103.535912,
107.148972, 111.335419, 115.275948, 118.187729,
119.422218, 118.542709, 115.370811, 109.996758,
102.753532, 94.1605377, 84.8466873, 75.4648056,
66.6101074, 58.7534676, 52.1976013, 47.060154,
43.2834015, 40.6665764, 38.9135551, 37.687233,
36.6617584, 35.5651474, 34.2073021, 32.4915314,
30.4104042, 28.0293503, 25.4625835, 22.846447,
20.3145943, 17.9784908, 15.9149876, 14.1614923,
12.7178574, 11.5534229, 10.6170483, 9.84803486,
9.18615246, 8.57944775, 7.98918104, 7.39176989,
6.7781477, 6.15120697, 5.52214813, 4.90653181,
4.32065678, 3.77872562, 3.29099298, 2.86292315,
2.49522948, 2.18456268, 1.92459655, 1.70725715,
1.52389836, 1.36627245, 1.22722602, 1.10109913,
0.983856142, 0.873001933, 0.767350674, 0.666714966,
0.571571648, 0.482747942, 0.401156694, 0.327595264,
0.262612402, 0.206437767, 0.158966437, 0.119785048,
0.0882275179, 0.0634471476, 0.0444943011, 0.0303900205,
0.0201888755, 0.0130267879, 0.00815197825, 0.0049398304,
0.00289382041, 0.00163603225, 0.000891013944, 0.000466574129,
0.000234438543, 0.00011279602, 5.18505076e-05,
/* Z=91 -> Pa */
0, 1.62769306, 1.75143683, 1.88444364,
2.02738786, 2.18098998, 2.3460207, 2.52330232,
2.71371365, 2.91819119, 3.13773489, 3.37340951,
3.62634921, 3.89776158, 4.18893051, 4.50122166,
4.83608389, 5.19505548, 5.57976723, 5.99194479,
6.43341589, 6.90611029, 7.41206646, 7.95343208,
8.53246784, 9.15155125, 9.81317711, 10.5199566,
11.2746248, 12.0800323, 12.939146, 13.855052,
14.8309441, 15.8701229, 16.9759846, 18.1520138,
19.4017715, 20.7288818, 22.1370106, 23.6298447,
25.2110691, 26.8843422, 28.6532574, 30.5213051,
32.4918289, 34.5679893, 36.7526932, 39.048542,
41.4577675, 43.982151, 46.6229553, 49.3808289,
52.2557106, 55.2467499, 58.3521805, 61.5692215,
64.8939667, 68.3212662, 71.8446121, 75.4560318,
79.1459579, 82.9031601, 86.7146225, 90.5654755,
94.4389725, 98.3164062, 102.177177, 105.998787,
109.756943, 113.425682, 116.977623, 120.384178,
123.615929, 126.643028, 129.435745, 131.964996,
134.20314, 136.124619, 137.706909, 138.931396,
139.784363, 140.258011, 140.35141, 140.071548,
139.434189, 138.464645, 137.19838, 135.681335,
133.970047, 132.13118, 130.240891, 128.383514,
126.649757, 125.134369, 123.933189, 123.139717,
122.841133, 123.113937, 124.019478, 125.599297,
127.870728, 130.823013, 134.414215, 138.569183,
143.179153, 148.102966, 153.170395, 158.187775,
162.945694, 167.229156, 170.829254, 173.556625,
175.255386, 175.816864, 175.192169, 173.402222,
170.543915, 166.79155, 162.392273, 157.654877,
152.931976, 148.595901, 145.009415, 142.493378,
141.293777, 141.551483, 143.278137, 146.341797,
150.465149, 155.238556, 160.148575, 164.620804,
168.074326, 169.982666, 169.935181, 167.691284,
163.220276, 156.720184, 148.61087, 139.499939,
130.122757, 121.262428, 113.658379, 107.914948,
104.422531, 103.302902, 104.387703, 107.234848,
111.181686, 115.428497, 119.140617, 121.554649,
122.073372, 120.335907, 116.253891, 110.009689,
102.018791, 92.8637238, 83.2104187, 73.7200165,
64.9685364, 57.3852768, 51.2165108, 46.5177231,
43.1723518, 40.9317436, 39.4680748, 38.4308929,
37.4983826, 36.41642, 35.0213165, 33.2453957,
31.1074562, 28.6922817, 26.124279, 23.5405598,
21.0674973, 18.8037853, 16.8111172, 15.112381,
13.6959848, 12.5244141, 11.5447502, 10.6991816,
9.93392754, 9.20558929, 8.48459816, 7.75590181,
7.01744652, 6.27718401, 5.54938364, 4.85093784,
4.19815779, 3.6043992, 3.07861257, 2.6248033,
2.24224448, 1.92623413, 1.66917205, 1.46174908,
1.29407275, 1.15661395, 1.04090607, 0.939977705,
0.848536491, 0.762946367, 0.6810534, 0.601917028,
0.525498211, 0.452347428, 0.383321434, 0.319349587,
0.261257708, 0.209650651, 0.164850265, 0.126880035,
0.0954864547, 0.0701863766, 0.0503294282, 0.0351656675,
0.0239102636, 0.0157989822, 0.0101305135, 0.00629413733,
0.00378314848, 0.00219612126, 0.00122908072, 0.000661943981,
0.000342399173, 0.000169755906, 8.04938245e-05,
/* Z=92 -> U */
0, 1.77268696, 1.90617299, 2.04955173,
2.20353532, 2.3688848, 2.54641223, 2.73698449,
2.94152594, 3.16102242, 3.39652371, 3.64914799,
3.92008471, 4.21059942, 4.52203512, 4.85582018,
5.21346855, 5.59658432, 6.00686693, 6.44611406,
6.91622591, 7.41920757, 7.95717192, 8.53234482,
9.14706612, 9.80379009, 10.5050917, 11.2536631,
12.0523119, 12.9039679, 13.8116732, 14.7785816,
15.8079548, 16.9031544, 18.0676327, 19.3049183,
20.6186161, 22.0123711, 23.4898682, 25.0547924,
26.7108173, 28.461565, 30.3105717, 32.2612495,
34.3168411, 36.4803696, 38.7545815, 41.1418762,
43.6442451, 46.2632027, 48.9996834, 51.8539696,
54.8255959, 57.9132309, 61.1145973, 64.4263458,
67.8439407, 71.3615494, 74.9719315, 78.6663208,
82.4343338, 86.2638397, 90.1409302, 94.0497971,
97.9727249, 101.890068, 105.780281, 109.619942,
113.383911, 117.045448, 120.5765, 123.947952,
127.129997, 130.092636, 132.806183, 135.241913,
137.372818, 139.174316, 140.625198, 141.708603,
142.412933, 142.73291, 142.670563, 142.236145,
141.449097, 140.338638, 138.944336, 137.316376,
135.515427, 133.612183, 131.686447, 129.825653,
128.122894, 126.674339, 125.576149, 124.920776,
124.7929, 125.264938, 126.392502, 128.209732,
130.725082, 133.917618, 137.734207, 142.087982,
146.858414, 151.89328, 157.012634, 162.015167,
166.686783, 170.811371, 174.183136, 176.620361,
177.979584, 178.169144, 177.161133, 175.000458,
171.809738, 167.78891, 163.208588, 158.396744,
153.718643, 149.550797, 146.250137, 144.120895,
143.381729, 144.136749, 146.353729, 149.853195,
154.31102, 159.276398, 164.205307, 168.507843,
171.606064, 172.996506, 172.311066, 169.368347,
164.208115, 157.102936, 148.542648, 139.19133,
129.819351, 121.217216, 114.101334, 109.02346,
106.296913, 105.950577, 107.718811, 111.070343,
115.273422, 119.488617, 122.87648, 124.704224,
124.436371, 121.796341, 116.791107, 109.696899,
101.009773, 91.369957, 81.4724121, 71.9768524,
63.4299278, 56.2097282, 50.4981804, 46.2830772,
43.3862801, 41.5113487, 40.3013268, 39.3967857,
38.4854126, 37.3366966, 35.8187637, 33.8976593,
31.6222038, 29.0994091, 26.4660358, 23.8614826,
21.4058914, 19.1858215, 17.2480412, 15.6007233,
14.2201681, 13.0608997, 12.066762, 11.1811361,
10.3549252, 9.55161953, 8.74935913, 7.94041157,
7.12874508, 6.32651854, 5.55024147, 4.81723022,
4.14276886, 3.53819299, 3.00992084, 2.55933094,
2.18329406, 1.8751384, 1.62582195, 1.42512417,
1.26271009, 1.12897515, 1.01562965, 0.916021585,
0.825228989, 0.739968657, 0.658379018, 0.579729676,
0.504105926, 0.432104319, 0.364565194, 0.302356541,
0.246216059, 0.196649894, 0.153883606, 0.117856257,
0.0882478654, 0.0645296127, 0.0460263453, 0.0319823176,
0.0216224026, 0.0142034264, 0.00905210339, 0.00558871683,
0.00333721889, 0.00192413072, 0.00106927846, 0.000571666285,
0.00029345206, 0.000144337057, 6.78769429e-05,
/* Z=93 -> Np */
0, 1.9315691, 2.07559729, 2.2301898,
2.39609885, 2.5741272, 2.76513076, 2.97002244,
3.18977499, 3.4254241, 3.67807269, 3.94889379,
4.23913383, 4.55011797, 4.88325167, 5.24002647,
5.62202263, 6.03091288, 6.46846771, 6.93655682,
7.43715382, 7.97233963, 8.54430389, 9.15535164,
9.80789948, 10.5044813, 11.2477503, 12.0404749,
12.8855419, 13.7859516, 14.7448206, 15.7653685,
16.8509197, 18.0048885, 19.2307816, 20.5321674,
21.9126797, 23.3759823, 24.9257622, 26.5657005,
28.2994366, 30.1305447, 32.0624924, 34.0985947,
36.2419739, 38.4954987, 40.861721, 43.3428268,
45.9405479, 48.656086, 51.4900284, 54.4422684,
57.5118904, 60.6970673, 63.9949722, 67.4016495,
70.911911, 74.5192032, 78.2155228, 81.9912949,
85.8352737, 89.7344284, 93.6739197, 97.637001,
101.60498, 105.557266, 109.471382, 113.323021,
117.086197, 120.733467, 124.236153, 127.564659,
130.688904, 133.578827, 136.204926, 138.538956,
140.554626, 142.228546, 143.541016, 144.477036,
145.027344, 145.189362, 144.968185, 144.377594,
143.440735, 142.190872, 140.671768, 138.937836,
137.053864, 135.094467, 133.142944, 131.289566,
129.629517, 128.260025, 127.277046, 126.771523,
126.825043, 127.505348, 128.861679, 130.920258,
133.680145, 137.109772, 141.144547, 145.685776,
150.601334, 155.728195, 160.877304, 165.840637,
170.400513, 174.341034, 177.460999, 179.588013,
180.592575, 180.401505, 179.009033, 176.48494,
172.977798, 168.712814, 163.983017, 159.133789,
154.540573, 150.580994, 147.602707, 145.889786,
145.630325, 146.888931, 149.587738, 153.499298,
158.253723, 163.36171, 168.252823, 172.327209,
175.016083, 175.845474, 174.495682, 170.848984,
165.018082, 157.349823, 148.400955, 138.886154,
129.602463, 121.338074, 114.776237, 110.407059,
108.45993, 108.867409, 111.267159, 115.04361,
119.404358, 123.481468, 126.442993, 127.598618,
126.484421, 122.914459, 116.99337, 109.089188,
99.7725677, 89.7325592, 79.6825409, 70.2700348,
62.0028381, 55.2008972, 49.9781494, 46.2546959,
43.7941437, 42.2581253, 41.267746, 40.4618645,
39.5437088, 38.3103561, 36.663208, 34.6009979,
32.1995621, 29.5839691, 26.89884, 24.2819824,
21.8446369, 19.6601353, 17.7608128, 16.1419411,
14.7704382, 13.595911, 12.5618248, 11.6150246,
10.7125359, 9.82526016, 8.9387598, 8.05171394,
7.1728301, 6.31707335, 5.50187302, 4.74388218,
4.05657291, 3.44879079, 2.92423201, 2.48167348,
2.11575174, 1.81806386, 1.57837808, 1.38578916,
1.22969747, 1.10054636, 0.990296066, 0.892647803,
0.803057194, 0.718587637, 0.63765955, 0.559745431,
0.485053837, 0.414233953, 0.34812206, 0.287542045,
0.233162999, 0.185412169, 0.144437149, 0.11010842,
0.0820520893, 0.0597027577, 0.0423662104, 0.0292835627,
0.0196896046, 0.0128605133, 0.00814807229, 0.00499988813,
0.00296669593, 0.00169924006, 0.00093783997, 0.000497826666,
0.00025365522, 0.000123800535, 5.77517021e-05,
/* Z=94 -> Pu */
0, 2.10576892, 2.26120639, 2.42792511,
2.60671854, 2.79843283, 3.00397015, 3.22429109,
3.46041846, 3.71344066, 3.98451495, 4.27487135,
4.58581543, 4.91873312, 5.27509451, 5.65645647,
6.06446695, 6.50086927, 6.96750546, 7.46631813,
7.99935627, 8.56877804, 9.17684937, 9.82595253,
10.5185852, 11.2573566, 12.0449991, 12.8843575,
13.7783909, 14.7301741, 15.7428865, 16.8198166,
17.9643421, 19.1799316, 20.4701309, 21.8385448,
23.2888241, 24.8246441, 26.4496899, 28.1676083,
29.9820061, 31.8963909, 33.9141426, 36.0384598,
38.2723236, 40.6184273, 43.0791168, 45.6563225,
48.35149, 51.165493, 54.0985451, 57.1501007,
60.3187752, 63.6022186, 66.9970093, 70.4985657,
74.1009903, 77.7970123, 81.5778275, 85.4330063,
89.3504257, 93.3161392, 97.3143692, 101.327393,
105.335579, 109.317368, 113.249382, 117.10643,
120.861771, 124.487259, 127.953659, 131.231003,
134.289017, 137.097672, 139.627777, 141.851654,
143.744034, 145.282745, 146.449783, 147.232239,
147.623306, 147.623291, 147.24057, 146.492477,
145.406097, 144.018784, 142.37854, 140.543976,
138.583984, 136.576965, 134.609467, 132.774399,
131.168625, 129.890015, 129.03389, 128.689087,
128.933533, 129.829712, 131.419891, 133.721832,
136.724686, 140.385956, 144.629333, 149.34433,
154.387344, 159.585083, 164.740067, 169.638535,
174.060425, 177.791473, 180.636642, 182.434387,
183.07077, 182.492371, 180.71669, 177.838867,
174.033508, 169.5504, 164.703644, 159.853943,
155.384216, 151.669983, 149.046295, 147.773666,
148.006638, 149.768173, 152.933777, 157.228348,
162.238266, 167.439224, 172.239487, 176.035126,
178.273056, 178.514954, 176.494644, 172.161346,
165.70137, 157.533722, 148.276764, 138.687851,
129.580887, 121.731018, 115.778152, 112.142487,
110.964539, 112.079781, 115.032951, 119.132179,
123.535812, 127.360527, 129.795013, 130.202713,
128.198914, 123.691643, 116.881554, 108.222397,
98.3499222, 87.9906464, 77.8649597, 68.5985489,
60.6539803, 54.2908173, 49.5572395, 46.3117867,
44.2686653, 43.0574608, 42.2864227, 41.5992813,
40.7177048, 39.4650078, 37.7705383, 35.657341,
33.2182617, 30.5864201, 27.9058819, 25.3071861,
22.8904305, 20.7169609, 18.8089237, 17.1550331,
15.7200594, 14.4557352, 13.3110132, 12.2402496,
11.2085924, 10.1944351, 9.18933105, 8.1960144,
7.22528887, 6.29253626, 5.41439295, 4.60602522,
3.8791914, 3.24114466, 2.69431019, 2.2365725,
1.86200345, 1.56184304, 1.32556605, 1.14190567,
0.999739528, 0.88878566, 0.800084352, 0.72627157,
0.66166836, 0.602220535, 0.545329809, 0.489615589,
0.434643775, 0.380652279, 0.32829529, 0.278422028,
0.231898978, 0.189478606, 0.151714534, 0.118918508,
0.0911534205, 0.0682543591, 0.0498694293, 0.0355118513,
0.0246154536, 0.0165870339, 0.0108506307, 0.00688069919,
0.00422311155, 0.0025046668, 0.001432986, 0.000789453217,
0.000418003474, 0.000212293031, 0.000103200618,
/* Z=95 -> Am */
0, 2.29702711, 2.46482611, 2.64467096,
2.83739877, 3.04390144, 3.26512885, 3.50209165,
3.75586462, 4.02759027, 4.31848335, 4.62983179,
4.96300268, 5.31944561, 5.70069551, 6.10837698,
6.54420757, 7.01000214, 7.50767469, 8.0392437,
8.60683441, 9.21268082, 9.85912704, 10.5486336,
11.2837763, 12.0672417, 12.9018373, 13.7904835,
14.7362099, 15.7421608, 16.8115807, 17.947813,
19.1542912, 20.4345284, 21.7921047, 23.2306461,
24.7538204, 26.3652992, 28.0687447, 29.867775,
31.7659321, 33.7666473, 35.8731956, 38.0886421,
40.4157982, 42.8571663, 45.4148483, 48.0905113,
50.8852806, 53.7996674, 56.833477, 59.985714,
63.2544746, 66.6368484, 70.1288071, 73.72509,
77.4190826, 81.2027359, 85.0664139, 88.9988403,
92.9869766, 97.0159454, 101.068993, 105.127441,
109.170708, 113.1763, 117.119911, 120.975548,
124.715714, 128.311646, 131.733627, 134.95137,
137.934525, 140.653229, 143.07872, 145.184082,
146.945084, 148.341095, 149.355911, 149.978897,
150.205902, 150.040268, 149.493805, 148.587616,
147.352768, 145.830826, 144.074036, 142.145203,
140.117279, 138.07225, 136.099747, 134.294983,
132.756195, 131.581406, 130.864807, 130.692566,
131.138397, 132.25885, 134.088684, 136.636627,
139.881485, 143.769424, 148.212326, 153.08783,
158.241196, 163.489304, 168.627075, 173.435974,
177.694839, 181.19252, 183.741684, 185.193314,
185.450562, 184.481125, 182.326752, 179.108551,
175.027039, 170.355896, 165.428848, 160.619705,
156.31604, 152.888016, 150.654373, 149.848618,
150.588516, 152.853027, 156.469604, 161.115677,
166.335373, 171.572723, 176.219147, 179.672485,
181.401642, 181.010147, 178.290817, 173.263626,
166.190323, 157.561127, 148.05246, 138.458252,
129.601166, 122.234154, 116.944679, 114.075233,
113.671997, 115.471184, 118.926224, 123.274178,
127.632469, 131.112762, 132.935471, 132.528107,
129.593613, 124.139297, 116.463493, 107.1036,
96.7549362, 86.1732025, 76.0758896, 67.0563431,
59.5220642, 53.664135, 49.459362, 46.7020187,
45.0571365, 44.125042, 43.5058517, 42.8540306,
41.9159622, 40.5472755, 38.7106743, 36.4580879,
33.9029999, 31.1893234, 28.4624271, 25.8466358,
23.4311066, 21.2645988, 19.3577003, 17.6905346,
16.2232456, 14.9070196, 13.6937294, 12.5430536,
11.4266481, 10.3294353, 9.24860859, 8.1910696,
7.17006493, 6.20173788, 5.30205393, 4.48444653,
3.75828862, 3.1281836, 2.59395981, 2.15119195,
1.79207146, 1.50644743, 1.28288746, 1.10964942,
0.975488007, 0.870258689, 0.785309434, 0.713674545,
0.650098801, 0.59092921, 0.533914685, 0.477950931,
0.422803551, 0.36883691, 0.316767305, 0.267453998,
0.221734866, 0.18030861, 0.143661946, 0.112036899,
0.0854317695, 0.0636277497, 0.0462329276, 0.0327353962,
0.0225580167, 0.0151086878, 0.00982174743, 0.00618795538,
0.00377248321, 0.00222186767, 0.00126203301, 0.000690074987,
0.000362547347, 0.000182642703, 8.80420339e-05};
numero *Rho_density(int Z) {return Rho_density_data+(Z-1)*Rho_imax;}
#ifdef jga_spline
void Rho_density(spline &rr, int Z)
{rr.init(Rho_radius,Rho_density(Z),Rho_imax);}
numero Rho_rmt(int Z, numero valmin)
{
spline density; Rho_density(density, Z);
numero val=0, r=1.5, rmax=Rho_radius[Rho_imax-1];
int Zt; if(Z<10) Zt=Z; else Zt=10;
while(val<valmin && r<rmax) {r+=0.1; val=(density.integ(0,r)-(Z-Zt))/Zt;}
density.free();
return r;
}
numero Rho_rmt(int Z) {return Rho_rmt(Z,0.8);}
#ifdef jga_Poisson
#ifdef jga_Salvat
#ifdef jga_exchange
void Rho_to_potential(int Z, spline &rho, spline &rho_1,
numero *r, numero *rV)
{
numero val,val_1;
int i;
for(i=0; i<rho.n; i++) {
r[i]=rho.x[i];
rV[i]=Poisson(r[i],rho_1)-Z;
if(i>0) {
val=rho.y[i]/(4*pi*sqr(r[i]));
val_1=rho_1.y[i]/(4*pi*sqr(r[i]));
rV[i] += r[i] * Vxc_Barth_Hedin(val_1,val_1-val/2);
} }
rV[rho.n-1]=0;
}
numero Rho_dbound(int Z, numero *r, numero *P, numero *Q,
numero &E, int n, int k, int &nmax)
{
Salvat state;
spline rho,rho_1;
numero rV[Rho_imax];
int i, it, nit=9;
numero E0;
Rho_density(rho, Z);
Rho_to_potential(Z,rho,rho,r,rV);
for(it=0; it<nit; it++) {
if(it>0) {
rho_1.init(rho.x,rho.y,rho.n);
for(i=0; i<rho.n; i++)
rho_1.y[i]=rho.y[i]-(sqr(state.P[i])+sqr(state.Q[i]));
rho_1.init();
Rho_to_potential(Z,rho,rho_1,r,rV); rho_1.free();
}
state.vint(r,rV,rho.n);
E0=E; state.dbound(E, 0.000001,n,k);
}
nmax=state.nmax;
for(i=0; i<state.nmax; i++) {
r[i]=state.rr[i];
P[i]=state.P[i]; Q[i]=state.Q[i];
}
rho.free(); state.free();
return (E-E0)/E;
}
numero Rho_dbound(int Z, spline &P, spline &Q, numero &E, int n, int k)
{
numero *r, *PP, *QQ, err;
int i, nmax;
r=new numero [Rho_imax];
PP=new numero [Rho_imax]; QQ=new numero [Rho_imax];
err=Rho_dbound(Z,r,PP,QQ,E,n,k,nmax);
P.free(); Q.free(); P.alloc(nmax); Q.alloc(nmax);
for(i=0; i<nmax; i++) {P.put(i,r[i],PP[i]); Q.put(i,r[i],QQ[i]);}
P.init(); Q.init();
delete [] r; delete [] PP; delete [] QQ;
return err;
}
void Rho_dfree(int Z, numero *r, numero *P, numero *Q,
numero E, int k, int &nmax)
{
Salvat state;
spline rho;
numero rV[Rho_imax];
numero phase;
int i;
Rho_density(rho, Z);
Rho_to_potential(Z,rho,rho,r,rV);
state.vint(r,rV,rho.n);
state.dfree(E,phase,k);
nmax=state.nmax;
for(i=0; i<state.nmax; i++) {
r[i]=state.rr[i];
P[i]=state.P[i]; Q[i]=state.Q[i];
}
rho.free(); state.free();
}
#endif
#endif
#endif
#endif
#endif
#ifndef jga_Mufpot
#define jga_Mufpot 1
class Mufpot {
public:
int init_flag;
int read_flag;
numero d_error;
numero d_local;
Mufpot(void) {init_flag=read_flag=NR=0; d_error=0.001; d_local=5/a0_au;}
void init(int n1, int n2, int *at, numero *x, numero *y, numero *z);
void read(int n1, int n2, int *at, numero *x, numero *y, numero *z);
void free();
int N;
int NR;
int ngrid;
int NX;
numero *RX;
numero **Vcoul;
numero **rho;
numero **VH;
numero **VS;
numero **V;
numero Vmt0;
int *atZ;
int *JRMT;
numero *RMT;
int *NCON;
int **IA;
int **NA;
numero **AD;
void SUMAX(int ii, numero *pot_out, int IR);
numero pot_in(int i, int j, int k);
void print(char *name, int cual);
void phases(int j,
numero Ei, numero Ef, int nE,
int lmax, numero *ph);
void phases(int j, numero Ei, int lmax, numero *ph)
{phases(j,Ei,Ei,1,lmax,ph);}
};
void Mufpot::free()
{
int i;
if(read_flag) {
for(i=0; i<NR; i++) {
if(init_flag) delete [] V[i];
delete [] IA[i]; delete [] NA[i]; delete [] AD[i];
}
delete [] NCON; delete [] JRMT;
delete [] IA; delete [] NA; delete [] AD;
delete [] atZ; delete [] RMT; delete [] RX;
if(init_flag) delete [] V;
}
init_flag=read_flag=NR=0;
}
void Mufpot::print(char *name, int cual)
{
int i,j;
FILE *fout;
if(!strcmp(name,"terminal") || !strcmp(name,"stdout")) fout=stdout;
else fout=fopen(name, "w");
for(i=0; i<78; i++) fprintf(fout, "="); fprintf(fout, "\n");
if(read_flag && cual>=0) {
fprintf(fout, "# atoms = %3d\n", N);
fprintf(fout, "# ineq. atoms = %3d\n", NR);
for(j=0; j<NR; j++) {
element_properties(atZ[j]);
fprintf(fout, "*** %2d-type -> %2d shells Rmt=%12.9f %s\n",
j, NCON[j], RMT[j], element_symbol);
for(i=0; i<NCON[j]; i++)
fprintf(fout, " shell=%2d ta=%2d n=%2d d=%12.9f\n",
i, IA[j][i], NA[j][i], AD[j][i]);
} }
if(init_flag && cual<=0) {
fprintf(fout, "Muffin-tin zero = %g eV\n", Vmt0*au_eV);
fprintf(fout, " JRMT -> ");
for(i=0; i<NR; i++) fprintf(fout, " %10d", JRMT[i]);
fprintf(fout, "\n");
for(j=0; j<NX; j++) {
fprintf(fout, "%10.7f", RX[j]);
for(i=0; i<NR; i++) fprintf(fout, " %10.6f", RX[j]*V[i][j]);
fprintf(fout, " // %3d\n", j);
} }
for(i=0; i<78; i++) fprintf(fout, "="); fprintf(fout, "\n");
if(strcmp(name,"terminal") && !strcmp(name,"stdout")) fclose(fout);
}
class atomic_environment {
public:
numero d;
int at, n;
atomic_environment *next;
atomic_environment(void) {next=NULL; n=0;}
void free(void) {
if(next!=NULL) {next->free(); delete next; next=NULL;}
n=0;
}
void add(numero &d_, int &at_, numero &d_error) {
if(at==at_ && ABS(d-d_)<=d*d_error) n++; else
if(next!=NULL) next->add(d_,at_,d_error); else {
next=new atomic_environment;
next->d=d_; next->at=at_; next->n=1; next->next=NULL;
} }
int natoms(void) {
if(next!=NULL) return n+next->natoms(); return n;
}
int find(atomic_environment &a, numero &d_error) {
if(n==a.n && at==a.at && ABS(a.d-d)<=d*d_error) return 1;
if(next==NULL) return 0;
return next->find(a, d_error);
}
void copy(atomic_environment &a) {
free();
n=a.n; at=a.at; d=a.d;
if(a.next!=NULL) {
next=new atomic_environment;
next->copy(*(a.next));
} else next=NULL;
}
void print(void) {
printf(" (%4.2f, %d, %d)", d, at, n);
if(next!=NULL) next->print();
}
};
int equal(atomic_environment &a, atomic_environment &b, numero &d_error)
{
if(a.natoms()!=b.natoms()) return 0;
atomic_environment *aa; aa=&a;
while(aa!=NULL) {if(b.find(*aa, d_error)==0) return 0; aa=aa->next;}
return 1;
}
void Mufpot::read(int n1, int n2, int *at, numero *x, numero *y, numero *z)
{
int i,j,jj, eq, *at_, ZZ;
numero *RMT_;
numero xi,yi,zi, d,val;
atomic_environment *a;
atomic_environment aa,*pa;
free(); read_flag=1;
ngrid=250;
RX=new numero [ngrid];
for(i=0, d=-8.8; i<ngrid; i++) {RX[i]=exp(d); d+=0.05;}
a=new atomic_environment [n1]; for(i=0; i<n1; i++) a[i].next=NULL;
at_=new int [n1];
N=n1; NR=0;
for(i=0; i<n1; i++) {
xi=x[i]; yi=y[i]; zi=z[i];
aa.free(); aa.d=0; aa.n=1; aa.at=at[i];
for(j=0; j<n2; j++) if(j!=i) {
d=sqrt(sqr(x[j]-xi)+sqr(y[j]-yi)+sqr(z[j]-zi));
if(d<d_local) aa.add(d, at[j], d_error);
}
for(j=0, eq=0; j<NR && eq==0; j++) {
eq=equal(aa,a[j],d_error);
if(eq==1) at_[i]=j;
}
if(eq==0) {a[NR].copy(aa); at_[i]=NR; NR++;}
}
for(i=0; i<n1; i++) at[i]=at_[i];
delete [] at_;
aa.free();
NCON=new int [NR]; JRMT=new int [NR];
IA=new int* [NR]; NA=new int* [NR]; AD=new numero* [NR];
atZ=new int [NR];
for(j=0; j<NR; j++) {
pa=a+j; NCON[j]=1;
while(pa->next!=NULL) {NCON[j]++; pa=pa->next;}
IA[j]=new int [NCON[j]];
NA[j]=new int [NCON[j]];
AD[j]=new numero [NCON[j]];
pa=a+j; atZ[j]=pa->at;
for(i=0; i<NCON[j]; i++) {
IA[j][i]=pa->at;
NA[j][i]=pa->n;
AD[j][i]=pa->d;
pa=pa->next;
} }
for(j=0; j<NR; j++) a[j].free();
delete [] a;
for(i=n1; i<n2; i++) {
jj=-1; d=infinity; zi=z[i];
for(j=0; j<n1; j++) if(atZ[at[j]]==at[i]) {
val=ABS(zi-z[j]);
if(val<d) {d=val; jj=j;}
}
if(jj>=0) at[i]=at[jj]; else at[i]=-1;
}
for(j=0; j<NR; j++)
for(i=1; i<NCON[j]; i++)
if(IA[j][i]<1 || Rho_Zmax<IA[j][i])
on_error("Mufpot::read", "atomic number out of range");
RMT=new numero [NR]; RMT_=new numero [Rho_Zmax+1];
if(n1==1) RMT[0]=Rho_radius[Rho_imax-1]; else {
for(j=1; j<=Rho_Zmax; j++) RMT_[j]=-1;
for(j=0; j<NR; j++) {
RMT[j]=Rho_radius[Rho_imax-1];
if(RMT_[atZ[j]]<0) RMT_[atZ[j]]=Rho_rmt(atZ[j]);
for(i=1; i<NCON[j]; i++) {
ZZ=IA[j][i];
if(RMT_[ZZ]<0) RMT_[ZZ]=Rho_rmt(ZZ);
d=RMT_[atZ[j]]/RMT_[ZZ];
d=AD[j][i] * d / (1+d);
if(d<RMT[j]) RMT[j]=d;
} } }
delete [] RMT_;
}
void Mufpot::init(int n1, int n2, int *at, numero *x, numero *y, numero *z)
{
spline rrho, ppot;
numero Ze;
int i,j,k, Zi;
read(n1,n2, at, x,y,z); init_flag=1;
rho=new numero* [Rho_Zmax+1]; Vcoul=new numero* [Rho_Zmax+1];
VH=new numero* [NR]; VS=new numero* [NR]; V=new numero* [NR];
for(i=0; i<NR; i++) {
VH[i]=new numero [ngrid];
VS[i]=new numero [ngrid];
V[i]=new numero [ngrid];
}
for(i=0; i<NR; i++)
for(j=0; j<ngrid; j++) VH[i][j]=VS[i][j]=V[i][j]=0;
for(i=1; i<=Rho_Zmax; i++) rho[i]=Vcoul[i]=NULL;
for(i=0; i<NR; i++)
for(j=0; j<NCON[i]; j++)
if(rho[IA[i][j]]==NULL) {
Zi=IA[i][j];
Rho_density(rrho, Zi);
Ze=rrho.integ(0,rrho.b);
rho[Zi]=new numero [ngrid];
Vcoul[Zi]=new numero [ngrid];
for(k=0; k<ngrid; k++) if(RX[k]<=rrho.b) {
Vcoul[Zi][k]=(Poisson(RX[k],rrho)-Ze)/RX[k];
rho[Zi][k]=rrho.val(RX[k])/(4*pi*sqr(RX[k]));
NX=k;
} else Vcoul[Zi][k]=rho[Zi][k]=0;
rrho.free();
}
for(i=0; i<NR; i++) {
JRMT[i]=int(20*(log(RMT[i])+8.8)+2);
SUMAX(0,VH[i],i);
SUMAX(1,VS[i],i);
for(j=0; j<NX; j++) VS[i][j]=Vxc_Barth_Hedin(VS[i][j],VS[i][j]/2);
}
for(i=0; i<NR; i++)
for(j=0; j<JRMT[i]; j++) V[i][j]=VH[i][j]+VS[i][j];
NX=0; for(i=0; i<NR; i++) if(NX<JRMT[i]) NX=JRMT[i];
for(i=1; i<=Rho_Zmax; i++) {
if(rho[i]!=NULL) delete [] rho[i];
if(Vcoul[i]!=NULL) delete [] Vcoul[i];
}
for(i=0; i<NR; i++) {delete [] VH[i]; delete [] VS[i];}
delete [] VH; delete [] VS; delete [] rho; delete [] Vcoul;
Vmt0=0; for(i=0; i<N; i++) Vmt0+=V[at[i]][JRMT[at[i]]-1]; Vmt0=Vmt0/N;
for(i=0; i<NR; i++)
for(j=0; j<JRMT[i]; j++) V[i][j]=V[i][j]-Vmt0;
}
numero Mufpot::pot_in(int i, int j, int ii)
{
if(j>ngrid) return 0;
if(ii==0) return Vcoul[i][j-1];
else return rho[i][j-1];
}
void Mufpot::SUMAX(int ii, numero *pot_out, int IR)
{
int ICON,JA,I,J,JTL,JBL;
numero TOPX,XINT,ET,BLX,XBL,G,X,FZN,FZ1,FZ2,FZ3,TLX,XTL,C;
ICON=IA[IR][0];
TOPX=0.05*(NX-1)-8.8;
for(J=1; J<=JRMT[IR]; J++) pot_out[J-1]=pot_in(ICON,J,ii);
if(NCON[IR]==1) goto gt16;
JA=1;
gt2: X=-8.8; I=1; ICON=IA[IR][JA];
gt3: XINT=0; ET=exp(X); BLX=log(AD[IR][JA]-ET);
if(BLX>=TOPX) goto gt12;
JBL=int(2+20*(BLX+8.8)); XBL=0.05*(JBL-1)-8.8; G=XBL-BLX;
XINT+=0.5*G*pot_in(ICON,JBL,ii)*(2-20*G)*exp(2*XBL);
XINT+=10*G*G*pot_in(ICON,JBL-1,ii)*exp(2*(XBL-0.05));
TLX=log(AD[IR][JA]+ET);
if(TLX<TOPX) goto gt6;
JTL=NX;
goto gt9;
gt6: JTL=1+int(20*(TLX+8.8));
if(JTL>=JBL) goto gt8;
FZN=pot_in(ICON,JTL,ii)*exp(2*(XBL-0.05));
FZ3=pot_in(ICON,JBL,ii)*exp(2*XBL);
FZ2=FZN+20*(FZ3-FZN)*(TLX-XBL+0.05);
FZ1=FZN+20*(FZ3-FZN)*(BLX-XBL+0.05);
XINT=0.5*(FZ1+FZ2)*(TLX-BLX);
goto gt12;
gt8: XTL=0.05*(JTL-1)-8.8; C=TLX-XTL;
XINT+=0.5*C*pot_in(ICON,JTL,ii)*(2-20*C)*exp(2*XTL);
XINT+=10*C*C*pot_in(ICON,JTL+1,ii)*exp(2*(XTL+0.05));
gt9: if(JTL<=JBL) goto gt12;
gt10: XINT+=0.025*pot_in(ICON,JBL,ii)*exp(2*XBL);
XINT+=0.025*pot_in(ICON,JBL+1,ii)*exp(2*(XBL+0.05));
JBL++;
if(JBL>=JTL) goto gt12;
XBL+=0.05;
goto gt10;
gt12: pot_out[I-1]+=0.5*XINT*NA[IR][JA]/(AD[IR][JA]*ET);
if(I>=JRMT[IR]) goto gt14;
I++; X+=0.05;
goto gt3;
gt14: if(JA+1>=NCON[IR]) goto gt16;
JA++;
goto gt2;
gt16: ;
}
void Mufpot::phases(int j,
numero Ei, numero Ef, int nE,
int lmax, numero *ph)
{
Salvat Dirac;
c_au*=1000;
Dirac.phases(RX,V[j],JRMT[j],atZ[j], Ei,Ef,nE, 0, lmax, ph);
c_au/=1000;
}
#endif
#ifdef jga_units
#else
#define jga_units 1
numero units_conv_fct(char *units)
{
if(!strcmpC(units,"E(eV)")) return 1/au_eV;
if(!strcmpC(units,"E(keV)")) return 1000/au_eV;
if(!strcmpC(units,"E(au)")) return 1.0;
if(!strcmpC(units,"E(Ry)")) return 0.5;
if(!strcmpC(units,"k(A)")) return a0_au;
if(!strcmpC(units,"k(au)")) return 1.0;
if(!strcmpC(units,"l(A)")) return 1/a0_au;
if(!strcmpC(units,"l(au)")) return 1.0;
if(!strcmpC(units,"l(nm)")) return 10/a0_au;
if(!strcmpC(units,"l(mi)")) return 10000/a0_au;
if(!strcmpC(units,"v(au)")) return 1.0;
if(!strcmpC(units,"v(c)")) return c_au;
if(!strcmpC(units,"v(m/s)")) return c_au/2.99792458e+8;
return -1;
}
numero units_conversion_factor(char *units)
{
numero val=units_conv_fct(units);
if(val<0) on_error(foutput, "units_conversion_factor",
"wrong units specification", units);
return val;
}
numero units_kvE(char *units, numero k, int i)
{
k=k*units_conversion_factor(units);
if(units[0]=='E' && i==0) {
if(particle_type==electrones) return sqrt(2*k);
if(particle_type==fotones) return k/c_au;
}
if(units[0]=='E' && i==1)
return c_au*sqrt(1-1/sqr(k/sqr(c_au)+1));
if(units[0]=='l' && i==2)
return 2*pi*c_au/k;
if(units[0]!='E' && i==2)
return sqr(k)/2;
return k;
}
numero units_v(char *units, numero k) {return units_kvE(units,k,1);}
numero units_E(char *units, numero k) {return units_kvE(units,k,2);}
numero units_k(char *units, numero k) {return units_kvE(units,k,0);}
char *str_units(char *units)
{
if(!strcmpC(units,"E(eV)")) return "eV";
if(!strcmpC(units,"E(keV)")) return "keV";
if(!strcmpC(units,"E(au)")) return "Hart.";
if(!strcmpC(units,"E(Ry)")) return "Rydb.";
if(!strcmpC(units,"k(A)")) return "1/A";
if(!strcmpC(units,"k(au)")) return "a.u.";
if(!strcmpC(units,"l(A)")) return "Angs.";
if(!strcmpC(units,"l(nm)")) return "nm";
if(!strcmpC(units,"l(mi)")) return "microns";
if(!strcmpC(units,"l(au)")) return "a.u.";
if(!strcmpC(units,"v(au)")) return "a.u.";
if(!strcmpC(units,"v(c)")) return "c";
if(!strcmpC(units,"v(m/s)")) return "m/s";
on_error(foutput,"*str_units","wrong units specification",units);
return units;
}
#endif
#ifndef jga_algebra
#define jga_algebra 1
class algebra_variable {
public:
algebra_variable *next;
char *name;
numero a;
algebra_variable(void) {name=NULL;}
} *algebra_var, *algebra_var0=NULL;
void algebra_free(void)
{
while(algebra_var0!=NULL) {
if(algebra_var0->name!=NULL) delete [] algebra_var0->name;
algebra_var=algebra_var0->next; delete algebra_var0;
algebra_var0=algebra_var;
} }
int algebra_find(char *name)
{
algebra_var=algebra_var0;
if(algebra_var==NULL) return 0;
while(strcmp(algebra_var->name,name)) {
if(algebra_var->next==NULL) return 0;
algebra_var=algebra_var->next;
}
return 1;
}
#define algebra_error \
on_error("algebraic evaluation", "wrong expression: ", ex);
int algebra_locate(char *ex, int i0, int i1, char c)
{
int i=i1+1, p=0;
int cond;
do {
i--;
if(ex[i]=='(' || ex[i]=='[' || ex[i]=='{') p--;
if(ex[i]==')' || ex[i]==']' || ex[i]=='}') p++;
if(p<0) algebra_error
cond=(ex[i]==c);
if(cond) if(c=='+' || c=='-') {
if(i>i0) if(ex[i-1]=='e' || ex[i-1]=='d')
if(i>i0+1) if(ex[i-2]=='.' || ('0'<=ex[i-2] && ex[i-2]<='9')) cond=0;
}
} while((!cond || p!=0) && i>i0);
if(p!=0) algebra_error
if(!cond) return -1;
return i;
}
int algebra_locate(char *ex, char c)
{return algebra_locate(ex,0,strlen(ex)-1,c);}
int algebra_locate_absolute(char *ex, int i0, int i1, char c)
{
int i=i0-1; do i++; while(ex[i]!=c && i<i1);
if(ex[i]!=c) return -1;
return i;
}
numero algebra_eval(char *ex, int i0, int i1)
{
char c,d; int i; if(i0>i1) return 0; c=ex[i0]; d=ex[i1];
numero val;
if(c=='*' || c==':' || c=='/' || c=='^' || c==')' || c==']' || c=='}' ||
d=='*' || d==':' || d=='/' || d=='^' || d=='(' || d=='[' || d=='{')
algebra_error
if((i=algebra_locate(ex,i0,i1,'+'))>=0)
return algebra_eval(ex,i0,i-1)+algebra_eval(ex,i+1,i1);
if((i=algebra_locate(ex,i0,i1,'-'))>=0)
return algebra_eval(ex,i0,i-1)-algebra_eval(ex,i+1,i1);
if((i=algebra_locate(ex,i0,i1,'*'))>=0)
return algebra_eval(ex,i0,i-1)*algebra_eval(ex,i+1,i1);
if((i=algebra_locate(ex,i0,i1,':'))>=0)
return algebra_eval(ex,i0,i-1)*algebra_eval(ex,i+1,i1);
if((i=algebra_locate(ex,i0,i1,'/'))>=0)
return algebra_eval(ex,i0,i-1)/algebra_eval(ex,i+1,i1);
if((i=algebra_locate(ex,i0,i1,'^'))>=0)
return pow(algebra_eval(ex,i0,i-1),algebra_eval(ex,i+1,i1));
if(c=='(' && d==')') return algebra_eval(ex,i0+1,i1-1);
if(c=='[' && d==']') return algebra_eval(ex,i0+1,i1-1);
if(c=='{' && d=='}') return algebra_eval(ex,i0+1,i1-1);
char *aux; aux=new char [i1-i0+2];
for(i=i0; i<=i1; i++) aux[i-i0]=ex[i]; aux[i1-i0+1]=0; i1=i1-i0; i0=0;
if(('a'<=c && c<='z') || ('A'<=c && c<='Z')) {d=aux[i1];
if(d==')' || d==']' || d=='}') {
if((i=algebra_locate_absolute(aux,i0,i1,'('))<0)
if((i=algebra_locate_absolute(aux,i0,i1,'['))<0)
if((i=algebra_locate_absolute(aux,i0,i1,'{'))<0)
algebra_error
val=algebra_eval(aux,i+1,i1-1);
aux[i]=0;
#ifdef jga_bessel
if(!strcmp(aux,"J0")) val=besselJJ(0,val); else
if(!strcmp(aux,"J1")) val=besselJJ(1,val); else
if(!strcmp(aux,"J2")) val=besselJJ(2,val); else
if(!strcmp(aux,"J3")) val=besselJJ(3,val); else
if(!strcmp(aux,"Y0")) val=besselYY(0,val); else
if(!strcmp(aux,"Y1")) val=besselYY(1,val); else
if(!strcmp(aux,"Y2")) val=besselYY(2,val); else
if(!strcmp(aux,"Y3")) val=besselYY(3,val); else
if(!strcmp(aux,"j0")) val=besselj(0,val); else
if(!strcmp(aux,"j1")) val=besselj(1,val); else
if(!strcmp(aux,"j2")) val=besselj(2,val); else
if(!strcmp(aux,"j3")) val=besselj(3,val); else
if(!strcmp(aux,"y0")) val=bessely(0,val); else
if(!strcmp(aux,"y1")) val=bessely(1,val); else
if(!strcmp(aux,"y2")) val=bessely(2,val); else
if(!strcmp(aux,"y3")) val=bessely(3,val); else
#endif
#ifdef jga_legendre
if(!strcmp(aux,"P00")) val=legendre(0,0,val); else
if(!strcmp(aux,"P10")) val=legendre(1,0,val); else
if(!strcmp(aux,"P11")) val=legendre(1,1,val); else
if(!strcmp(aux,"P20")) val=legendre(2,0,val); else
if(!strcmp(aux,"P21")) val=legendre(2,1,val); else
if(!strcmp(aux,"P22")) val=legendre(2,2,val); else
#endif
if(!strcmp(aux,"ln")) val=log(val); else
if(!strcmp(aux,"log")) val=log(val); else
if(!strcmp(aux,"exp")) val=exp(val); else
if(!strcmp(aux,"sin")) val=sin(val); else
if(!strcmp(aux,"cos")) val=cos(val); else
if(!strcmp(aux,"tan")) val=tan(val); else
if(!strcmp(aux,"asin")) val=asin(val); else
if(!strcmp(aux,"acos")) val=acos(val); else
if(!strcmp(aux,"atan")) val=atan(val); else
if(!strcmp(aux,"abs")) val=ABS(val); else
if(!strcmp(aux,"mod")) val=ABS(val); else
if(!strcmp(aux,"ABS")) val=ABS(val); else
if(!strcmp(aux,"sqr")) val=sqr(val); else
if(!strcmp(aux,"sqrt")) val=sqrt(val); else
if(!strcmp(aux,"sinh")) val=(exp(val)-exp(-val))/2; else
if(!strcmp(aux,"cosh")) val=(exp(val)+exp(-val))/2; else
on_error("algebraic evaluation", "undefined function", aux);
} else
if(!strcmp(aux,"pi")) val=pi; else
if(!strcmp(aux,"PI")) val=pi; else
if(!strcmp(aux,"Pi")) val=pi; else
if(!strcmp(aux,"e")) val=exp(1.0); else
if(!strcmp(aux,"E")) val=exp(1.0); else
if(!strcmp(aux,"eV")) val=1/au_eV; else
if(!strcmp(aux,"nm")) val=nm; else
if(!strcmp(aux,"c")) val=c_au; else
if(!strcmp(aux,"infinite")) val=infinity; else
if(!strcmp(aux,"infinity")) val=infinity; else
if(!strcmp(aux,"zero")) val=0; else
if(algebra_find(aux)==0) on_error("algebraic evaluation",
"undefined variable", aux);
else val=algebra_var->a;
delete [] aux; return val;
}
val=read_numero(aux);
delete [] aux; return val;
}
numero algebra_eval(char *ex)
{
int i,l=strlen(ex); char c;
for(i=0; i<l; i++) {
c=ex[0];
if(c!='+' && c!='-' && c!='*' && c!=':' && c!='/' && c!='^' && c!='.' &&
c!='(' && c!=')' && c!='[' && c!=']' && c!='{' && c!='}' &&
(c<'a' || c>'z') && (c<'A' || c>'Z') && (c<'0' || c>'9'))
algebra_error
}
return algebra_eval(ex,0,l-1);
}
int algebra_verbose=0;
void algebra_define(char *name, char *ex)
{
numero val=algebra_eval(ex);
if(algebra_find(name)==0) {
algebra_var=new algebra_variable;
algebra_var->name=new char [strlen(name)+1];
strcpy(algebra_var->name,name);
algebra_var->next=algebra_var0;
algebra_var0=algebra_var;
}
algebra_var->a=val;
if(algebra_verbose)
printf(">>> %s = %s = %g <<<\n", algebra_var->name,ex,algebra_var->a);
}
numero alread_numero(char *name)
{
strcpy(read_command,name);
return algebra_eval(read_command);
}
int alread_int(char *name)
{
strcpy(read_command,name);
return ((int) algebra_eval(read_command));
}
numero alread_numero(FILE *f)
{
read_name(f,read_command);
return algebra_eval(read_command);
}
int alread_int(FILE *f)
{
read_name(f,read_command);
return ((int) algebra_eval(read_command));
}
#endif
class green;
class green_z;
class rotation_th;
class rotation_fi;
class t_matrix;
class vector;
class cluster;
class atomic_scattering;
class propagation;
class multiple_scattering;
class final_state;
class calculation;
class electron_bin;
class green {
public:
numero *re,*im;
numero d,th,fi;
green(void) {d=th=fi=0;}
green *next;
void free(void) {delete [] re; delete [] im;}
void init(complex k, numero dd, numero tth, numero ffi, int periodic);
void prod(vector &a);
};
class green_z {
public:
numero *re,*im,d;
int trans;
green_z(void);
green_z *next;
void free(void) {delete [] re; delete [] im;}
void init(complex k, numero dd, int translation_type, int att_type);
};
class rotation_th {
public:
numero *val,th;
rotation_th *next;
rotation_th(void);
void free(void) {delete [] val;}
int init(numero tth);
};
class rotation_fi {
public:
numero *re,*im,fi;
rotation_fi *next;
rotation_fi(void);
void free(void) {delete [] re; delete [] im;}
int init(numero ffi);
};
class t_matrix {
public:
numero *re,*im;
numero rmt;
int lmax;
int n_c;
int ta;
int select;
t_matrix *next;
void free(void) {if(n_c>0) {delete [] re; delete [] im; n_c=0;}}
t_matrix (void) {n_c=0; ta=-1; lmax=-1; rmt=0;}
};
class vector {
public:
int lmax;
int n_c;
numero *re,*im;
vector(void);
void free(void);
void alloc(int lmax_, int n_c_);
void copy(vector &a);
void copy_to_array(complex *a);
void copy_to_array(complex *a, int cc);
void copy_to_array(complex *a, int lmax_, int cc);
void copy_from_array(complex *a, int lmax_, int n_c_);
void substitute_lmax(int lmax_);
void substitute_n_c(int n_c_, int c_flag);
int spin_rotation(numero al, numero be, numero ga);
friend vector operator*(numero x, vector &b);
int add(vector &b);
int ext(numero x);
int Rth(rotation_th *R, int op);
int Rfi(rotation_fi *R, int op);
int Gz(green_z *G, int lmax_final);
int tmat(t_matrix *t);
private:
void copy(vector &a, int lmax_, int n_c_, int c_flag);
void tmat_diagonal(t_matrix *t);
void tmat_full(t_matrix *t);
void tmat_so(t_matrix *t);
};
class cluster {
public:
int n,
nn,
nnn;
numero *x,*y,*z;
int *atom;
int *atZ;
numero Rmax;
numero x0,y0,z0;
int oriented;
numero *th,*fi;
numero eps_d;
numero eps_th;
int n_emit,
*emit,
*emit_s;
void add_emitter(int a);
void add_emitter(int a, int sc);
void add_emitter_plane(numero x_, numero y_, numero z_,
numero th_, numero fi_);
void add_emitter_column(numero x_, numero y_);
int is_emitter(int i);
void free_emitters(void);
void all_emitters(int ta, int sc);
void report_emitters(void);
numero zs;
int surface;
cluster(void);
void free(void);
void free_coordinates();
int set_n(void);
int read_atomic_type(FILE *fin);
void read(FILE *fin, char *my_file);
void write(char *name, char *units);
void read(FILE *fcoordinates);
void write(FILE *fout, char *units);
numero distance(numero x0_, numero y0_, numero z0_,
numero x1, numero y1, numero z1);
int get_atom(numero x_, numero y_, numero z_);
int get_atom(numero x_, numero y_, numero z_, numero err);
void sort(int emitter);
int add_atom(numero x_, numero y_, numero z_,
numero th_, numero fi_, int at);
int delete_atom(numero x_, numero y_, numero z_);
void add_layer(numero x_, numero y_, numero z_,
numero a, numero b,
numero al, numero be,
numero th_, numero fi_, int at);
void delete_layer(numero x_, numero y_, numero z_,
numero a, numero b,
numero al, numero be);
void add_surface(numero x_, numero y_, numero z_,
numero a, numero c, char *name,
numero th_, numero fi_, int at);
void add_half_layer(numero x_, numero y_, numero z_,
numero a, numero b,
numero al, numero be, numero ff,
numero th_, numero fi_, int at);
void add_row(numero x_, numero y_, numero z_, numero a,
numero tt, numero ff, numero th_, numero fi_, int at);
void delete_row(numero x_, numero y_, numero z_,
numero a, numero tt, numero ff);
void displace(numero xx, numero yy, numero zz);
void rotate(int axis, numero ang);
void rotate(double &xx, double &yy, double ang);
int delete_non_emitters(void);
};
class atomic_scattering {
public:
atomic_scattering(void);
atomic_scattering *next;
int ta;
int select;
int n_c;
int lmax;
numero *re, *im;
int magnetic;
int n_k;
numero *k;
numero mass;
void free(void);
void init_t_matrix(t_matrix *t);
int read(FILE *fin, char *name);
int scan(FILE *fout, int sel);
int comp;
spline *rr, *ii;
void read_phases(FILE *fin, char *units);
complex *tl_phases(int n_c_, int &lmax_);
void cut_tl_phases(complex *tl, int n_c_, int &lmax_);
numero Gaunt_j(int l, int j, int mu, int lp, int jp, int lpp);
complex *tl_temperature(complex *tl, int n_c_, int &lmax_);
complex *tl_temperature_so(complex *tl, int &lmax_);
numero tl_deltal(complex tl) {return atan2(imag(tl), real(tl));}
void init_t_matrix_diag(t_matrix *t);
void init_t_matrix_diag(complex *tl, t_matrix *t);
void init_t_matrix_so(t_matrix *t);
void init_t_matrix_so(complex *tl, t_matrix *t);
numero a,V;
complex *tl_sphere(int lmax_);
void init_t_matrix_sphere(t_matrix *t);
int n_rad;
numero *rad;
int atZ;
complex *tl_potential(int n_c_, int &lmax_);
void init_t_matrix_potential(t_matrix *t);
void read_potential(FILE *fin);
void read_full(FILE *fin, char *units);
void init_t_matrix_full(numero kk, t_matrix *t);
void free_full(void);
numero *copy_(numero *a_, numero *b_, int n, numero x);
};
#define n_Debye_temperature_elements 100
class propagation {
public:
int n_d,
n_th,
n_fi,
n_t;
numero dmax;
complex k;
int translation_type;
int attenuation_type;
numero T;
numero T_Debye[n_Debye_temperature_elements];
numero V0;
numero refraction;
spline iimfp;
int iimfp_flag;
numero Vi;
void scan_imfp(char *name);
void scan_imfp(FILE *fout);
numero iimfp_TPP(numero kr);
numero iimfp_SD(numero kr);
numero TPP_rho, TPP_Nv, TPP_Ep, TPP_Eg;
numero screening_length;
int scattering_so;
void set_k(int ik);
void set_k(complex k_);
void read_imfp(FILE *fin, char *my_file);
void set_muffin_tin_potentials(void);
green_z *Gz,*Gz0;
rotation_th *Rth,*Rth0;
rotation_fi *Rfi,*Rfi0;
t_matrix *t_mat,
*t_mat0;
numero d,
th,
fi;
int ifi;
int n_a;
atomic_scattering *a, *a0;
numero epsilon;
propagation(void);
void R_1TR(vector &gg, int i, t_matrix *tt);
void R_1TR(vector &gg, int i);
void Rab(vector &gg);
void Rab_1(vector &gg);
void propagate(vector &gg, int lmax_final);
void free_Green_functions(void);
void free_rotations(void);
void free_t_matrix(void);
void report_links(void);
int get_ij(int i, int j);
void get_ij(void);
int get_d(void);
int get_th(numero th_);
int get_fi(numero fi_);
int get_t_matrix(int ta);
int get_scatterer(int ta, int opt);
int get_scatterer(int ta) {return get_scatterer(ta,1);}
int free_scatterer(int ta);
void free_scatterers(void);
void add_scatterer(int ta);
void add_screened_scatterer(int ta, int ta_old);
void scan_scatterer(int ta, char *name, int sel);
void set_lmax(void);
int get_n_c(void);
int dim;
matrix aa;
int lmax_aa;
void get_exact(int n_c, int lmax_);
void free_exact();
char aa_output[100];
int aa_output_flag;
int separation;
int n_G;
green *Gab,*Gab0;
numero *Gab_cg;
int Gab_cg_flag;
int get_Gab(void);
int nn_d,nn_th,nn_fi,nn_t,nn_G,nn_c;
};
class wave_function {
public:
int n;
vector *g;
wave_function(void) {n=0;}
void alloc(int n_) {
free(); n=n_; g=new vector [n];
int i; for(i=0; i<n; i++) {g[i].lmax=-1; g[i].n_c=1;}
}
void clear(void) {int a; for(a=0; a<n; a++) g[a].free();}
void free(void) {clear(); if(n>0) delete [] g; n=0;}
};
class multiple_scattering {
public:
wave_function o,n;
int method;
numero eta;
multiple_scattering(void);
void next_scattering(void);
void exact(void);
void free(void);
void clear(void);
void alloc(void);
void write(FILE *fout, int o_, int max_order_);
int read(FILE *fin, int o_);
int max_order;
};
class array {
public:
complex *a;
int n;
array(void) {n=0;}
void free(void) {if(n>0) delete [] a; n=0;}
void alloc(int n_) {free(); n=n_; a=new complex [n];
int i; for(i=0; i<n; i++) a[i]=0;}
};
class final_state {
public:
int n_th;
int n_fi;
int n_ang;
numero *th, *fi;
numero *th_out,
*transmission;
final_state(void);
void free(void);
void init_th(numero thi, numero thf, int nth);
void init_phi(numero fii, numero fif, int nfi);
void read_angles(FILE *fin, char *my_file);
void init_refraction(
numero refraction);
void init_transmission(
numero refraction);
void free_mesh(void);
void init_mesh(int n_1_, int n_2_);
void init_mesh(numero x0, numero y0, numero z0,
numero x1, numero y1, numero z1,
numero x2, numero y2, numero z2, int n_1_, int n_2_);
void init_mesh(numero r,
numero th1, numero th2, numero fi1, numero fi2,
int n_1_, int n_2_);
int mesh_flag;
numero *x,*y,*z;
int n_1,n_2;
void init_Ylm(void);
void init_Ylm(numero th_, numero fi_, complex *Ylm_);
complex *Ylm(int i, int j);
vector Ylm(complex *Ylm_);
void free_Ylm(void);
array *Ylm0_th;
array *Ylm0_fi;
int Ylm0_th_flag;
int Ylm0_fi_flag;
};
class calculation {
public:
int n_final,
n_ang,
n_mesh,
n_initial,
n_initial_used,
n_c;
numero thave;
numero *III0;
numero IIIthfi(int no, numero th, numero fi);
numero IIIave(int no, numero th, numero fi);
int n_atoms_last;
numero e_th, e_fi,
e_tth, e_ffi,
alpha, delta;
complex eps[3];
int integ;
numero *k, *kk;
char *k_units;
numero V0;
int n_k;
int k_flag;
complex *kc;
numero beta;
int mode_beta,
mode_sample,
mode_eps;
int beamline;
numero beamline_th, beamline_fi;
int *orders,
n_orders,
max_order;
int n_orders_eff(void);
char *wf_in,
*wf_out;
FILE *wf_fin,
*wf_fout;
int ms;
array *results;
FILE *fout;
int verbose;
int select_wf;
int n_intensities;
int n_f;
calculation(void);
void free_results(void);
void free_k(void);
void free_orders(void);
void free(void);
void alloc(int n_intial_);
void init_k(numero kki, numero kkf, int n_k_, char *k_units_);
void init_k(complex *kc_, int n_k_, char *k_units_);
void init_incidence(numero e_th_, numero e_fi_);
void init_polarization(numero alpha_, numero delta_);
void init_orders(int n_orders_, int *o);
void init_final_dist(void);
void init_final_f(int n_f_);
void init_mode_sample(int mode_sample_);
void init_mode_beta(int mode_beta_);
void init_beamline(int beamline_);
void init(char *name, char *title);
void init(char *name);
int lmax;
int lmax_inter;
int dim;
int center;
void init_wf_tmat(int c, int l, int m);
complex *wave_function_tmat(complex *wf);
void scan_tmat(char *name, int lmax_);
complex *wave_function(complex *wf);
int evaluation(int initial);
void eval_recursion(int initial);
complex *wave_function(int i, int j, complex *wf);
void intensity(numero *intensity_, complex *wf);
void write(int ik);
void set_polarization(void);
void set_polarization(int pol);
void eval_polarization(void);
private:
int polarization_flag;
void write_title(FILE *fout, char *title);
void write_orders(FILE *fout);
void write_ang(FILE *fout, char *title);
void write_mesh(FILE *fout, char *title);
void write_f(FILE *fout, char *title);
void write_k(FILE *fout_, int ik);
void write_ang(FILE *fout, int ik);
void write_mesh(FILE *fout, int ik);
void write_f(FILE *fout, int ik);
void write_numeros(FILE *fout_, numero *intensity_, complex *wf);
void write_numeros(FILE *fout_, numero val);
void intensity(numero *intensity_, int no, int i, int j, complex *wf);
};
class electron_bin {
public:
int spin_flag;
numero th_spin,
fi_spin;
int molecule;
int n0,l0,
m0,
ms0,
j0, mj0,
ljmj;
int n_c;
int excitation;
int n_rmat;
splinec *rmat;
int emitter;
int CR_nterms, CR_flag;
numero CR_C[10], CR_xhi[10];
int CR_n[10];
numero intensity(complex *wf);
void wf_far(int i, int j, complex *wf);
void wf_far(numero th, numero fi, complex *Ylm, complex *wf);
void wf_far(vector &a, complex *Ylm, complex *wf);
void wf_near(int i, int j, complex *wf);
int scan_PD(char *name);
int scan_MS(char *name, int nwf);
int wf_ns;
complex rrm[4];
void init_wf_PD(int jm, int mjms, complex *eps);
void init_wf_lmms(int m0_, int ms0_, complex *eps);
void init_wf_ljmj(int j0_, int mj0_, complex *eps);
complex ang_mat_el(int m0_, int l, int m, complex *eps);
void read_rmat(FILE *fin);
void free_rmat(void);
complex rmat_el_MT(int l);
complex rmat_el_CR(int l);
numero CR_wf(numero r);
spline P0,Q0;
void init_rmat_MT(void);
void free_rmat_MT(void) {P0.free(); Q0.free();}
complex *manual;
int manual_flag;
int lmax_manual;
int n_c_manual;
void init_wf_manual(void);
int leed_i, leed_j;
numero leed_th;
numero leed_x, leed_y;
numero leed_a, leed_b;
numero ax,ay,bx,by;
numero Gax,Gay,Gbx,Gby;
numero area;
numero k0x,k0y,k0z;
void surface_lattice(numero a, numero b, numero al, numero be);
void init_leed_emitters(void);
int init_wf_LEED(int spin_);
int scan_DLEED(char *name);
int scan_LEED(char *name);
void wf_LEED(complex *wf);
void program(char *my_file);
electron_bin(void)
{
th_spin=fi_spin=0; spin_flag=0;
ljmj=0; n0=1; l0=0;
m0=infinite_int+1;
ms0=1;
j0=infinite_int+1; mj0=infinite_int+1;
n_c=1; wf_ns=1;
manual=NULL; manual_flag=0;
rmat=NULL;
leed_i=leed_j=0;
leed_x=leed_y=0;
surface_lattice(5/a0_au,5/a0_au, 0,pi/2);
CR_flag=0;
molecule=0;
} };
void init_lmax(int &lmax);
void init_lmax(void);
void free_lmax(void);
void report_size(void);
cluster coord;
propagation scat;
multiple_scattering iter;
final_state final;
calculation calc;
electron_bin electron;
int size_of_rotation_th=0,
size_of_rotation_fi=0,
size_of_green_z=0,
size_of_lmax=-1;
int interpolation_type=0;
#define str_length_files 100
#define str_length_comments 100
#define str_length_units 10
int lmax_eff=-1,
lmax_max=15;
numero *Gaunt_integrals,
*cgcg12;
int *lp12;
void init_lmax(int &lmax)
{
free_lmax(); size_of_lmax=lmax_eff=lmax=(lmax>lmax_max)?lmax_max:lmax;
init_lmax();
}
void init_lmax(void)
{
int l1,l2,l3,m1,m2,p, n_CG;
for(l1=0, size_of_green_z=0, n_CG=0; l1<=lmax_eff; l1++)
for(m1=-l1; m1<=l1; m1++)
for(l2=(m1>0?m1:-m1); l2<=lmax_eff; l2++, size_of_green_z++)
for(l3=(l1>l2?l1-l2:-l1+l2); l3<=l1+l2; l3+=2) n_CG++;
Gaunt_integrals = new numero [n_CG];
numero pi_factor=sqrt(4*pi); int i;
for(l1=0, i=0; l1<=lmax_eff; l1++)
for(m1=-l1; m1<=l1; m1++)
for(l2=(m1>0?m1:-m1); l2<=lmax_eff; l2++)
for(l3=(l1>l2?l1-l2:-l1+l2); l3<=l1+l2; l3+=2)
Gaunt_integrals[i++]=pi_factor*sqrt(2*l3+1)*Gaunt(l1,l3,l2,m1,0,m1);
for(l1=0, size_of_rotation_th=0; l1<=lmax_eff; l1++)
for(m1=-l1; m1<=l1; m1++)
for(m2=-l1; m2<=l1; m2++) size_of_rotation_th++;
size_of_rotation_fi=2*lmax_eff+1;
lp12 = new int [lmax_eff+3];
for(l1=0; l1<=lmax_eff+2; l1++) lp12[l1]=(l1+1)*(l1+1);
cgcg12 = new numero [8*lp12[lmax_eff]];
for(l1=p=0; l1<=lmax_eff; l1++)
for(m1=-l1; m1<=l1; m1++, p+=8) {
l2=l1+l1; m2=m1+m1;
cgcg12[p ]=CGspin1_2(l2,l2+1, 1,m2+1) * CGspin1_2(l2,l2+1, 1,m2+1);
cgcg12[p+1]=CGspin1_2(l2,l2-1, 1,m2+1) * CGspin1_2(l2,l2-1, 1,m2+1);
cgcg12[p+2]=CGspin1_2(l2,l2+1,-1,m2-1) * CGspin1_2(l2,l2+1,-1,m2-1);
cgcg12[p+3]=CGspin1_2(l2,l2-1,-1,m2-1) * CGspin1_2(l2,l2-1,-1,m2-1);
cgcg12[p+4]=CGspin1_2(l2,l2+1, 1,m2+1) * CGspin1_2(l2,l2+1,-1,m2+1);
cgcg12[p+5]=CGspin1_2(l2,l2-1, 1,m2+1) * CGspin1_2(l2,l2-1,-1,m2+1);
cgcg12[p+6]=CGspin1_2(l2,l2+1,-1,m2-1) * CGspin1_2(l2,l2+1, 1,m2-1);
cgcg12[p+7]=CGspin1_2(l2,l2-1,-1,m2-1) * CGspin1_2(l2,l2-1, 1,m2-1);
} }
void free_lmax(void)
{
if(lmax_eff>=0) {
delete [] Gaunt_integrals; delete [] lp12;
delete [] cgcg12;
lmax_eff=-1;
} }
void report_size(void)
{
fprintf(foutput,"%s%s%4d%s%4d%s%4d%s%4d\n",
"--- size of different elements",
"\n lmax = ", size_of_lmax,
"\n Green's function = ", size_of_green_z,
"\n Rotation (0,th,0) = ", size_of_rotation_th,
"\n Rotation (0,0,fi) = ", size_of_rotation_fi);
}
calculation::calculation(void)
{
n_final=n_orders=n_c=n_k=0;
thave=0;
init_incidence(0,0);
init_polarization(0,0);
beta=0;
mode_beta=0;
mode_sample=0;
mode_eps=1;
fout=NULL;
verbose=1;
k_units=new char [str_length_units];
integ=0;
n_atoms_last=0;
select_wf=0;
n_intensities=1;
n_ang=n_mesh=n_f=0;
n_initial=n_initial_used=0;
wf_in=new char [str_length_files]; strcpy(wf_in,"none");
wf_out=new char [str_length_files]; strcpy(wf_out,"none");
wf_fin=NULL; wf_fout=NULL;
ms=0;
beamline=0;
}
void calculation::init(char *name)
{
close_file(fout);
close_file(wf_fin);
close_file(wf_fout);
wf_fin =open_file(foutput,wf_in, "r");
wf_fout=open_file(foutput,wf_out,"a");
fout =open_file(foutput,name, "w");
}
void calculation::init(char *name, char *title)
{
init(name);
if(n_ang>0) {
if(verbose) write_ang(foutput,title);
if(fout!=NULL) write_ang(fout,title);
} else
if(n_mesh>0) {
if(verbose) write_mesh(foutput,title);
if(fout!=NULL) write_mesh(fout,title);
} else
if(n_f>0) {
if(verbose) write_f(foutput,title);
if(fout!=NULL) write_f(fout,title);
} }
void calculation::init_final_dist(void)
{
n_f=0;
n_ang=final.n_th * final.n_fi;
if(n_ang>0) n_mesh=0;
else n_mesh=final.n_1 * final.n_2;
n_final=n_ang+n_mesh;
}
void calculation::init_final_f(int n_f_)
{
n_ang=n_mesh=0; n_final=n_f=n_f_;
}
void calculation::init_orders(int n_orders_, int *o)
{
int i,j,l,m;
free_orders();
n_orders=n_orders_;
orders=new int [n_orders];
for(i=n_orders-1; i>=0; i--) {
l=-1;
for(j=0; j<n_orders; j++) if(l<o[j]) {l=o[j]; m=j;}
orders[i]=l; o[m]=-1;
}
delete [] o;
max_order=orders[n_orders-1];
}
void calculation::init_k(numero kki, numero kkf, int n_k_, char *k_units_)
{
numero dkk;
int i;
free_k();
if(n_k_<1) n_k=1; n_k=n_k_; k_flag=1;
strcpy(k_units,k_units_);
kk=new numero [n_k]; k=new numero [n_k];
if(n_k>1) dkk=(kkf-kki)/(n_k-1); else dkk=0;
for(i=0; i<n_k; i++) {
kk[i]=kki+i*dkk;
k[i]=units_k(k_units,kk[i]);
if(k[i]<=0) on_warning(foutput, "calculation::init_k", "momentum k<0");
} }
void calculation::init_k(complex *kc_, int n_k_, char *k_units_)
{
free_k();
n_k=n_k_;
strcpy(k_units,k_units_);
kc=kc_; k_flag=2;
}
void calculation::init_incidence(numero e_th_, numero e_fi_)
{
normalize_angles(e_th_,e_fi_); e_th=e_tth=e_th_; e_fi=e_ffi=e_fi_;
}
void calculation::init_polarization(numero alpha_, numero delta_)
{
alpha=-alpha_; delta=delta_;
}
void calculation::init_beamline(int beamline_)
{
beamline=beamline_;
if(beamline==1) {mode_eps=3; beta=pi/3;}
if(beamline==2) {mode_eps=3; beta=pi/3;}
}
void calculation::init_mode_beta(int mode_beta_)
{
beamline=0;
mode_beta=mode_beta_;
mode_eps=(mode_beta||mode_sample)?3:1;
}
void calculation::init_mode_sample(int mode_sample_)
{
beamline=0;
mode_sample=mode_sample_;
mode_eps=(mode_beta||mode_sample)?3:1;
}
int calculation::n_orders_eff(void)
{
if(iter.method==3) return 1;
else return n_orders;
}
void calculation::set_polarization(void)
{light_polarization_mu(e_tth,e_ffi,alpha,delta, eps);}
void calculation::set_polarization(int pol)
{
if(mode_eps>1) {eps[0]=eps[1]=eps[2]=0; eps[pol]=1;}
else light_polarization_mu(e_tth,e_ffi,alpha,delta, eps);
}
void calculation::free_results(void)
{
int i;
for(i=0; i<n_initial_used; i++) results[i].free();
if(n_initial>0) delete [] results; n_initial=n_initial_used=0;
}
void calculation::free_k(void)
{
if(n_k>0)
if(k_flag==1) {delete [] kk; delete [] k;} else
if(k_flag==2) delete [] kc;
n_k=0;
}
void calculation::free_orders(void)
{
if(n_orders>0) {n_orders=0; delete [] orders;}
}
void calculation::free(void)
{
integ=n_f=0;
close_file(fout); fout=NULL;
close_file(wf_fin); wf_fin=NULL;
close_file(wf_fout); wf_fout=NULL;
}
void calculation::alloc(int n_initial_)
{
free_results();
n_initial=n_initial_*mode_eps;
results=new array [n_initial];
int i; for(i=0; i<n_initial; i++) results[i].n=0;
}
complex *calculation::wave_function(complex *wf)
{
int i,j;
if(select_wf<0) {
if(select_wf==-1) return wf=wave_function_tmat(wf);
if(n_f>0) for(i=0; i<n_f; i++) wf=wave_function(i,0,wf);
}
if(n_ang>0) for(i=0; i<final.n_th; i++)
for(j=0; j<final.n_fi; j++)
wf=wave_function(i,j,wf);
if(n_mesh>0) for(i=0; i<final.n_1; i++)
for(j=0; j<final.n_2; j++)
wf=wave_function(i,j,wf);
return wf;
}
int calculation::evaluation(int initial)
{
int o,no, next;
complex *wf;
if(n_orders==0) on_error("calc::evaluation", "undefined orders of scat.");
n_atoms_last=coord.n;
polarization_flag=0;
if(iter.method==-1) results[initial].alloc(n_final * n_c*(max_order+1));
else results[initial].alloc(n_final * n_c*n_orders_eff());
n_initial_used++;
wf=results[initial].a;
if(iter.method==3) {
iter.exact();
wave_function(wf);
return 0;
}
for(o=0, no=0, next=0; o<=max_order; o++) {
if(next) iter.next_scattering();
if(wf_fin!=NULL && next==0)
next=iter.read(wf_fin, o);
else next=1;
if(wf_fout!=NULL)
iter.write(wf_fout, o, max_order);
if(orders[no]==o || iter.method==-1) {
wf=wave_function(wf);
if(orders[no]==o) no++;
} }
if(iter.method==-1) eval_recursion(initial);
return 0;
}
void calculation::eval_recursion(int initial)
{
int i,j, o,no, nn=n_final*n_c;
array *results_temp;
recurs *val;
val=new recurs [nn];
results_temp=new array [nn];
for(i=0; i<nn; i++) {
results_temp[i].n=0; results_temp[i].alloc(max_order+1);
}
for(o=j=0; o<=max_order; o++)
for(i=0; i<nn; i++, j++) results_temp[i].a[o]=results[initial].a[j];
results[initial].free();
for(i=0; i<nn; i++) val[i].init(max_order, results_temp[i].a);
for(i=0; i<nn; i++) results_temp[i].free();
delete [] results_temp;
results[initial].alloc(nn * n_orders_eff());
for(no=j=0; no<n_orders_eff(); no++)
for(i=0; i<nn; i++, j++)
results[initial].a[j]=val[i].eval(1,orders[no],0);
for(i=0; i<nn; i++) val[i].free();
delete [] val;
}
void calculation::eval_polarization(void)
{
int i,j,no,c,index,initial,initial3;
numero tt,ff,rr, beamx,beamy,beamz;
numero beamxp,beamyp,beamzp;
numero beamxi,beamyi,beamzi;
if(mode_eps>1) {
polarization_flag=1;
for(initial=0; initial<n_initial_used/3; initial++)
for(no=index=0; no<n_orders_eff(); no++)
for(i=0; i<final.n_th; i++)
for(j=0; j<final.n_fi; j++) {initial3=3*initial;
tt=final.th_out[i]; ff=final.fi[j];
if(beamline==0) {
if(mode_sample) {
if(mode_beta) {e_th=tt-beta; e_fi=ff;}
else {e_th=-e_tth; e_fi=ff;}
normalize_angles(e_th, e_fi);
light_polarization_mu(e_th, e_fi, alpha, delta, eps);
} else {e_th=e_tth; e_fi=e_ffi;}
} else
if(beamline==1) {
cartesian_to_spherical(sin(beta)*sin(tt)*cos(ff)-cos(beta)*sin(ff),
sin(beta)*sin(tt)*sin(ff)+cos(beta)*cos(ff),
sin(beta)*cos(tt),
rr,e_th,e_fi);
e_th=pi/2-e_th;
e_fi=pi +e_fi;
light_polarization_mu(e_th,e_fi,0,0, eps);
}
if(beamline==2) {
beamx=-sin(beamline_th)*cos(beamline_fi);
beamy=-sin(beamline_th)*sin(beamline_fi);
beamz= cos(beamline_th);
beamxp= beamx*cos(tt)+beamz*sin(tt);
beamyp= beamy;
beamzp=-beamx*sin(tt)+beamz*cos(tt);
beamxi= beamxp*cos(ff)+beamyp*sin(ff);
beamyi=-beamxp*sin(ff)+beamyp*cos(ff);
beamzi= beamzp;
cartesian_to_spherical(beamxi,beamyi,beamzi,
rr,e_th,e_fi);
normalize_angles(e_th, e_fi);
light_polarization_mu(e_th,e_fi,alpha,delta, eps);
}
for(c=0; c<n_c; c++, index++)
results[initial].a[index]= eps[0]*results[initial3 ].a[index]
+ eps[1]*results[initial3+1].a[index]
+ eps[2]*results[initial3+2].a[index];
} } }
void calculation::intensity(numero *intensity_,
int no, int i, int j, complex *wf)
{
int c, initial, n_initial_, index;
complex *wf_;
if(select_wf<0) index=(no*n_final+n_ang+n_mesh +i)*n_c; else
if(select_wf<1000) index=(no*n_final+ i*final.n_fi+j)*n_c; else
index=(no*n_final+n_ang+ i*final.n_2 +j)*n_c;
if(polarization_flag && select_wf==0) n_initial_=n_initial_used/3;
else n_initial_=n_initial_used;
if(n_intensities==0 && n_initial_>1)
on_error("calculation::intensity", "amplitude for multi-initial state");
if(n_intensities==0) {
wf_=results[0].a + index;
for(c=0; c<n_c; c++) wf[c]=wf_[c];
} else {
for(c=0; c<n_intensities; c++) intensity_[c]=0;
for(initial=0; initial<n_initial_; initial++) {
wf_=results[initial].a + index;
intensity(intensity_, wf_);
} }
if(select_wf==0 && n_intensities==1)
intensity_[0]=final.transmission[i] * intensity_[0];
}
void calculation::intensity(numero *II_, complex *wf)
{
switch(select_wf) {
case 0: II_[0]+= electron.intensity(wf); break;
case 1000: II_[0]+= electron.intensity(wf); break;
case -2: II_[0]+= sqr(pi/electron.area)
/(sqr(real(scat.k))/2-scat.V0)
/(cos(electron.leed_th)*cos(0))
*electron.intensity(wf); break;
} }
complex *calculation::wave_function(int i, int j, complex *wf)
{
switch(select_wf) {
case 0: electron.wf_far(i,j,wf); break;
case 1000: electron.wf_near(i,j,wf); break;
case -2: electron.wf_LEED(wf); break;
}
return wf+n_c;
}
void calculation::write(int ik)
{
eval_polarization();
if(n_ang>0) {
if(verbose) write_ang(foutput,ik);
if(fout!=NULL) write_ang(fout,ik);
} else
if(n_mesh>0) {
if(verbose) write_mesh(foutput,ik);
if(fout!=NULL) write_mesh(fout,ik);
} else
if(n_f>0) {
if(verbose) write_f(foutput,ik);
if(fout!=NULL) write_f(fout,ik);
}
free_results();
}
void calculation::write_numeros(FILE *fout_, numero val)
{
if(ABS(val)<100 && ABS(val)>0.01) fprintf(fout_," %12.8f", val);
else fprintf(fout_," %12g", val);
}
void calculation::write_numeros(FILE *fout_, numero *intensity_, complex *wf)
{
int i,c;
if(n_intensities==0)
for(c=0; c<n_c; c++) {
fprintf(fout_, " ");
write_numeros(fout_, real(wf[c]));
write_numeros(fout_, imag(wf[c]));
}
else for(i=0; i<n_intensities; i++)
write_numeros(fout_, intensity_[i]);
}
numero calculation::IIIthfi(int no, numero th, numero fi)
{
numero ii,xth,xfi;
numero th0=final.th_out[0], th1=final.th_out[final.n_th-1];
numero fi0=final.fi[0], fi1=final.fi[final.n_fi-1];
int ith,ifi,ij;
while(fi<0) fi+=2*pi;
while(fi>2*pi) fi-=2*pi;
xth=(final.n_th-1)*(th-th0)/(th1-th0); ith=int(floor(xth-0.0001));
xfi=(final.n_fi-1)*(fi-fi0)/(fi1-fi0); ifi=int(floor(xfi-0.0001));
if(ifi==-1) ifi=0;
if(ith==-1) ith=0;
if(0<=ith && ith<final.n_th-1 && 0<=ifi && ifi<final.n_fi-1) {
ij=no*n_ang+ith*final.n_fi+ifi;
xth = xth-ith;
xfi = xfi-ifi;
ii=III0[ij]*(1-xth)*(1-xfi) + III0[ij+final.n_fi]*xth*(1-xfi) + III0[ij+1]*(1-xth)*xfi + III0[ij+final.n_fi+1]*xth*xfi;
} else ii=0;
if(ii<0) ii=0;
return ii;
}
numero calculation::IIIave(int no, numero th, numero ph)
{
if(thave<=1e-6) return IIIthfi(no,th,ph);
int i,j, nn=10, mm=50;
numero tth, ffi, val=0, th1, ph1, cf, nw=0, x0, y0, z0, x1, y1, th2, ph2;
for(i=0; i<nn; i++)
for(j=0; j<mm; j++) {
th1=i*2*thave/(nn-1); //2*sigma range
ph1=j*2*pi/mm;
//rotation of (001) around Y by th1 and around Z by ph1
x0 = cos(ph1)*sin(th1);
y1 = sin(ph1)*sin(th1);
z0 = cos(th1);
//rotation around Y by th
x1 = x0*cos(th) + z0*sin(th);
z0 = -x0*sin(th) + z0*cos(th);
//rotation around Z by ph
x0 = x1*cos(ph) - y1*sin(ph);
y0 = x1*sin(ph) + y1*cos(ph);
th2 = acos(z0);
ph2 = atan2(y0,x0);
cf = exp(-(th1*th1/thave*thave))*(i>0.1?i:0.1); //gauss weight * radial weight
nw += cf; //sum of weights
val+=IIIthfi(no,th2,ph2)*cf;
}
return val/nw;
}
void calculation::write_ang(FILE *fout_, int ik)
{
int no,nno,i,j;
numero h,fc;
complex *wf;
numero intensity_[1], val, *III;
wf=new complex [n_c];
if(integ==0) {
nno=n_orders_eff();
if(thave>1e-6 && n_intensities>0 && final.n_fi>1 && final.n_th>1) {
if(n_intensities>1)
on_error(foutput, "scan pd/ms", "only scalars can be averaged");
III=new numero [nno*n_ang];
III0=new numero [nno*n_ang];
for(i=0; i<final.n_th; i++)
for(j=0; j<final.n_fi; j++)
for(no=0; no<nno; no++) {
intensity(intensity_, no,i,j, wf);
III0[no*n_ang+i*final.n_fi+j]=intensity_[0];
III[no*n_ang+i*final.n_fi+j]=0;
}
for(no=0; no<nno; no++)
for(i=0; i<final.n_th; i++)
for(j=0; j<final.n_fi; j++)
III[no*n_ang+i*final.n_fi+j]=IIIave(no, final.th_out[i], final.fi[j]);
delete [] III0;
}
for(i=0; i<final.n_th; i++)
for(j=0; j<final.n_fi; j++) {
write_k(fout_,ik);
if(final.n_th>1) fprintf(fout_, " %6.2f", final.th_out[i]*180/pi);
if(final.n_fi>1) fprintf(fout_, " %7.2f", final.fi[j]*180/pi);
for(no=0; no<n_orders_eff(); no++) {
if(thave>1e-6 && n_intensities>0 && final.n_fi>1 && final.n_th>1)
write_numeros(fout_, III[no*n_ang+i*final.n_fi+j]);
else {
intensity(intensity_, no,i,j, wf);
write_numeros(fout_, intensity_, wf);
} }
fprintf(fout_, "\n");
}
if(thave>1e-6 && n_intensities>0 && final.n_fi>1 && final.n_th>1)
delete [] III;
} else
if(integ==1) {
h = ABS((final.fi[final.n_fi-1]-final.fi[0])/(final.n_fi-1));
for(i=0; i<final.n_th; i++) {
write_k(fout_,ik);
if(final.n_th>1) fprintf(fout_, " %6.2f", final.th_out[i]*180/pi);
for(no=0; no<n_orders_eff(); no++) {
val=0;
for(j=0; j<final.n_fi; j++) {
if((j==0 || j==final.n_fi-1) && final.n_fi>1)
{intensity(intensity_, no,i,j, wf); val+=0.5*intensity_[0];}
else {intensity(intensity_, no,i,j, wf); val+= intensity_[0];}
}
intensity_[0]=val*h; write_numeros(fout_, intensity_, wf);
}
fprintf(fout_, "\n");
} } else
if(integ==2) {
write_k(fout_,ik);
h = ABS( (final.th_out[final.n_th-1]-final.th_out[0])/(final.n_th-1)
*(final.fi[final.n_fi-1]-final.fi[0])/(final.n_fi-1));
for(no=0; no<n_orders_eff(); no++) {
val=0;
for(i=0; i<final.n_th; i++)
for(j=0; j<final.n_fi; j++) {
if((i==0 || i==final.n_th-1) && final.n_th>1) fc=0.5; else fc=1;
if((j==0 || j==final.n_fi-1) && final.n_fi>1) fc=0.5*fc;
intensity(intensity_, no,i,j, wf);
val+=fc*sin(final.th_out[i])*intensity_[0];
}
intensity_[0]=val*h; write_numeros(fout_, intensity_, wf);
}
fprintf(fout_, "\n");
}
delete [] wf;
}
void calculation::write_mesh(FILE *fout_, int ik)
{
complex *wf; wf=new complex [n_c];
numero r,theta,phi, intensity_[1];
int no,i,j,ij;
for(i=ij=0; i<final.n_1; i++)
for(j=0; j<final.n_2; j++, ij++) {
write_k(fout_,ik);
if(final.mesh_flag==1) {
if(final.n_1>1) fprintf(fout_, " %9.4f", final.x[ij]*a0_au);
if(final.n_2>1) fprintf(fout_, " %9.4f", final.z[ij]*a0_au);
}
if(final.mesh_flag==2) {
cartesian_to_spherical(final.x[ij],final.y[ij],final.z[ij],
r,theta,phi);
if(final.n_1>1) fprintf(fout_, " %6.2f", theta*180/pi);
if(final.n_2>1) fprintf(fout_, " %7.2f", phi*180/pi);
}
for(no=0; no<n_orders_eff(); no++) {
intensity(intensity_, no,i,j, wf);
write_numeros(fout_, intensity_, wf);
}
fprintf(fout_, "\n");
}
delete [] wf;
}
void calculation::write_f(FILE *fout_, int ik)
{
complex *wf; wf=new complex [n_c];
numero *intensity_;
int no,i;
if(n_intensities>0) intensity_=new numero [n_intensities];
for(i=0; i<n_f; i++) {
write_k(fout_,ik);
for(no=0; no<n_orders_eff(); no++) {
intensity(intensity_, no,i,0, wf);
write_numeros(fout_, intensity_, wf);
}
fprintf(fout_, "\n");
}
delete [] wf;
}
void calculation::write_k(FILE *fout_, int ik)
{
if(n_k>1 || ms)
if(k_flag==1 || ms) fprintf(fout_, " %9.4f", kk[ik]); else
if(k_flag==2) fprintf(fout_, " %9.4f %9.4f",
real(kc[ik])/units_conv_fct(k_units),
imag(kc[ik])/units_conv_fct(k_units));
}
void calculation::write_ang(FILE *fout_, char *title)
{
write_title(fout_, title);
if(final.n_th>1 && (integ==0 || integ==1)) fprintf(fout_," theta");
if(final.n_fi>1 && integ==0) fprintf(fout_," phi");
write_orders(fout_);
}
void calculation::write_mesh(FILE *fout_, char *title)
{
write_title(fout_, title);
if(final.mesh_flag==1) {
if(final.n_1>1) fprintf(fout_," x1 (Ang)");
if(final.n_2>1) fprintf(fout_," x2 (Ang)");
}
if(final.mesh_flag==2) {
if(final.n_1>1) fprintf(fout_," theta");
if(final.n_2>1) fprintf(fout_," phi");
}
write_orders(fout_);
}
void calculation::write_f(FILE *fout_, char *title)
{
write_title(fout_, title);
write_orders(fout_);
}
void calculation::write_title(FILE *fout_, char *title)
{
fprintf(fout_, "--- %s\n", title);
if(n_k>1 || ms)
if(k_flag==1 || ms) fprintf(fout_," %5.5s", str_units(k_units)); else
if(k_flag==2) fprintf(fout_," complex k in %5.5s", str_units(k_units));
}
void calculation::write_orders(FILE *fout_)
{
int i, c;
if(iter.method==3) fprintf(fout_," exact");
else
for(i=0; i<n_orders_eff(); i++)
if(n_intensities==0)
for(c=0; c<n_c; c++)
fprintf(fout_," order %2d component %d", orders[i], c+1);
else
for(c=0; c<n_intensities; c++)
if(i==0 && c==0) fprintf(fout_," order %2d", orders[i]);
else if(c==0) fprintf(fout_," --- order %2d", orders[i]);
else fprintf(fout_,"-------------", orders[i]);
fprintf(fout_,"\n");
}
void calculation::init_wf_tmat(int c, int l, int m)
{
int a;
vector gg;
scat.translation_type=1;
for(a=0; a<coord.n; a++) if(coord.atom[a]>=0) {
gg.alloc(l,n_c);
gg.re[c*sqr(l+1)+l*l+l+m]=1;
if(a!=center) {
scat.get_ij(a,center);
scat.get_ij();
scat.propagate(gg,lmax_inter);
}
scat.R_1TR(gg, a);
iter.o.g[a].copy(gg);
iter.n.g[a].copy(gg);
gg.free();
} else {iter.o.g[a].alloc(-1,n_c); iter.n.g[a].alloc(-1,n_c);}
scat.translation_type=0;
}
complex *calculation::wave_function_tmat(complex *wf)
{
int a;
vector gg, sum;
scat.translation_type=1;
sum.alloc(-1,n_c);
for(a=0; a<coord.n; a++) if(coord.atom[a]>=0) {
gg.copy(iter.n.g[a]);
if(a!=center) {
scat.get_ij(center,a);
scat.get_ij();
scat.propagate(gg,lmax_eff);
}
sum.add(gg);
gg.free();
}
scat.translation_type=0;
int c,i,lm,ll=lp12[sum.lmax];
for(c=i=0; c<n_c ; c++)
for(lm=0; lm<lp12[lmax]; lm++, i++)
if(lm<ll) wf[i]=complex(sum.re[c*ll+lm], sum.im[c*ll+lm]);
else wf[i]=0;
sum.free();
return wf+dim;
}
void calculation::scan_tmat(char *name, int lmax_)
{
int ik, i,j,ij, c,l,m, cp,lp,mp;
numero val;
complex *aa;
lmax=lmax_; n_c=scat.get_n_c();
dim=n_c*sqr(lmax+1);
scat.set_lmax();
lmax_inter=lmax_eff;
if(lmax>lmax_eff) {
free_lmax(); lmax_eff=lmax;
init_lmax();
}
coord.sort(-1);
if(coord.get_atom(coord.x0,coord.y0,coord.z0)<0)
coord.add_atom(coord.x0,coord.y0,coord.z0,0,0,-1);
center=coord.get_atom(coord.x0,coord.y0,coord.z0);
init_final_f(dim/n_c); select_wf=-1;
init(name);
iter.alloc();
if(fout!=NULL) {
fprintf(fout, "%d", n_k);
if(n_k>1) fprintf(fout, " E(eV)");
fprintf(fout, " %d full %d\n", lmax, n_c);
}
if(verbose) {
fprintf(foutput,"--- t matrix of the cluster, lmax=%d", lmax);
fprintf(foutput," %d component(s), output file %s\n", n_c, name);
}
aa=new complex [dim*dim];
for(ik=0; ik<n_k; ik++) {
val=scat.iimfp.val(k[ik])/2;
scat.k=complex(k[ik], val);
if(iter.method==3) {
scat.get_exact(n_c,lmax_inter);
if(verbose)
fprintf(foutput,
" exact inversion completed with lmax=%d\n", lmax_inter);
}
for(cp=j=0; cp<n_c ; cp++)
for(lp=0; lp<=lmax; lp++) {
for(mp=-lp; mp<=lp; mp++, j++) {
alloc(1);
if(wf_fin==NULL)
init_wf_tmat(cp, lp, mp);
evaluation(0);
iter.clear();
for(i=0; i<dim; i++) aa[i*dim+j]=results[0].a[i];
free_results();
}
if(verbose && iter.method!=3)
fprintf(foutput," ik=%2d c'=%d l'=%2d\n", ik+1, cp+1, lp);
}
if(iter.method==3) scat.free_exact();
scat.free_Green_functions();
scat.free_t_matrix();
if(n_k>1) fprintf(fout, "\n%g\n\n", sqr(k[ik])/2*au_eV);
for(c=ij=0; c<n_c ; c++)
for(l=0; l<=lmax; l++)
for(m=-l; m<=l; m++)
for(cp=0; cp<n_c ; cp++)
for(lp=0; lp<=lmax; lp++)
for(mp=-lp; mp<=lp; mp++, ij++) {
if(n_c>1) fprintf(fout, "%d", c+1);
fprintf(fout, " %d %2d", l,m);
if(n_c>1) fprintf(fout, " %d", cp+1);
fprintf(fout, " %d %2d", lp,mp);
if(mod(aa[ij])<1e-20) fprintf(fout, " 0 0\n"); else
fprintf(fout, " %g %g\n", real(aa[ij]), imag(aa[ij]));
} }
if(coord.atom[center]<0)
coord.delete_atom(coord.x0,coord.y0,coord.z0);
free();
iter.free();
scat.free_rotations();
free_lmax();
delete [] aa;
}
green_z::green_z(void)
{
re = new numero [size_of_green_z];
im = new numero [size_of_green_z];
}
void green_z::init(complex k, numero dd, int translation_type, int att_type)
{
int i; int m1,l1,l2,l3, il;
numero fct=1,j,y,hr,hi, *pre,*pim, *spherical_hr, *spherical_hi, kdr,kdi;
complex kd, val;
kd=k*dd; d=dd; trans=translation_type;
kdr=real(kd); kdi=imag(kd);
spherical_hr=new numero [2*lmax_eff+1];
spherical_hi=new numero [2*lmax_eff+1];
if(att_type==0) for(l3=0; l3<=2*lmax_eff; l3++) {
val=besselilh(l3,kd);
spherical_hr[l3]=real(val);
spherical_hi[l3]=imag(val);
}
else {
fct = exp(-kdi);
if(kdr) fct *= sqrt(pi/(2*kdr));
for(l3=0; l3<=2*lmax_eff; l3++) if(kdr) {
besselJY(l3+0.5,kdr,j,y,hr,hi); il=l3%4;
if(translation_type==1) {y=-j; j=0;}
if (il==0) {hr=-y; hi= j;}
else if(il==1) {hr=-j; hi=-y;}
else if(il==2) {hr= y; hi=-j;}
else {hr= j; hi= y;}
spherical_hr[l3]=fct*hr;
spherical_hi[l3]=fct*hi;
} else {spherical_hr[l3]=1; spherical_hi[l3]=0;}
}
for(l1=0, pre=re,pim=im, i=0; l1<=lmax_eff; l1++)
for(m1=-l1; m1<=l1; m1++)
for(l2=(m1>0?m1:-m1); l2<=lmax_eff; l2++, pre++,pim++)
for(l3=(l1>l2?l1-l2:-l1+l2), *pre=*pim=0; l3<=l1+l2; l3+=2) {
(*pre)+=spherical_hr[l3]*Gaunt_integrals[i];
(*pim)+=spherical_hi[l3]*Gaunt_integrals[i++];
}
delete [] spherical_hr;
delete [] spherical_hi;
}
int vector::Gz(green_z *G, int lmax_final)
{
int n,c,nele,nelet, l1,l2,m1, *llpl; vector temp;
numero *Gr,*Gi,*ptr,*pti, *rre,*iim;
if(lmax<0) return 0;
if(lmax_final>lmax_eff) lmax_final=lmax_eff;
temp.alloc(lmax_final, n_c);
llpl=new int [lmax+1]; for(l2=0; l2<=lmax; l2++) llpl[l2]=l2*l2+l2;
for(c=0; c<n_c; c++) {
nele =c*lp12[lmax];
nelet=c*lp12[temp.lmax];
ptr=temp.re+nelet; rre=re+nele;
pti=temp.im+nelet; iim=im+nele;
for(l1=0, Gr=G->re,Gi=G->im; l1<=temp.lmax; l1++)
for(m1=-l1; m1<=l1; m1++, ptr++,pti++) { *ptr=*pti=0;
for(l2=(m1>0?m1:-m1); l2<=lmax; l2++, Gi++,Gr++) {
n=llpl[l2]+m1;
(*ptr)+= (*Gr)*rre[n]-(*Gi)*iim[n];
(*pti)+= (*Gr)*iim[n]+(*Gi)*rre[n];
}
if(l2<=lmax_eff) {Gi+=(lmax_eff-l2+1); Gr+=(lmax_eff-l2+1);}
}}
free(); delete [] llpl;
*this=temp;
return 0;
}
rotation_th::rotation_th(void) {val = new numero [size_of_rotation_th];}
int rotation_th::init(numero tth)
{
int l,m1,m2,t,e1,e2; numero qsi,eta,pot, *pval,*ppval,*pnval;
qsi=cos(tth/2.0); eta=sin(tth/2.0);
for(l=0, pval=val; l<=lmax_eff; l++) {
pnval=pval;
for(m1=-l; m1<=l; m1++)
for(m2=0, pval+=l; m2<=l; m2++, pval++)
for(t=(0>m1-m2?0:m1-m2), *pval=0; t<=(l+m1<l-m2?l+m1:l-m2); t++) {
e2=t+t-m1+m2; e1=l+l-e2;
if(!qsi) if(e1) pot=0; else pot=1; else pot=pow(qsi,e1+0.0);
if(!eta) if(e2) pot=0; else pot=pot; else pot=pot*pow(eta,e2+0.0);
*pval+= (t&1?-1:1) * pot
* (fact2[m1+l]/fact[l+m1-t]) * (fact2[l-m1]/fact[l-m2-t])
* (fact2[m2+l]/fact[t]) * (fact2[l-m2]/fact[t-m1+m2]);
}
for(m1=-l, ppval=pval-1; m1<=l; m1++) {
for(m2=-l; m2<0; m2++, pnval++,ppval--)
*pnval=((m1&1)^(m2&1))?-(*ppval):(*ppval);
pnval+=(l+1); ppval-=(l+1);
}
}
return 0;
}
int vector::Rth(rotation_th *R, int op)
{
int l,m1,m2, c,nele,nelet; vector temp;
numero *rlm,*pre,*pim,*ptre,*ptim,*tr,*ti,ee;
if(lmax<0) return 0;
if(*(R->val)>1) {
if(*(R->val)==2) return 0;
for(c=0; c<n_c; c++)
for(l=0, pre=re+(c*lp12[lmax]),
pim=im+(c*lp12[lmax]); l<=lmax; l++) {
pre=pre+l; pim=pim+l; tr=pre; ti=pim;
for(m1=0; m1<=l; m1++, pre++,pim++, tr--,ti--)
if((l&1)^(m1&1)) {ee=*pre; *pre=-(*tr); (*tr)=-ee;
ee=*pim; *pim=-(*ti); (*ti)=-ee;}
else {ee=*pre; *pre= *tr; (*tr)= ee;
ee=*pim; *pim= *ti; (*ti)= ee;}
}
return 0;
}
temp.alloc(lmax,n_c);
for(c=0; c<n_c; c++) {
nele =c*lp12[lmax];
nelet=c*lp12[temp.lmax];
ptre=temp.re+nelet; pre=re+nele;
ptim=temp.im+nelet; pim=im+nele; rlm=R->val;
if(op)
for(l=0; l<=temp.lmax; l++) { tr=ptre; ti=ptim;
for(m1=-l; m1<=l; m1++, pre++,pim++) { ptre=tr; ptim=ti;
for(m2=-l; m2<=l; m2++, rlm++, ptre++,ptim++) {
(*ptre)+=(*rlm)*(*pre);
(*ptim)+=(*rlm)*(*pim);
}}}
else
for(l=0; l<=temp.lmax; l++) { tr=pre; ti=pim;
for(m1=-l; m1<=l; m1++, ptre++,ptim++) { pre=tr; pim=ti;
for(m2=-l; m2<=l; m2++, rlm++, pre++,pim++) {
(*ptre)+=(*rlm)*(*pre);
(*ptim)+=(*rlm)*(*pim);
}}}}
free();
*this=temp;
return 0;
}
rotation_fi::rotation_fi(void)
{
re = new numero [size_of_rotation_fi];
im = new numero [size_of_rotation_fi];
}
int rotation_fi::init(numero ffi)
{
int m; numero ang;
if(ABS(ffi) <coord.eps_th) {re[0]=2; return 1;}
if(ABS(ffi-pi)<coord.eps_th ||
ABS(ffi+pi)<coord.eps_th) {re[0]=3; return 2;}
for(m=0, ang=-lmax_eff*ffi; m<=2*lmax_eff; m++) {
re[m]= cos(ang);
im[m]=-sin(ang); ang+=ffi;
}
return 0;
}
int vector::Rfi(rotation_fi *R, int op)
{
int l,m,c; numero *pre,*pim,*pRre,*pRim,tre,tim;
if(lmax<0) return 0;
if(*(R->re)>1) {
if((*(R->re)==3||op>1)&&(*(R->re)==2||op<=1))
for(c=0, pre=re, pim=im; c<n_c; c++)
for(l=0; l<=lmax; l++)
for(m=-l; m<=l; m++, pre++,pim++)
if(m&1) {*pre=-(*pre); *pim=-(*pim);}
return 0;
}
for(c=0, pre=re, pim=im; c<n_c; c++)
for(l=0; l<=lmax; l++)
for(m=-l, pRre=R->re+(lmax_eff-l), pRim=R->im+(lmax_eff-l); m<=l;
m++, pRre++,pRim++,pre++,pim++) {
switch(op) {
case 0: case 2: tre=(*pRre)*(*pre)-(*pRim)*(*pim);
tim=(*pRre)*(*pim)+(*pRim)*(*pre); break;
case 1: case 3: tre=(*pRre)*(*pre)+(*pRim)*(*pim);
tim=(*pRre)*(*pim)-(*pRim)*(*pre); break;
}
if(op>1&&(m&1)) {*pre=-tre; *pim=-tim;}
else {*pre= tre; *pim= tim;}
}
return 0;
}
vector::vector(void) {lmax=-1; n_c=1;}
void vector::free(void)
{
if(lmax>=0) {delete [] re; delete [] im;}
lmax=-1; n_c=1;
}
void vector::alloc(int lmax_, int n_c_)
{
int i,dimension;
if(lmax>=0) free();
n_c = n_c_;
lmax=lmax_;
if(lmax>lmax_eff) lmax=lmax_eff;
if(lmax>=0) {
dimension=n_c*lp12[lmax];
re = new numero [dimension];
im = new numero [dimension];
for(i=0; i<dimension; i++) re[i]=im[i]=0;
} }
void vector::copy_from_array(complex *a, int lmax_, int n_c_)
{
int n,c; numero *rre,*iim; complex *va;
free(); alloc(lmax_,n_c_); rre=re; iim=im; va=a;
if(lmax>=0)
for(c=0; c<n_c; c++)
for(n=0; n<lp12[lmax]; n++, rre++, iim++, va++) {
*rre=real(*va); *iim=imag(*va);
} }
void vector::copy_to_array(complex *a, int lmax_, int cc)
{
int l,m,c; numero *rre,*iim; complex *va;
rre=re; iim=im; va=a;
if(lmax>=0)
for(c=0; c<n_c; c++)
for(l=0; l<=lmax; l++)
for(m=-l; m<=l; m++, rre++, iim++) if((c==cc || cc<0) && l<=lmax_) {
*va=complex(*rre, *iim);
va++;
} }
void vector::copy_to_array(complex *a, int cc) {copy_to_array(a, lmax, cc);}
void vector::copy_to_array(complex *a) {copy_to_array(a,-1);}
void vector::copy(vector &a, int lmax_, int n_c_, int c_flag)
{
int n,c; numero *tr,*ti,*rre,*iim;
n_c_=(a.n_c<n_c_)?n_c_:a.n_c;
lmax_=(a.lmax>lmax_)?lmax_:a.lmax;
free(); alloc(lmax_,n_c_);
if(lmax>=0)
for(c=0, tr=re, ti=im; c<n_c_; c++) {
if((c%a.n_c)==0) {rre=a.re; iim=a.im;}
for(n=0; n<lp12[a.lmax]; n++, rre++, iim++)
if(n<lp12[lmax]) {
if(c_flag<0 || c==c_flag) {*tr=*rre; *ti=*iim;}
else {*tr=0; *ti=0;}
tr++; ti++;
} } }
void vector::copy(vector &a)
{
copy(a, lmax_eff, a.n_c, -1);
}
void vector::substitute_lmax(int lmax_)
{
vector temp; temp.copy(*this, lmax_, n_c, -1); free(); *this=temp;
}
void vector::substitute_n_c(int n_c_, int c_flag)
{
vector temp; temp.copy(*this, lmax, n_c_, c_flag); free(); *this=temp;
}
int vector::add(vector &b)
{
int l,m, c; numero *ar,*ai,*br,*bi,*tr,*ti; vector temp;
if(b.lmax<0) return 0;
if(lmax<0) {copy(b); return 0;}
if(n_c!=b.n_c) on_error(foutput,"vector::add","unphysical case");
temp.alloc((b.lmax>lmax)?b.lmax:lmax,n_c);
for(c=0, tr=temp.re, ti=temp.im,
ar=re, ai=im, br=b.re, bi=b.im; c<temp.n_c; c++) {
for(l=0; l<=temp.lmax; l++)
for(m=-l; m<=l; m++, tr++, ti++) {
(*tr)=(*ti)=0;
if(l<=lmax) {(*tr)+=(*ar); (*ti)+=(*ai); ar++; ai++;}
if(l<=b.lmax) {(*tr)+=(*br); (*ti)+=(*bi); br++; bi++;}
} }
free(); *this=temp; return 0;
}
int vector::ext(numero x)
{
int l,m, c; numero *br,*bi;
if(lmax<0 || x==1) return 0;
for(c=0, br=re, bi=im; c<n_c; c++) {
if(x==-1) for(l=0; l<=lmax; l++)
for(m=-l; m<=l; m++, br++,bi++) {(*br)=-(*br); (*bi)=-(*bi);}
else for(l=0; l<=lmax; l++)
for(m=-l; m<=l; m++, br++,bi++) {(*br)=x*(*br); (*bi)=x*(*bi);}
}
return 0;
}
int vector::tmat(t_matrix *t)
{
if(lmax<0) return 0;
if(t->ta<0) {free(); return 0;}
if(lmax>t->lmax) substitute_lmax(t->lmax);
if(t->select==0) tmat_diagonal(t); else
if(t->select==1) tmat_full(t); else
if(t->select==2) tmat_full(t); else
if(t->select==4) tmat_so(t); else
on_error(foutput,"tmat", "undefined case");
return 0;
}
void vector::tmat_diagonal(t_matrix *t)
{
int l,m,c,j;
numero *br,*bi,*tr,*ti,rr,ii,ttr,tti;
if(t->n_c!=1 && n_c!=1 && t->n_c!=n_c)
on_error(foutput,"vector::tmat_diagonal","unphysical case");
for(c=0, br=re, bi=im; c<n_c; c++) {
if(t->n_c==1 || c==0) {tr=t->re; ti=t->im;}
else {
tr=t->re+c*(t->lmax+1);
ti=t->im+c*(t->lmax+1);
}
for(l=0; l<=lmax; l++, tr++, ti++) {
ttr=*tr; tti=*ti;
if(t->n_c>1 && n_c==1) {
for(j=0; j<t->n_c; j++) {ttr+=(*(tr+j*(t->lmax+1)));
tti+=(*(ti+j*(t->lmax+1)));}
ttr/=t->n_c; tti/=t->n_c;
}
for(m=-l; m<=l; m++, br++,bi++) {
rr =ttr*(*br); ii =ttr*(*bi);
rr-=tti*(*bi); ii+=tti*(*br);
*br=rr; *bi=ii;
} } } }
void vector::tmat_full(t_matrix *t)
{
int c,l,m,cp,lp,mp;
numero *ar,*ai,*br,*bi,*tr,*ti;
vector a;
if(t->n_c!=n_c)
on_error(foutput,"vector::tmat_full","unphysical case");
a.alloc(t->lmax,n_c);
ar=a.re; ai=a.im; tr=t->re; ti=t->im;
for(c=0; c<n_c; c++)
for(l=0; l<=t->lmax; l++)
for(m=-l; m<=l; m++) {
br=re; bi=im; *ar=*ai=0;
for(cp=0; cp<n_c; cp++)
for(lp=0; lp<=t->lmax; lp++)
for(mp=-lp; mp<=lp; mp++) {
if(t->select==2 || m==mp) {
if(lp<=lmax) {
*ar+=(*tr)*(*br)-(*ti)*(*bi);
*ai+=(*tr)*(*bi)+(*ti)*(*br);
}
tr++; ti++;
}
if(lp<=lmax) {br++; bi++;}
}
ar++; ai++;
}
free(); *this=a;
}
void vector::tmat_so(t_matrix *t)
{
int l,m, lp12p1=lp12[lmax]+1, lp12p0=lp12[lmax];
numero *ar, *ai, *br,*bi,*tr,*ti,rr,ii,
truu,trud,trdu,trdd,tiuu,tiud,tidu,tidd;
vector a; a.copy(*this);
for(l=0, tr=t->re,ti=t->im, br=re,bi=im, ar=a.re,ai=a.im; l<=lmax; l++)
for(m=-l; m<=l; m++, ar++,ai++, br++,bi++, tr+=4,ti+=4) {
truu=*tr; trdd=*(tr+2); tiuu=*ti; tidd=*(ti+2);
if(a.n_c==1) {
*br=((truu+trdd)*(*ar)-(tiuu+tidd)*(*ai))/2;
*bi=((truu+trdd)*(*ai)+(tiuu+tidd)*(*ar))/2;
} else {
trud=*(tr+1); trdu=*(tr+3); tiud=*(ti+1); tidu=*(ti+3);
rr =truu*(*ar) -tiuu*(*ai);
ii =truu*(*ai) +tiuu*(*ar);
if(m<l) {rr+=trud*(*(ar+lp12p1))-tiud*(*(ai+lp12p1));
ii+=trud*(*(ai+lp12p1))+tiud*(*(ar+lp12p1));}
*br=rr; *bi=ii;
rr =trdd*(*(ar+lp12p0))-tidd*(*(ai+lp12p0));
ii =trdd*(*(ai+lp12p0))+tidd*(*(ar+lp12p0));
if(m>-l) {rr+=trdu*(*(ar-1)) -tidu*(*(ai-1));
ii+=trdu*(*(ai-1)) +tidu*(*(ar-1));}
*(br+lp12p0)=rr; *(bi+lp12p0)=ii;
} }
a.free();
}
int vector::spin_rotation(numero al, numero be, numero ga)
{
if(lmax<0 || n_c==1) return 0;
numero cp=cos((al+ga)/2), sp=sin((al+ga)/2), cb=cos(be/2),
cm=cos((al-ga)/2), sm=sin((al-ga)/2), sb=sin(be/2),
uur,uui,udr,udi,dur,dui,ddr,ddi, ur,dr,ui,di, *br,*bi;
int n,dim=lp12[lmax];
uur=cp*cb; uui=-sp*cb; udr=-cm*sb; udi=sm*sb;
dur=cm*sb; dui= sm*sb; ddr= cp*cb; ddi=sp*cb;
for(n=0, br=re, bi=im; n<lp12[lmax]; n++, br++, bi++) {
ur=(*br); dr=(*(br+dim));
ui=(*bi); di=(*(bi+dim));
(*br) =(uur*ur-uui*ui)+(udr*dr-udi*di);
(*bi) =(uur*ui+uui*ur)+(udr*di+udi*dr);
(*(br+dim))=(dur*ur-dui*ui)+(ddr*dr-ddi*di);
(*(bi+dim))=(dur*ui+dui*ur)+(ddr*di+ddi*dr);
}
return 0;
}
cluster::cluster(void)
{
x0=y0=z0=0;
oriented=0;
zs=0; surface=0;
Rmax=infinity;
n=nn=0;
nnn=infinite_int;
n_emit=0;
eps_d=0.00005;
eps_th=0.003*pi/180;
}
int cluster::set_n(void)
{
n=(nnn>nn)?nn:nnn;
return n;
}
void cluster::free(void)
{
free_coordinates();
free_emitters();
}
void cluster::free_coordinates(void)
{
if(nn) {
delete [] x; delete [] y; delete [] z;
delete [] atom; delete [] atZ; delete [] th; delete [] fi;
n=nn=0;
} }
void cluster::free_emitters(void)
{
if(ABS(n_emit)>0) {n_emit=0; delete [] emit; delete [] emit_s;}
}
int cluster::read_atomic_type(FILE *fin)
{
char name[str_length_comments]; read_name(fin,name);
int jj=0;
jj=element_properties(name);
if(jj==0) jj=read_int(name);
return jj;
}
void cluster::read(FILE *fin, char *my_file)
{
FILE *fcoordinates;
if(!strcmpC(my_file,"inline")) fcoordinates=fin;
else fcoordinates=open_file(foutput,my_file,"r");
free();
read(fcoordinates);
if(strcmpC(my_file,"inline")) fclose(fcoordinates);
}
void cluster::read(FILE *fcoordinates)
{
int i,j;
numero factor2;
char units2[str_length_units];
nn=read_int(fcoordinates); set_n();
read_name(fcoordinates,units2);
factor2=units_conversion_factor(units2);
x=new numero [nn]; y=new numero [nn]; z=new numero [nn];
atom=new int [nn]; atZ=new int [nn];
th= new numero [nn]; fi= new numero [nn];
for(j=0; j<nn; j++) {
i=read_int(fcoordinates)-1;
atZ[i]=atom[i]=read_atomic_type(fcoordinates);
x[i]=factor2*read_numero(fcoordinates);
y[i]=factor2*read_numero(fcoordinates);
z[i]=factor2*read_numero(fcoordinates);
if(oriented) {
th[i]=pi/180*read_numero(fcoordinates);
fi[i]=pi/180*read_numero(fcoordinates);
} else {th[i]=fi[i]=0;}
} }
void cluster::write(char *name, char *units)
{
FILE *fout;
set_n();
if(!strcmpC(name,"none")) fout=foutput;
else fout=open_file(foutput,name,"w");
write(fout, units);
close_file(fout);
}
void cluster::write(FILE *fout, char *units)
{
int i; numero factor=units_conversion_factor(units);
fprintf(fout, "%3d %s\n", n, units);
for(i=0; i<n; i++) {
fprintf(fout, "%3d %3d %15.9f %15.9f %15.9f", i+1, atom[i],
x[i]/factor, y[i]/factor, z[i]/factor);
if(oriented)
fprintf(fout, " %9.4f %9.4f", 180/pi*th[i], 180/pi*fi[i]);
fprintf(fout, "\n");
} }
numero cluster::distance(numero x0_, numero y0_, numero z0_,
numero x1, numero y1, numero z1)
{
numero ddd=sqrt( (x0_-x1)*(x0_-x1)
+(y0_-y1)*(y0_-y1)
+(z0_-z1)*(z0_-z1));
if(surface) ddd=ddd+zs-z1;
return ddd;
}
int cluster::get_atom(numero x_, numero y_, numero z_, numero err)
{
int i;
for(i=0; i<nn; i++)
if(sqr(x[i]-x_)+sqr(y[i]-y_)+sqr(z[i]-z_) < sqr(err))
return i;
return -1;
}
int cluster::get_atom(numero x_, numero y_, numero z_)
{return get_atom(x_,y_,z_,eps_d);}
void cluster::sort(int emitter)
{
int *atom_,*atZ_,*am, i,j,l;
numero *x_,*y_,*z_,*th_,*fi_,*d, dis, xe,ye,ze;
x_=new numero [nn];
y_=new numero [nn];
z_=new numero [nn];
atom_=new int [nn];
atZ_=new int [nn];
th_=new numero [nn];
fi_=new numero [nn];
d=new numero [nn];
am=new int [nn];
if(emitter>=0) {
xe=x[emitter]; ye=y[emitter]; ze=z[emitter];
} else {xe=x0; ye=y0; ze=z0;}
for(i=n=0; i<nn; i++) {
d[i]=distance(xe,ye,ze,
x[i],y[i],z[i]);
if(d[i]<=Rmax) n++;
am[i]=-1;
}
if(nn<n) n=nn;
if(nnn<n) n=nnn;
for(i=0; i<nn; i++) {
if(i>=n) for(l=0; am[l]>=0; l++);
else for(j=0,dis=infinity; j<nn; j++)
if(am[j]<0 && d[j]<dis) {dis=d[j]; l=j;}
am[l]=i;
x_[i]=x[l]; y_[i]=y[l]; z_[i]=z[l];
atom_[i]=atom[l]; atZ_[i]=atZ[l]; th_[i]=th[l]; fi_[i]=fi[l];
}
for(j=0; j<ABS(n_emit); j++) emit[j]=am[emit[j]];
delete [] x; delete [] y; delete [] z;
delete [] atom; delete [] atZ; delete [] th; delete [] fi;
delete [] d; delete [] am;
x=x_; y=y_; z=z_; atom=atom_; atZ=atZ_; th=th_; fi=fi_;
}
int cluster::add_atom(numero x_, numero y_, numero z_,
numero th_, numero fi_, int at)
{
if(distance(x0,y0,z0, x_,y_,z_)>Rmax) return 0;
int i,*atom_,*atZ_; numero *xx,*yy,*zz,*tt,*ff;
i=get_atom(x_,y_,z_);
if(i>=0) {atZ[i]=atom[i]=at; th[i]=th_; fi[i]=fi_; return 0;}
if(nn) {xx=x; yy=y; zz=z; atom_=atom; atZ_=atZ; tt=th; ff=fi;}
x=new numero [nn+1]; y=new numero [nn+1]; z=new numero [nn+1];
atom=new int [nn+1]; atZ=new int [nn+1];
th=new numero [nn+1]; fi=new numero [nn+1];
for(i=0; i<nn; i++) {
x[i]=xx[i]; y[i]=yy[i]; z[i]=zz[i];
atom[i]=atom_[i]; atZ[i]=atZ_[i]; th[i]=tt[i]; fi[i]=ff[i];
}
x[nn]=x_; y[nn]=y_; z[nn]=z_;
atZ[nn]=atom[nn]=at;
th[nn]=th_; fi[nn]=fi_;
if(nn) {
delete [] xx; delete [] yy; delete [] zz;
delete [] atom_; delete [] atZ_; delete [] tt; delete [] ff;
}
nn++; set_n(); return 0;
}
int cluster::delete_atom(numero x_, numero y_, numero z_)
{
if(distance(x0,y0,z0, x_,y_,z_)>Rmax) return 0;
int ii=get_atom(x_,y_,z_); if(ii<0) return 0;
if(nn==1) {free(); return 0;}
int i,j,*atom_,*atZ_; numero *xx,*yy,*zz,*tt,*ff;
xx=x; yy=y; zz=z; atom_=atom; atZ_=atZ; tt=th; ff=fi;
x=new numero [nn-1]; y=new numero [nn-1]; z=new numero [nn-1];
atom=new int [nn-1]; atZ=new int [nn-1];
th=new numero [nn-1]; fi=new numero [nn-1];
for(i=j=0; i<nn; i++) if(i!=ii) {
x[j]=xx[i]; y[j]=yy[i]; z[j]=zz[i];
atom[j]=atom_[i]; atZ[j]=atZ_[i]; th[j]=tt[i]; fi[j]=ff[i];
j++;
}
delete [] xx; delete [] yy; delete [] zz;
delete [] atom_; delete [] atZ_; delete [] tt; delete [] ff;
nn=nn-1; set_n(); return 0;
}
void cluster::add_layer(numero x_, numero y_, numero z_, numero a, numero b,
numero al, numero be, numero th_, numero fi_, int at)
{
int i,j,imax,jmax;
numero d, ca=a*cos(al),cb=b*cos(al+be), sa=a*sin(al),sb=b*sin(al+be);
if((Rmax/infinity)>0.9) on_error(foutput,"add_layer","Rmax too large");
d=Rmax + sqrt(sqr(x_-x0)+sqr(y_-y0));
imax=int(floor(d/a+1)); jmax=int(floor(d/b+1));
for(i=-imax; i<=imax; i++)
for(j=-jmax; j<=jmax; j++)
add_atom(x_+i*ca+j*cb, y_+i*sa+j*sb, z_, th_,fi_,at);
}
void cluster::delete_layer(numero x_, numero y_, numero z_,
numero a, numero b, numero al, numero be)
{
int i,j,imax,jmax;
numero d, ca=a*cos(al),cb=b*cos(al+be), sa=a*sin(al),sb=b*sin(al+be);
if((Rmax/infinity)>0.9) on_error(foutput,"delete_layer","Rmax too large");
d=Rmax + sqrt(sqr(x_-x0)+sqr(y_-y0));
imax=int(floor(d/a+1)); jmax=int(floor(d/b+1));
for(i=-imax; i<=imax; i++)
for(j=-jmax; j<=jmax; j++) delete_atom(x_+i*ca+j*cb, y_+i*sa+j*sb, z_);
}
void cluster::add_surface(numero x_, numero y_, numero z_, numero a, numero c,
char *name, numero th_, numero fi_, int at)
{
int i,imax, hcp=0;
numero d, dx,dy,dz,ax,ay,bx,by, a1,a2, al,be, s2=sqrt(2), s3=sqrt(3);
if((Rmax/infinity)>0.9) on_error(foutput,"add_surface","Rmax too large");
if(!strcmpC(name,"sc100")) {
dx=0; dy=0; dz=-a;
ax=a; ay=0; bx=0; by=a;
} else
if(!strcmpC(name,"sc110")) {
dx=a/s2; dy=0; dz=-a/s2;
ax=a*s2; ay=0; bx=0; by=a;
} else
if(!strcmpC(name,"sc111")) {
dx=a*s2/s3; dy=0; dz=-a/s3;
ax=a*s3/s2; ay=-a/s2; bx=a*s3/s2; by=a/s2;
} else
if(!strcmpC(name,"bcc100")) {
dx=a/2; dy=a/2; dz=-a/2;
ax=a; ay=0; bx=0; by=a;
} else
if(!strcmpC(name,"bcc110")) {
dx=a/s2; dy=0; dz=-a/s2;
ax=a/s2; ay=-a/2; bx=a/s2; by=a/2;
} else
if(!strcmpC(name,"bcc111")) {
dx=a*s2/s3; dy=0; dz=-a/2/s3;
ax=a*s3/s2; ay=-a/s2; bx=a*s3/s2; by=a/s2;
} else
if(!strcmpC(name,"fcc100")) {
dx=a/2; dy=0; dz=-a/2;
ax=a/2; ay=-a/2; bx=a/2; by=a/2;
} else
if(!strcmpC(name,"fcc110")) {
dx=a/2/s2; dy=a/2; dz=-a/2/s2;
ax=a/s2; ay=0; bx=0; by=a;
} else
if(!strcmpC(name,"fcc111")) {
dx=a/s2/s3; dy=0; dz=-a/s3;
ax=a*s3/2/s2; ay=-a/2/s2; bx=a*s3/2/s2; by=a/2/s2;
} else
if(!strcmpC(name,"hcp0001")) {
dx=a/s3; dy=0; dz=-c;
ax=a*s3/2; ay=-a/2; bx=a*s3/2; by=a/2;
hcp=1;
} else on_error(foutput, "add_surface", "undefined surface type:", name);
a1=sqrt(sqr(ax)+sqr(ay));
a2=sqrt(sqr(bx)+sqr(by));
al=acos(ax/a1); if(ay<0) al=-al;
be=ABS(acos((ax*bx+ay*by)/(a1*a2)));
if(ax*bx+ay*by<0) be=pi-be;
d=Rmax + ABS(z_-z0);
imax=int(floor(ABS(d/dz)+1));
for(i=0; i<=imax; i++)
if(hcp==0)
add_layer(x_+i*dx, y_+i*dy, z_+i*dz, a1,a2, al,be, th_,fi_,at);
else
add_layer(x_+(i%2)*dx, y_+(i%2)*dy, z_+i*dz, a1,a2, al,be, th_,fi_,at);
}
void cluster::add_half_layer(numero x_, numero y_, numero z_,
numero a, numero b,
numero al, numero be, numero ff,
numero th_, numero fi_, int at)
{
int i,j,imax,jmax;
numero d, ca=a*cos(al),cb=b*cos(al+be), sa=a*sin(al),sb=b*sin(al+be);
numero xx, yy, cf=cos(ff), sf=sin(ff);
if((Rmax/infinity)>0.9) on_error(foutput,"add_half_layer",
"Rmax too large");
d=Rmax + sqrt(sqr(x_-x0)+sqr(y_-y0));
imax=int(floor(d/a+1)); jmax=int(floor(d/b+1));
for(i=-imax; i<=imax; i++)
for(j=-jmax; j<=jmax; j++) {
xx=x_+i*ca+j*cb;
yy=y_+i*sa+j*sb;
if(cf*(xx-x_)+sf*(yy-y_)>-eps_d) add_atom(xx, yy, z_, th_,fi_,at);
} }
void cluster::add_row(numero x_, numero y_, numero z_, numero a,
numero tt, numero ff, numero th_, numero fi_, int at)
{
int i,imax;
numero d, ax=a*sin(tt)*cos(ff), ay=a*sin(tt)*sin(ff), az=a*cos(tt);
if((Rmax/infinity)>0.9) on_error(foutput,"add_row","Rmax too large");
d=Rmax + sqrt(sqr(x_-x0)+sqr(y_-y0)+sqr(z_-z0));
imax=int(floor(d/a+1));
for(i=-imax; i<=imax; i++)
add_atom(x_+i*ax, y_+i*ay, z_+i*az, th_,fi_,at);
}
void cluster::delete_row(numero x_, numero y_, numero z_,
numero a, numero tt, numero ff)
{
int i,imax;
numero d, ax=a*sin(tt)*cos(ff), ay=a*sin(tt)*sin(ff), az=a*cos(tt);
if((Rmax/infinity)>0.9) on_error(foutput,"delete_row","Rmax too large");
d=Rmax + sqrt(sqr(x_-x0)+sqr(y_-y0)+sqr(z_-z0));
imax=int(floor(d/a+1));
for(i=-imax; i<=imax; i++) delete_atom(x_+i*ax, y_+i*ay, z_+i*az);
}
void cluster::add_emitter(int a)
{
add_emitter(a, atom[a]);
}
void cluster::add_emitter(int a, int sc)
{
int *emit_,*emit_s_,add,i;
for(i=0, add=1; i<n_emit && add; i++) if(emit[i]==a) add=0;
if(add) {
emit_=new int [n_emit+1]; emit_s_=new int [n_emit+1];
for(i=0; i<n_emit; i++) {emit_[i]=emit[i]; emit_s_[i]=emit_s[i];}
if(n_emit>0) {delete [] emit; delete [] emit_s;}
emit_[n_emit]=a; emit_s_[n_emit]=sc;
emit=emit_; emit_s=emit_s_; n_emit++;
} }
void cluster::add_emitter_plane(numero x_, numero y_, numero z_,
numero th_, numero fi_)
{
int i; numero cth=cos(th_),sth=sin(th_),cfi=cos(fi_),sfi=sin(fi_);
for(i=0; i<n; i++)
if(ABS( ( (x[i]-x_)*cfi
+(y[i]-y_)*sfi)*sth
+ (z[i]-z_)*cth) < eps_d) add_emitter(i,atom[i]);
}
void cluster::add_emitter_column(numero x_, numero y_)
{
int i;
for(i=0; i<n; i++)
if(sqrt(sqr(x[i]-x_)+sqr(y[i]-y_))<eps_d) add_emitter(i,atom[i]);
}
void cluster::all_emitters(int ta, int sc)
{
int a;
for(a=0; a<nn; a++) if(atom[a]==ta) add_emitter(a,sc);
}
int cluster::delete_non_emitters(void)
{
numero *x_,*y_,*z_,*th_,*fi_;
int i,j, *atom_,*atZ_;
if(n_emit<=0) return 1;
x_=new numero [n_emit]; y_=new numero [n_emit]; z_=new numero [n_emit];
atom_=new int [n_emit]; atZ_=new int [n_emit];
th_=new numero [n_emit]; fi_=new numero [n_emit];
for(i=j=0; i<nn && j<n_emit; i++) if(is_emitter(i)) {
x_[j]=x[i]; y_[j]=y[i]; z_[j]=z[i];
atom_[j]=atom[i]; atZ_[j]=atZ[i]; th_[j]=th[i]; fi_[j]=fi[i]; j++;
}
free_coordinates();
x=x_; y=y_; z=z_; atom=atom_; atZ=atZ_; th=th_; fi=fi_;
nn=n_emit; set_n();
free_emitters();
return 0;
}
void cluster::displace(numero xx, numero yy, numero zz)
{
int i;
for(i=0; i<nn; i++) {x[i]+=xx; y[i]+=yy; z[i]+=zz;}
}
void cluster::rotate(double &xx, double &yy, double ang)
{
numero rho,phi;
rho=sqrt(xx*xx+yy*yy);
if(!xx&&!yy) phi=0; else phi=atan2(yy,xx);
xx=rho*cos(phi+ang);
yy=rho*sin(phi+ang);
}
void cluster::rotate(int axis, numero ang)
{
numero mux,muy,muz, rr;
int i;
for(i=0; i<nn; i++) {
if(axis==0) rotate(y[i],z[i],ang); else
if(axis==1) rotate(z[i],x[i],ang); else
if(axis==2) rotate(x[i],y[i],ang);
if(oriented) {
mux=sin(th[i])*cos(fi[i]);
muy=sin(th[i])*sin(fi[i]);
muz=cos(th[i]);
if(axis==0) rotate(muy,muz,ang); else
if(axis==1) rotate(muz,mux,ang); else
if(axis==2) rotate(mux,muy,ang);
cartesian_to_spherical(mux,muy,muz, rr,th[i],fi[i]);
} } }
int cluster::is_emitter(int i)
{
int j;
if(n_emit==0) return 1;
for(j=0; j<n_emit; j++) if(emit[j]==i) return 1;
return 0;
}
void cluster::report_emitters(void)
{
int i;
if(n_emit<1) fprintf(foutput, "--- no emitters\n"); else
if(n_emit==1) fprintf(foutput, "--- 1 emitter (in Angstroms)\n"); else
fprintf(foutput, "--- %d emitters (in Angstroms)\n",n_emit);
for(i=0; i<n_emit; i++)
fprintf(foutput, " %3d %3d %15.9f %15.9f %15.9f\n",
i+1, atom[emit[i]],
x[emit[i]]*a0_au, y[emit[i]]*a0_au, z[emit[i]]*a0_au);
}
multiple_scattering::multiple_scattering(void)
{
method=0;
eta=1;
}
void multiple_scattering::free(void)
{
o.free(); n.free();
}
void multiple_scattering::clear(void)
{
o.clear(); n.clear();
}
void multiple_scattering::alloc(void)
{
o.alloc(coord.n);
n.alloc(coord.n);
}
void multiple_scattering::exact(void)
{
int i,c,l,m, j,cp,lp,mp, n_c=o.g[0].n_c;
numero *ri, *ii, *rj, *ij;
complex *a, val;
for(i=0; i<coord.n; i++) {
n.g[i].free();
n.g[i].alloc(scat.lmax_aa,n_c);
}
for(i=0, a=scat.aa.p; i<coord.n; i++)
for(c=0, ri=n.g[i].re, ii=n.g[i].im; c<n_c; c++)
for(l=0; l<=scat.lmax_aa; l++)
for(m=-l; m<=l; m++, ri++, ii++)
for(j=0; j<coord.n; j++)
for(cp=0, rj=o.g[j].re, ij=o.g[j].im; cp<n_c; cp++)
for(lp=0; lp<=scat.lmax_aa; lp++)
for(mp=-lp; mp<=lp; mp++, a++) if(lp<=o.g[j].lmax) {
val= (*a) * complex(*rj,*ij);
*ri += real(val);
*ii += imag(val);
rj++; ij++;
} }
void multiple_scattering::next_scattering(void)
{
int a,b; vector gg;
wave_function np;
np.alloc(coord.n);
for(a=0; a<coord.n; a++) {
np.g[a].alloc(-1,n.g[a].n_c);
scat.get_t_matrix(coord.atom[a]);
scat.nn_c=n.g[a].n_c;
if(scat.t_mat->ta>=0) {
for(b=0; b<coord.n; b++)
if(scat.get_ij(a,b)) {
if((method==1 || method==2) && b<a) gg.copy(np.g[b]);
else gg.copy(n.g[b]);
if(gg.lmax>=0) {
scat.get_ij();
scat.propagate(gg, scat.t_mat->lmax);
np.g[a].add(gg);
}
gg.free();
time_update();
}
scat.R_1TR(np.g[a],a,scat.t_mat);
if(method!=-1) np.g[a].add(o.g[a]);
} else if(method!=-1) np.g[a].add(o.g[a]);
}
for(a=0; a<coord.n; a++)
if(method==2) {n.g[a].ext(1-eta); np.g[a].ext(eta);
n.g[a].add(np.g[a]); np.g[a].free();}
else {n.g[a].free(); n.g[a].copy(np.g[a]);}
np.free();
}
void multiple_scattering::write(FILE *fout, int o_, int max_order_)
{
int a,c,l,m;
numero *re,*im;
if(o_==0) {
fprintf(fout,"Momentum (a.u.) %g %g\n", real(scat.k), imag(scat.k));
fprintf(fout,"Maximum order %d\n", max_order_);
fprintf(fout,"lmax_eff %d\n\n", lmax_eff);
fprintf(fout,"Cluster\n\n");
coord.write(fout,"l(A)");
fprintf(fout,"\n");
fprintf(fout,"Coefficients\n");
}
for(a=0; a<coord.n; a++) {
fprintf(fout,"\n");
fprintf(fout,"order %d atom %d nc %d lmax %2d\n",
o_, a+1, n.g[a].n_c, n.g[a].lmax);
if(n.g[a].lmax>0) fprintf(fout,"\n");
re=n.g[a].re; im=n.g[a].im;
for(c=0; c<n.g[a].n_c; c++)
for(l=0; l<=n.g[a].lmax; l++)
for(m=-l; m<=l; m++, re++, im++)
fprintf(fout," %1d %2d %3d %16g %16g\n", c+1,l,m, *re,*im);
}
fprintf(fout,"\n");
}
int multiple_scattering::read(FILE *fin, int o_)
{
char name[str_length_comments];
int a,c,l,m, n_c,lmax;
numero *re,*im;
float x,y;
if(o_==0) {
fscanf(fin,"%s%s%f%f", name, name, &x,&y);
fscanf(fin,"%s%s%d", name, name, &max_order);
fscanf(fin,"%s", name); free_lmax();
fscanf(fin,"%d", &lmax);
if(lmax>lmax_max)
on_error(foutput, "wf input", "lmax is too large in wf");
fscanf(fin,"%s", name); coord.read(fin);
scat.set_lmax();
if(lmax>lmax_eff) init_lmax(lmax);
final.init_Ylm();
scat.set_k(complex(x,y));
calc.kk[0]=sqr(real(scat.k))/2*au_eV;
fscanf(fin,"%s", name);
o.free(); o.alloc(coord.n);
n.free(); n.alloc(coord.n);
} else n.clear();
for(a=0; a<coord.n; a++) {
fscanf(fin,"%s%d", name, &o_);
fscanf(fin,"%s%d", name, &a); a--;
fscanf(fin,"%s%d", name, &n_c);
fscanf(fin,"%s%d", name, &lmax);
n.g[a].alloc(lmax,n_c);
re=n.g[a].re; im=n.g[a].im;
for(c=0; c<n.g[a].n_c; c++)
for(l=0; l<=n.g[a].lmax; l++)
for(m=-l; m<=l; m++, re++, im++) {
fscanf(fin,"%d%d%d%f%f\n", &c,&l,&m, &x,&y); c--;
*re=x; *im=y;
}
if(o_==0) o.g[a].copy(n.g[a]);
}
if(o_==max_order) return 1; else return 0;
}
propagation::propagation(void)
{
n_d=n_th=n_fi=n_t=n_G=nn_d=nn_th=nn_fi=nn_t=nn_G=0; nn_c=1;
dmax=infinity;
translation_type=0;
attenuation_type=0;
t_mat0=NULL;
iimfp.n=0;
iimfp_flag=0;
T=0;
int i; for(i=0; i<n_Debye_temperature_elements; i++) T_Debye[i]=100;
V0=Vi=0;
screening_length=1/a0_au;
scattering_so=0;
separation=1;
Gab_cg_flag=0;
n_a=0;
a0=NULL;
epsilon=0.00005;
dim=0;
aa.n=aa.m=aa.nm=0;
aa_output_flag=0;
}
void propagation::R_1TR(vector &gg, int i, t_matrix *tt)
{
if(coord.oriented) if(coord.th[i]!=0) {
get_th(coord.th[i]); ifi=get_fi(coord.fi[i]); Rab(gg);
gg.spin_rotation(0, coord.th[i], pi-coord.fi[i]);
}
gg.tmat(tt);
if(coord.oriented) if(coord.th[i]!=0) { Rab_1(gg);
gg.spin_rotation(coord.fi[i]-pi, -coord.th[i], 0);
} }
void propagation::R_1TR(vector &gg, int i)
{
get_t_matrix(coord.atom[i]);
R_1TR(gg, i, t_mat);
}
void propagation::Rab(vector &gg)
{
if(ifi<0) gg.Rfi(Rfi,2);
else gg.Rfi(Rfi,0);
gg.Rth(Rth,0);
}
void propagation::Rab_1(vector &gg)
{
gg.Rth(Rth,1);
if(ifi<0) gg.Rfi(Rfi,3);
else gg.Rfi(Rfi,1);
}
void propagation::propagate(vector &gg, int lmax_final)
{
if(separation>0) {
Rab(gg);
gg.Gz(Gz, lmax_final);
Rab_1(gg);
} else Gab->prod(gg);
}
int propagation::get_ij(int i, int j)
{
numero x,y,z;
if(i==j) x=y=z=d=th=fi=0;
else {
x=coord.x[i]-coord.x[j];
y=coord.y[i]-coord.y[j];
z=coord.z[i]-coord.z[j];
cartesian_to_spherical(x,y,z, d,th,fi);
if(d>dmax || (coord.surface && coord.zs-coord.z[i]+d>dmax)) return 0;
}
if(i==j && separation>=0) return 0;
return 1;
}
void propagation::get_ij(void)
{
if(separation>0) {
get_d();
get_th(th);
ifi=get_fi(fi);
} else
get_Gab();
}
int propagation::get_d(void)
{
int n;
if(n_d) {
Gz=Gz0; n=n_d;
while(n--)
if(fabs(d-Gz->d)<coord.eps_d
&& Gz->trans==translation_type) return 0;
else Gz=Gz->next;
} else Gz0=NULL;
Gz=new green_z; n_d++; nn_d=n_d; nn_G=0;
Gz->next=Gz0; Gz0=Gz;
Gz->init(k,d,translation_type,attenuation_type);
return 0;
}
int propagation::get_th(numero th_)
{
int n, hz,l,m1,m2,v2l1;
rotation_th *Rtp;
numero *pval,*pnval,*pth,*ppth,*th_save;
if(n_th) {
Rth=Rth0; n=n_th;
while(n--) if(fabs(th_-Rth->th)<coord.eps_th) return 0;
else Rth=Rth->next;
} else Rth0=NULL;
Rth=new rotation_th; n_th++; nn_th=n_th;
Rth->next=Rth0; Rth0=Rth; Rth->th=th_;
if(fabs(th_) <coord.eps_th) {Rth->val[0]=2; return 0;}
if(fabs(th_-pi)<coord.eps_th) {Rth->val[0]=3; return 0;}
for(Rtp=Rth->next, hz=1, n=n_th; hz && --n;)
if(fabs(pi-Rtp->th-th_)<coord.eps_th) hz=0; else Rtp=Rtp->next;
if(hz) {Rth->init(th_); return 0;}
th_save=new numero [sqr(2*lmax_eff+1)];
for(l=0, pval=Rtp->val,pnval=Rth->val; l<=lmax_eff; l++) {
v2l1=2*l+1;
for(m1=-l,pth=th_save; m1<=l; m1++)
for(m2=-l; m2<=l; m2++, pval++,pth++)
*pth=*pval;
for(m1=-l,pth=th_save+v2l1; m1<=l; m1++)
for(m2=-l,ppth=(--pth); m2<=l; m2++, pnval++,ppth+=v2l1)
*pnval=((l&1)^(m1&1))?-(*ppth):(*ppth);
}
delete [] th_save;
return 0;
}
int propagation::get_fi(numero fi_)
{
int n;
if(n_fi) {
Rfi=Rfi0; n=n_fi;
while(n--) if(fabs(fi_-Rfi->fi)<coord.eps_th) return 1; else
if(fabs(fi_-pi-Rfi->fi)<coord.eps_th ||
fabs(fi_+pi-Rfi->fi)<coord.eps_th) return -1; else
Rfi=Rfi->next;
} else Rfi0=NULL;
Rfi=new rotation_fi; n_fi++; nn_fi=n_fi;
Rfi->next=Rfi0; Rfi0=Rfi; Rfi->fi=fi_;
Rfi->init(pi-fi_);
return 1;
}
int propagation::get_t_matrix(int ta)
{
int n;
if(n_t) {
t_mat=t_mat0; n=n_t;
while(n--) if((t_mat->ta)==ta) return 0; else t_mat=t_mat->next;
} else t_mat0=NULL;
t_mat=new t_matrix; n_t++; nn_t=n_t;
t_mat->next=t_mat0; t_mat0=t_mat; t_mat->ta=ta;
if(ta>=0) {get_scatterer(ta); a->init_t_matrix(t_mat);}
return 1;
}
void propagation::free_Green_functions(void)
{
while(n_d) { n_d--;
Gz=Gz0->next; Gz0->free();
delete Gz0; Gz0=Gz;
}
if(Gab_cg_flag) {delete [] Gab_cg; Gab_cg_flag=0;}
while(n_G) { n_G--;
Gab=Gab0->next; Gab0->free();
delete Gab0; Gab0=Gab;
} }
void propagation::free_rotations(void)
{
while(n_th) {
Rth=Rth0->next; Rth0->free(); delete Rth0;
Rth0=Rth; n_th--;
}
while(n_fi) {
Rfi=Rfi0->next; Rfi0->free(); delete Rfi0;
Rfi0=Rfi; n_fi--;
} }
void propagation::free_t_matrix(void)
{
while(n_t) {
t_mat=t_mat0->next; t_mat0->free(); delete t_mat0;
t_mat0=t_mat; n_t--;
} }
int propagation::get_scatterer(int ta, int opt)
{
int n=n_a;
if(ta<0) return 0;
a=a0;
while(n--) if((a->ta)==ta) return 0; else a=a->next;
if(opt) on_error(foutput,"get_scatterer","scatterer",ta,"undefined");
return 1;
}
int propagation::free_scatterer(int ta)
{
int n; atomic_scattering *previous;
if(n_a>0) {
if(a0->ta==ta) {
a=a0->next; a0->free(); delete a0; n_a--; a0=a;
return 0;
}
if(n_a>1) {
a=a0->next;
previous=a0;
n=n_a-1;
while(n--)
if((a->ta)==ta) {
n_a--; previous->next=a->next; a->free(); delete a;
return 0;
} else {previous=a; a=a->next;}
} }
on_warning(foutput,"free_scatterer","scatterer",ta,"undefined");
return 0;
}
void propagation::free_scatterers(void)
{
while(n_a) {
a=a0->next; a0->free(); delete a0;
a0=a; n_a--;
} }
void propagation::add_scatterer(int ta)
{
int i;
a=a0; i=1;
while(a!=NULL && i)
if(a->ta==ta) {
free_scatterer(ta);
i=0;
} else a=a->next;
a=new atomic_scattering;
a->ta=ta;
a->next=a0;
a0=a; n_a++;
}
void propagation::add_screened_scatterer(int ta, int ta_old)
{
int n,Z,i, magnetic;
numero *r,*V,*V2, rr;
get_scatterer(ta_old);
n=a->n_rad; Z=a->atZ; r=a->rad; V=a->re; V2=a->im; magnetic=a->magnetic;
add_scatterer(ta);
a->select=3; a->lmax=infinite_int; a->n_rad=n; a->atZ=Z;
a->magnetic=magnetic;
a->rad=copy(r,n); a->re=copy(V,n); if(magnetic) a->im=copy(V2,n);
for(i=0; i<n; i++) {
rr=a->rad[i];
a->re[i] += -exp(-rr/screening_length)/rr;
if(magnetic) a->im[i] += -exp(-rr/screening_length)/rr;
} }
void propagation::scan_scatterer(int ta, char *name, int sel)
{
FILE *fout=NULL;
if(ta>=0) get_scatterer(ta);
if(strcmpC(name,"none")) fout=open_file(foutput,name,"w");
if(calc.verbose && sel!=2 && sel!=3) {
fprintf(foutput,"--- properties of scatterer %d\n", ta);
if(ta>=0) a->scan(foutput, sel);
}
if(fout!=NULL) {
if(sel!=2 && sel!=3) fprintf(fout,"--- properties of scatterer %d\n", ta);
if(ta>=0) a->scan(fout, sel);
close_file(fout);
} }
void propagation::set_k(int ik)
{
numero kr,ki;
if(calc.k_flag==1) {
if(iimfp_flag==2) set_k(sqrt(sqr(calc.k[ik])+2*V0+2*i_c*Vi));
else {
kr=sqrt(sqr(calc.k[ik])+2*V0);
if(iimfp_flag==0) ki=iimfp.val(kr)/2;
else if(iimfp_flag==3) ki=iimfp_SD(kr)/2;
else ki=iimfp_TPP(kr)/2;
set_k(complex(kr,ki));
} } else if(calc.k_flag==2) set_k(calc.kc[ik]);
}
void propagation::set_k(complex k_)
{
k=k_;
refraction=V0/(sqr(real(k))/2-V0);
final.init_refraction(refraction);
}
numero propagation::iimfp_TPP(numero kr)
{
numero E=sqr(kr)/2*au_eV;
numero beta=-0.10+0.944/sqrt(TPP_Ep*TPP_Ep+TPP_Eg*TPP_Eg)
+0.069*pow(TPP_rho,0.1);
numero gamma=0.191/sqrt(TPP_rho);
numero U=TPP_Ep*TPP_Ep/829.4;
numero C=1.97-0.91*U;
numero D=53.4-20.8*U;
numero imfp=E/(TPP_Ep*TPP_Ep*(beta*log(gamma*E)-C/E+D/(E*E)))/a0_au;
return 1/imfp;
}
numero propagation::iimfp_SD(numero kr)
{
numero E=sqr(kr)/2*au_eV;
numero imfp = (1.43e3/sqr(E) + 0.54*sqrt(E))/a0_au;
return 1/imfp;
}
void propagation::scan_imfp(char *name)
{
FILE *fout=NULL;
if(strcmpC(name,"none")) fout=open_file(foutput,name,"w");
if(calc.verbose) scan_imfp(foutput);
if(fout!=NULL) {scan_imfp(fout); close_file(fout);}
}
void propagation::scan_imfp(FILE *fout)
{
int ik;
fprintf(fout,"--- electron inelastic mean free path\n");
fprintf(fout," %5.5s imfp(Angs)\n", str_units(calc.k_units));
for (ik=0; ik<calc.n_k; ik++) {
set_k(ik);
fprintf(fout, " %9.4f", calc.kk[ik]);
fprintf(fout, " %9.4f\n", 1/(2*imag(k))*a0_au);
} }
void propagation::read_imfp(FILE *fin, char *my_file)
{
FILE *fimfp; int j, n_k; numero k_,lam;
char units1[str_length_units];
char units2[str_length_units]; numero factor2;
if(!strcmpC(my_file,"inline")) fimfp=fin;
else fimfp=open_file(foutput,my_file,"r");
n_k=read_int(fimfp);
if(n_k>1) read_name(fimfp,units1);
read_name(fimfp,units2);
factor2=units_conversion_factor(units2);
iimfp.alloc(n_k,interpolation_type);
if(n_k>1) {
for(j=0; j<n_k; j++) {
k_=read_numero(fimfp);
k_=units_k(units1,k_);
lam=read_numero(fimfp);
if(lam<=0) on_error(foutput,"read_imfp","negative i.m.f.p. =",lam,"");
iimfp.put(j,k_,1/(factor2*lam));
}
iimfp.init();
} else {
lam=read_numero(fimfp);
if(lam<=0) on_error(foutput,"read_imfp","negative i.m.f.p. =",lam,"");
iimfp.init(1/(factor2*lam),0);
}
if(strcmpC(my_file,"inline")) fclose(fimfp);
}
void propagation::set_muffin_tin_potentials(void)
{
Mufpot s;
int i,j, nn;
free_scatterers();
coord.sort(-1);
for(i=0; i<coord.nn; i++) coord.atom[i]=coord.atZ[i];
s.init(coord.n, coord.nn, coord.atom, coord.x, coord.y ,coord.z);
for(j=0; j<s.NR; j++) {
add_scatterer(j);
nn=s.JRMT[j];
a->select=3;
a->lmax=infinite_int;
a->atZ=s.atZ[j];
element_properties(s.atZ[j]);
a->mass=element_mass*amu_au;
a->n_rad=nn;
a->rad=new numero [nn];
a->re=new numero [nn];
for(i=0; i<nn; i++) {
a->rad[i]=s.RX[i];
a->re[i]=s.V[j][i];
} }
s.free();
}
void propagation::set_lmax(void)
{
int lmax=-1, i;
for(i=0; i<coord.nn; i++)
if(coord.atom[i]>=0) {
get_scatterer(coord.atom[i]);
if((a->lmax)>lmax) lmax=a->lmax;
}
init_lmax(lmax);
if(lmax_eff<0) on_error(foutput,"set_lmax","lmax =",lmax_eff,"< 0");
}
int propagation::get_n_c(void)
{
int i;
for(i=0; i<coord.nn; i++) if(coord.atom[i]>=0) {
get_scatterer(coord.atom[i]);
if((a->select==0 && a->n_c==2) ||
(a->select==1 && a->n_c==2) ||
(a->select==2 && a->n_c==2) ||
(a->select==3 && scattering_so) ||
(a->select==3 && a->magnetic) ||
a->select==4) return 2;
}
return 1;
}
void propagation::report_links(void)
{
int n_at=calc.n_atoms_last;
if(nn_G>0)
fprintf(foutput," Number of Gab's = %3d\n", nn_G);
else {
fprintf(foutput,"--- number of elements used in the last calculation\n");
fprintf(foutput," Number of atoms = %3d\n", n_at);
fprintf(foutput," Number of bond distances = %3d\n", nn_d);
fprintf(foutput," Number of polar angles = %3d\n", nn_th);
fprintf(foutput," Number of azim. angles = %3d\n", nn_fi);
fprintf(foutput," Number of t matrices = %3d\n", nn_t);
fprintf(foutput," Number of spin components = %3d\n", nn_c);
} }
void propagation::get_exact(int n_c, int lmax_)
{
int i,j, c,l,m, cp,lp,mp, ia,ja;
vector gg;
numero *rr,*ii;
if(lmax_>lmax_eff) lmax_=lmax_eff;
lmax_aa=lmax_;
dim=coord.n*n_c*lp12[lmax_aa];
aa.alloc(dim,dim);
for(i=0; i<coord.n; i++) {
get_t_matrix(coord.atom[i]);
for(j=0; j<coord.n; j++) if(get_ij(i,j)) {
for(cp=0; cp<n_c; cp++)
for(lp=0; lp<=lmax_aa; lp++)
for(mp=-lp; mp<=lp; mp++) {
gg.free();
gg.alloc(lp,n_c);
gg.re[cp*lp12[lp]+lp*lp+lp+mp]=1;
get_ij();
if(t_mat->lmax<lmax_aa) propagate(gg, t_mat->lmax);
else propagate(gg, lmax_aa);
R_1TR(gg, i, t_mat);
for(c=0, rr=gg.re, ii=gg.im; c<n_c; c++)
for(l=0; l<=lmax_aa; l++)
for(m=-l; m<=l; m++) if(l<=gg.lmax) {
ia=(i*n_c + c) *lp12[lmax_aa] +l*l +l +m;
ja=(j*n_c + cp)*lp12[lmax_aa] +lp*lp +lp +mp;
aa.a(ia,ja, -complex(*rr,*ii));
rr++; ii++;
} } } }
for(i=0; i<dim; i++) aa.add(i,i,1);
--aa; gg.free();
FILE *fout_aa;
if(aa_output_flag) {
fout_aa=open_file(foutput, aa_output, "a");
fprintf(fout_aa, "%d %d %d %g\n",
coord.n, n_c, lmax_aa, real(sqr(k))/2*au_eV);
for(i=0; i<coord.n; i++)
fprintf(fout_aa, "%d %g %g %g\n", i, coord.x[i],coord.y[i],coord.z[i]);
for(i=0; i<dim; i++)
for(j=0; j<dim; j++)
fprintf(fout_aa, "%g %g\n", real(aa.a(i,j)), imag(aa.a(i,j)));
close_file(fout_aa);
} }
void propagation::free_exact(void)
{
if(dim>0) {aa.free(); dim=0;}
}
int propagation::get_Gab(void)
{
int n;
if(n_G) {
Gab=Gab0; n=n_G;
while(n--)
if(fabs(d -Gab->d) <coord.eps_d &&
fabs(th-Gab->th)<coord.eps_th &&
fabs(fi-Gab->fi)<coord.eps_th) return 0;
else Gab=Gab->next;
} else Gab0=NULL;
Gab=new green; n_G++; nn_G=n_G;
Gab->next=Gab0; Gab0=Gab;
Gab->init(k,d,th,fi, separation);
return 0;
}
atomic_scattering::atomic_scattering(void)
{
n_k=0;
comp=0;
select=0;
n_rad=0; rad=NULL;
lmax=-1; n_rad=0; atZ=0;
mass=infinite;
magnetic=0;
}
void atomic_scattering::free(void)
{
int l;
if(select==1 || select==2) {
if(n_k>0) {delete [] re; delete [] im; delete [] k; n_k=0;}
} else
if(select==3) {
if(n_rad>0) {delete [] rad; delete [] re; if(magnetic) delete [] im;}
n_rad=0; rad=NULL; atZ=0; magnetic=0;
} else
if(lmax>=0 && select!=-1) {
for(l=0; l<=lmax; l++) {rr[l].free(); if(comp) ii[l].free();}
delete [] rr;
if(comp) delete [] ii;
lmax=-1;
} }
int atomic_scattering::read(FILE *fin, char *name)
{
char units[str_length_units],
idx[str_length_comments];
FILE *ffin;
free();
if(!strcmpC(name,"inline")) ffin=fin;
else ffin=open_file(foutput,name,"r");
read_name(ffin,idx);
if(!strcmpC(idx,"potential") || !strcmpC(idx,"potential2")) {
if(n_rad>0) {delete [] rad; delete [] re; if(magnetic) delete [] im;}
if(!strcmpC(idx,"potential2")) magnetic=1; else magnetic=0;
select=3; lmax=infinite_int; read_potential(ffin); return 0;
}
n_k=read_int(idx);
if(n_k>1) read_name(ffin, units);
lmax=read_int(ffin);
read_name(ffin, idx);
if(!strcmpC(idx,"regular")){select=0;n_c=1; read_phases(ffin,units);} else
if(!strcmpC(idx,"ex")) {select=0;n_c=2; read_phases(ffin,units);} else
if(!strcmpC(idx,"so")) {select=4;n_c=2; read_phases(ffin,units);} else
if(!strcmpC(idx,"axial")) {select=1; read_full (ffin,units);} else
if(!strcmpC(idx,"full")) {select=2; read_full (ffin,units);} else
on_error(foutput,"scatterer","wrong argument:",idx);
if(strcmpC(name,"inline")) fclose(ffin);
return 0;
}
void atomic_scattering::read_potential(FILE *fin)
{
char l_units[str_length_units], E_units[str_length_units];
char name[str_length_comments];
int i, rV;
n_rad=read_int(fin); atZ=read_int(fin);
read_name(fin,l_units);
read_name(fin,E_units);
read_name(fin,name); if(!strcmpC(name,"rV")) rV=1; else rV=0;
rad=new numero [n_rad];
re=new numero [n_rad];
if(magnetic)
im=new numero [n_rad];
for(i=0; i<n_rad; i++) {
rad[i]=units_k(l_units, read_numero(fin));
if(rV) re[i]=units_k(l_units, units_E(E_units, read_numero(fin)))/rad[i];
else re[i]=units_E(E_units, read_numero(fin));
if(magnetic)
if(rV) im[i]=units_k(l_units, units_E(E_units, read_numero(fin)))/rad[i];
else im[i]=units_E(E_units, read_numero(fin));
} }
void atomic_scattering::read_phases(FILE *fin, char *units)
{
int j,l,p,c; numero k_, x,y;
char cmpl[str_length_comments];
read_name(fin, cmpl);
if(!strcmpC(cmpl,"real")) comp=0; else
if(!strcmpC(cmpl,"complex")) comp=1; else
comp=2;
rr = new spline [n_c*(lmax+1)];
if(comp) ii = new spline [n_c*(lmax+1)];
for(c=p=0; c<n_c; c++)
for(l=0; l<=lmax; l++, p++) {
rr[p].alloc(n_k,interpolation_type);
if(comp) ii[p].alloc(n_k,interpolation_type);
}
for(j=0; j<n_k; j++) {
if(n_k>1) k_=units_k(units,read_numero(fin));
for(c=p=0; c<n_c; c++)
for(l=0; l<=lmax; l++, p++) {
x=read_numero(fin);
if(comp) y=read_numero(fin); else y=0;
if(n_k==1) {rr[p].init(x,0); if(comp) ii[p].init(y,0);}
else {rr[p].put(j,k_,x); if(comp) ii[p].put(j,k_,y);}
if((comp==0 || comp==1) && j>0) {
x=rr[p].y[j-1]; y=rr[p].y[j];
while(rr[p].y[j]>x+pi) rr[p].y[j]-=2*pi;
while(rr[p].y[j]<=x-pi) rr[p].y[j]+=2*pi;
} } }
if(n_k>1)
for(c=p=0; c<n_c; c++)
for(l=0; l<=lmax; l++, p++) {
if(comp) ii[p].init(); rr[p].init();
} }
void atomic_scattering::read_full(FILE *fin, char *units)
{
int i,j,n;
numero *r_,*i_;
n_c=read_int(fin);
if(select==1) n=(sqr(lmax+1)+(lmax*(lmax+1)*(2*lmax+1))/3);
else n=sqr(sqr(lmax+1));
n=n*sqr(n_c);
r_=re=new numero [n_k*n];
i_=im=new numero [n_k*n]; k=new numero [n_k];
for(i=0; i<n_k; i++) {
if(n_k>1) k[i]=units_k(units, read_numero(fin));
else k[i]=0;
for(j=0; j<n; j++) {
if(n_c>1) read_int(fin);
read_int(fin); read_int(fin);
if(n_c>1) read_int(fin);
read_int(fin); read_int(fin);
*r_=read_numero(fin); r_++;
*i_=read_numero(fin); i_++;
} } }
void atomic_scattering::init_t_matrix(t_matrix *t)
{
t->free();
t->lmax=(lmax>lmax_eff)?lmax_eff:lmax;
if(select== 0) init_t_matrix_diag(t); else
if(select== 1) init_t_matrix_full(real(scat.k),t); else
if(select== 2) init_t_matrix_full(real(scat.k),t); else
if(select== 3) init_t_matrix_potential(t); else
if(select== 4) init_t_matrix_so(t); else
if(select==-1) init_t_matrix_sphere(t); else
on_error(foutput,"init_t_matrix","select =", select, "not implemented");
}
complex *atomic_scattering::tl_phases(int n_c_, int &lmax_)
{
complex *tl;
int c,l,p;
numero psre,psim, expdi;
if(lmax_>lmax) lmax_=lmax;
tl=new complex [n_c_*(lmax_+1)];
for(c=p=0; c<n_c_; c++)
for(l=0; l<=lmax_; l++, p++) {
psre=rr[c*(lmax+1)+l].val(real(scat.k));
if(comp) psim=ii[c*(lmax+1)+l].val(real(scat.k));
if(comp==0) expdi=1;
if(comp==1) expdi=exp(-2*psim);
if(comp==0 || comp==1)
tl[p]=complex(sin(2*psre)*expdi/2, (1-cos(2*psre)*expdi)/2);
else tl[p]=complex(psre, psim);
}
cut_tl_phases(tl, n_c_, lmax_);
if(select==4) tl=tl_temperature_so(tl, lmax_);
else tl=tl_temperature(tl, n_c_, lmax_);
return tl;
}
void atomic_scattering::cut_tl_phases(complex *tl, int n_c_, int &lmax_)
{
int c,l,p, llmax=-1;
for(c=p=0; c<n_c_; c++)
for(l=0; l<=lmax_; l++, p++) {
if(scat.epsilon<mod(tl[p]) && l>llmax) llmax=l;
}
if(llmax<lmax_) {
if(n_c_>1) for(l=0; l<=llmax; l++) tl[l+(llmax+1)]=tl[l+(lmax_+1)];
lmax_=llmax;
} }
complex *atomic_scattering::tl_temperature(complex *tl, int n_c_, int &lmax_)
{
if(scat.T<1e-10) return tl;
complex *ttl; ttl=new complex [n_c_*(lmax_max+1)];
numero alpha=3*scat.T/(2*mass*kb_au*sqr(scat.T_Debye[atZ]));
complex alphak=2*alpha*mod2(scat.k), jl;
int c,l,p, ll,lpp;
for(c=p=0; c<n_c_; c++)
for(l=0; l<=lmax_max; l++, p++) ttl[p]=0;
for(ll=0; ll<=lmax_max+lmax_; ll++) {
jl=i_l(ll) * exp(-alphak) * besselj(ll,-i_c*alphak);
for(c=p=0; c<n_c_; c++)
for(l=0; l<=lmax_max; l++, p++)
for(lpp=ABS(l-ll); lpp<=ABS(l+ll) && lpp<=lmax_; lpp+=2)
ttl[p] += jl * tl[lpp+c*(lmax_+1)]
* sqrt(4*pi*(2*ll+1)*(2*lpp+1)/(2*l+1.0))
* Gaunt(lpp,ll,l,0,0,0);
}
lmax_=lmax_max; cut_tl_phases(ttl, n_c_, lmax_);
delete [] tl; return ttl;
}
numero atomic_scattering::Gaunt_j(int l, int j, int mu, int lp, int jp,
int lpp)
{
if(ABS(j-l-l)>1 || ABS(jp-lp-lp)>1 || ABS(mu)>j) return 0;
numero val0=0, val;
int s,mup,mpp;
for(mup=-jp; mup<=jp; mup+=2) {
mpp=(mu-mup)/2;
if(ABS(mpp)<=lpp) {
val=0;
for(s=-1; s<=1; s+=2)
val += CGspin1_2(l+l,j,s,mu) * CGspin1_2(lp+lp,jp,s,mup)
* Gaunt(lp,lpp,l,(mup-s)/2,mpp,(mu-s)/2);
val0+=sqr(val);
} }
return val0;
}
complex *atomic_scattering::tl_temperature_so(complex *tl, int &lmax_)
{
if(scat.T<1e-10) return tl;
complex *ttl; ttl=new complex [2*(lmax_max+1)];
numero alpha=3*scat.T/(2*mass*kb_au*sqr(scat.T_Debye[atZ]));
complex alphak=2*alpha*mod2(scat.k), jl;
int l,j,c,p, lp,jp,cp, mu,lpp;
for(c=p=0; c<2; c++)
for(l=0; l<=lmax_max; l++, p++) ttl[p]=0;
for(lpp=0; lpp<=lmax_max+lmax_; lpp++) {
jl=4*pi*i_l(lpp) * exp(-alphak) * besselj(lpp,-i_c*alphak);
for(c=p=0; c<2; c++)
for(l=0; l<=lmax_max; l++, p++) if(l>0 || c==0) {
if(c==0) j=l+l+1; else j=l+l-1;
for(lp=0; lp<=lmax_; lp++)
for(cp=0; cp<2; cp++) if(lp>0 || cp==0) {
if(cp==0) jp=lp+lp+1; else jp=lp+lp-1;
ttl[p] += jl * tl[lp+cp*(lmax_+1)] * Gaunt_j(l,j,j,lp,jp,lpp);
} } }
lmax_=lmax_max; cut_tl_phases(ttl, 2, lmax_);
delete [] tl; return ttl;
}
void atomic_scattering::init_t_matrix_diag(complex *tl, t_matrix *t)
{
int c,l,p;
t->select=0;
t->re = new numero [(t->n_c)*(t->lmax+1)];
t->im = new numero [(t->n_c)*(t->lmax+1)];
for(c=p=0; c<t->n_c; c++)
for(l=0; l<=t->lmax; l++, p++) {
t->re[p]=real(tl[p]); t->im[p]=imag(tl[p]);
} }
void atomic_scattering::init_t_matrix_diag(t_matrix *t)
{
complex *tl;
t->n_c=n_c; tl=tl_phases(t->n_c, t->lmax);
init_t_matrix_diag(tl, t);
delete [] tl;
}
void atomic_scattering::init_t_matrix_so(complex *tl, t_matrix *t)
{
numero trp,tip,trm,tim;
int l,m,p,q;
t->select=4;
t->re = new numero [4*lp12[t->lmax]];
t->im = new numero [4*lp12[t->lmax]];
for(l=p=q=0; l<=t->lmax; l++)
for(m=-l; m<=l; m++, p+=8, q+=4) {
trp=real(tl[l]); tip=imag(tl[l]);
if(l==0) trm=tim=0;
else {trm=real(tl[l+(t->lmax+1)]); tim=imag(tl[l+(t->lmax+1)]);}
t->re[q ]= cgcg12[p ]*trp + cgcg12[p+1]*trm;
t->re[q+1]= cgcg12[p+4]*trp + cgcg12[p+5]*trm;
t->re[q+2]= cgcg12[p+2]*trp + cgcg12[p+3]*trm;
t->re[q+3]= cgcg12[p+6]*trp + cgcg12[p+7]*trm;
t->im[q ]= cgcg12[p ]*tip + cgcg12[p+1]*tim;
t->im[q+1]= cgcg12[p+4]*tip + cgcg12[p+5]*tim;
t->im[q+2]= cgcg12[p+2]*tip + cgcg12[p+3]*tim;
t->im[q+3]= cgcg12[p+6]*tip + cgcg12[p+7]*tim;
} }
void atomic_scattering::init_t_matrix_so(t_matrix *t)
{
complex *tl;
t->n_c=2; tl=tl_phases(t->n_c, t->lmax);
init_t_matrix_so(tl, t);
delete [] tl;
}
complex *atomic_scattering::tl_potential(int n_c_, int &lmax_)
{
complex *tl;
numero E=sqr(real(scat.k))/2, *ph, cc;
Salvat Dirac;
int l, ll, rel;
if(magnetic) ll=lmax_+1; else ll=n_c_*(lmax_+1);
tl=new complex [n_c_*(lmax_+1)];
if(n_rad<1) on_error(foutput,"scatterer", "undefined MT potential");
if(n_c_==1 || magnetic) {cc=c_au; c_au*=1000; rel=0;} else rel=1;
ph=new numero [ll];
Dirac.phases(rad,re,n_rad, atZ, E, rel, lmax_, ph);
for(l=0; l<ll; l++) tl[l]=sin(ph[l])*exp(i_c*ph[l]);
if(magnetic) {
Dirac.phases(rad,im,n_rad, atZ, E, rel, lmax_, ph);
for(l=0; l<ll; l++) tl[l+ll]=sin(ph[l])*exp(i_c*ph[l]);
}
if(n_c_==1) c_au=cc;
delete [] ph; Dirac.free();
cut_tl_phases(tl, n_c_, lmax_);
if(n_c_==1 || magnetic) tl=tl_temperature(tl, n_c_, lmax_);
else tl=tl_temperature_so(tl, lmax_);
return tl;
}
void atomic_scattering::init_t_matrix_potential(t_matrix *t)
{
complex *tl;
if(scat.scattering_so || magnetic) t->n_c=2;
else t->n_c=1;
tl=tl_potential(t->n_c, t->lmax);
if(scat.scattering_so) init_t_matrix_so(tl, t);
else init_t_matrix_diag(tl, t);
delete [] tl;
}
complex *atomic_scattering::tl_sphere(int lmax_)
{
complex *tl;
complex r=scat.k*a;
complex rp=sqrt(sqr(scat.k)+2*V)*a;
complex jl,jlp;
int l;
tl=new complex [lmax_+1];
for(l=0; l<=lmax_; l++) {
jl=besselj(l,rp);
jlp=rp*besseljp(l,rp);
tl[l]= (-jlp * besselj(l,r) + jl * r*besseljp(l,r))
/(jlp * besselh(l,r) - jl * r*besselhp(l,r));
}
cut_tl_phases(tl, 1, lmax_);
tl=tl_temperature(tl, 1, lmax_);
return tl;
}
void atomic_scattering::init_t_matrix_sphere(t_matrix *t)
{
complex *tl;
t->n_c=1; tl=tl_sphere(t->lmax);
init_t_matrix_diag(tl, t);
delete [] tl;
}
void atomic_scattering::init_t_matrix_full(numero kk, t_matrix *t)
{
int i,n, c,l,m,cp,lp,mp;
numero x, *re_,*im_, *r1,*i1,*r2,*i2;
if(select==1) n=(sqr(lmax+1)+(lmax*(lmax+1)*(2*lmax+1))/3);
else n=sqr(sqr(lmax+1));
n=n*sqr(n_c);
t->select=select;
t->n_c=n_c;
if(n_k==1) {t->re=copy(re,n); t->im=copy(im,n);}
else {
if(kk<k[0] || k[n_k-1]<kk)
on_error(foutput,"init_t_matrix_full", "momentum", kk, "out of range");
i=1; while(kk>k[i]) i++;
x=(kk-k[i-1])/(k[i]-k[i-1]);
t->re=copy_(re+(i-1)*n, re+i*n, n, x);
t->im=copy_(im+(i-1)*n, im+i*n, n, x);
}
if(t->lmax<lmax) {
r1=t->re; i1=t->im;
if(select==1) n=sqr(t->lmax+1)+(t->lmax*(t->lmax+1)*(2*t->lmax+1))/3;
else n=sqr(sqr(t->lmax+1)); n=n*sqr(n_c);
r2=re_=new numero [n];
i2=im_=new numero [n];
for(c=0; c<n_c; c++)
for(l=0; l<=lmax; l++)
for(m=-l; m<=l; m++)
for(cp=0; cp<n_c; cp++)
for(lp=0; lp<=lmax; lp++)
for(mp=-lp; mp<=lp; mp++) if(select==2 || m==mp) {
if(l<=t->lmax && lp<=t->lmax) {*r2=*r1; *i2=*i1; r2++; i2++;}
r1++; i1++;
}
delete [] t->re; delete [] t->im;
t->re=re_; t->im=im_;
} }
numero *atomic_scattering::copy_(numero *a_, numero *b_, int n, numero x)
{
int i;
numero *c;
c=new numero [n];
for(i=0; i<n; i++) c[i]=(1-x)*a_[i]+x*b_[i];
return c;
}
int atomic_scattering::scan(FILE *fout, int sel)
{
numero k_,th, dp,dm, mu,Pl0,Pl1, ps;
complex f,g, val, *tl;
int ik,j,l, so_on, ex_on, n_c_, lmax_;
if(sel==-1) {
if(select!=-1 && select!=3 && n_k<1)
fprintf(fout, " no scattering properties are defined\n"); else {
if(select==-1) fprintf(fout, " sphere of constant potential\n");
if(select== 0) fprintf(fout, " non-relativistic phase shifts\n");
if(select== 1) fprintf(fout, " t matrix for axially-symmetric atom\n");
if(select== 2) fprintf(fout, " t matrix for arbitrary atom\n");
if(select== 3) fprintf(fout, " muffin-tin potential\n");
if(select== 4) fprintf(fout, " relativistic phase shifts\n");}
fprintf(fout, " atomic mass = ");
if(mass<infinite/2) fprintf(fout, "%g a.u.\n", mass);
else fprintf(fout, "infinite\n");
if(select==3) fprintf(fout, " atomic number = %d\n", atZ);
if(select!=-1 && select!=3) {
fprintf(fout, " lmax = %d\n", lmax);
fprintf(fout, " number of momenta = %d\n", n_k);
if(n_k>1) fprintf(fout, " momentum in the range %g-%g a.u.\n",
k[0], k[n_k-1]);
}
return 0;
}
if(sel==3) {
if(select!=3) on_warning(fout,"scan scatterer potential",
"the muffin-tin potential is not stored");
if(magnetic) fprintf(fout, "potential2\n");
else fprintf(fout, "potential\n");
fprintf(fout, "%d %d l(au) E(au) rV\n", n_rad, atZ);
for(j=0; j<n_rad; j++) {
fprintf(fout, "%g %g", rad[j], rad[j]*re[j]);
if(magnetic) fprintf(fout, " %g\n", rad[j]*im[j]);
else fprintf(fout, "\n");
}
return 0;
}
if(select==1 || select==2) {
on_warning(fout, "scan scatterer", "scatterer defined by its t matrix");
return 0;
}
if(select==0 && n_k<1) {
on_warning(fout, "scan scatterer", "empty set of phase shifts");
return 0;
}
init_lmax(lmax_max);
if(select==-1 || select==0 || (select==3 && scat.scattering_so==0))
so_on=0;
else so_on=1;
if((select==0 && n_c==2) || (select==3 && magnetic)) ex_on=1;
else ex_on=0;
if(scat.scattering_so || (select==3 && magnetic)) n_c_=2; else n_c_=1;
if(sel==0) {
if(calc.n_k>1) fprintf(fout, " eV");
if(final.n_th>1) fprintf(fout, " theta");
fprintf(fout, " cross sect.");
if(so_on==0) fprintf(fout, " Re{f} Im{f}\n");
else fprintf(fout, " S S |f|^2\n");
for(ik=0; ik<calc.n_k; ik++) {
scat.k=k_=calc.k[ik]; lmax_=lmax_max;
if(select==-1) tl=tl_sphere(lmax_); else
if(select== 3) tl=tl_potential(n_c_, lmax_); else
if(select== 0) tl=tl_phases(n_c, lmax_); else
if(select== 4) tl=tl_phases(2, lmax_); else
on_error(foutput, "scan scatterer", "undefined option");
for(j=0; j<final.n_th; j++) {
th=final.th_out[j]; mu=cos(th);
f=g=0;
for(l=0; l<=lmax_; l++) {
if(l && so_on) Pl1=legendre(l,1,mu);
Pl0=legendre(l,0,mu);
if(so_on) {dp=tl_deltal(tl[l]); dm=tl_deltal(tl[l+lmax_+1]);}
else
if(select==0 && n_c==2) dp=tl_deltal((tl[l]+tl[l+lmax_+1])/2.0);
else dp=tl_deltal(tl[l]);
if(so_on) {
f+=1/(2*i_c*k_)
*((l+1)*(exp(2*i_c*dm)-1.0)+l*(exp(2*i_c*dp)-1.0))*Pl0;
if(l) g+=1/(2*i_c*k_)*(exp(2*i_c*dp)-exp(2*i_c*dm))*Pl1;
} else
f+=1/k_*(2*l+1)*tl[l]*Pl0;
}
if(calc.n_k>1) fprintf(fout, " %6.2f", au_eV*sqr(k_)/2);
if(final.n_th>1) fprintf(fout, " %6.2f", 180/pi*th);
if(so_on)
fprintf(fout, " %12g %12g %12g\n",
mod2(f)+mod2(g),
-2*imag(f*conj(g))/(mod2(f) + mod2(g)),
-2*imag(f*conj(g))
);
else
fprintf(fout, " %12g %12g %12g\n",
mod2(f),
real(f),
imag(f)
);
}
delete [] tl;
} }
if(sel==2) {
fprintf(fout, "%d", calc.n_k);
if(calc.n_k>1) fprintf(fout, " %s", calc.k_units);
fprintf(fout, " %d", lmax_max);
if(so_on) fprintf(fout, " so"); else
if(ex_on) fprintf(fout, " ex"); else
fprintf(fout, " regular");
fprintf(fout, " tl\n");
for(ik=0; ik<calc.n_k; ik++) {
scat.k=k_=calc.k[ik]; lmax_=lmax_max;
if(select==-1) tl=tl_sphere(lmax_); else
if(select== 3) tl=tl_potential(n_c_, lmax_); else
if(select== 0) tl=tl_phases(n_c, lmax_); else
if(select== 4) tl=tl_phases(2, lmax_); else
on_error(foutput, "scan scatterer", "undefined option");
if(calc.n_k>1) fprintf(fout, "%6.2f", calc.kk[ik]);
for(l=0; l<=lmax_max; l++)
if(l<=lmax_) fprintf(fout, " %g %g", real(tl[l]), imag(tl[l]));
else fprintf(fout, " 0 0");
if(so_on || ex_on || (select==3 && magnetic))
for(l=0; l<=lmax_max; l++)
if(l<=lmax_)
fprintf(fout, " %g %g", real(tl[l+lmax_+1]), imag(tl[l+lmax_+1]));
else fprintf(fout, " 0 0");
fprintf(fout, "\n");
delete [] tl;
} }
free_lmax(); return 0;
}
final_state::final_state(void)
{
n_th=n_fi=n_ang=0;
n_1=n_2=0;
Ylm0_th_flag=Ylm0_fi_flag=0;
mesh_flag=0;
}
void final_state::init_th(numero thi, numero thf, int nth)
{
int i;
free_mesh();
if(n_th>0) {delete [] th; delete [] th_out; delete [] transmission;}
if(nth<1) n_th=0; else {
n_th=nth;
th=new numero [n_th];
th_out=new numero [n_th];
transmission=new numero [n_th];
if(n_th==1) {th[0]=th_out[0]=thi; transmission[0]=1;} else
for(i=0; i<n_th; i++) {
th[i]=th_out[i]=thi+i*(thf-thi)/(n_th-1);
transmission[i]=1;
} } }
void final_state::init_phi(numero fii, numero fif, int nfi)
{
int j;
free_mesh();
if(n_fi>0) {delete [] fi;}
if(nfi<1) n_fi=0; else {
n_fi=nfi;
fi=new numero [n_fi];
if(n_fi==1) fi[0]=fii;
else for(j=0; j<n_fi; j++) fi[j]=fii+j*(fif-fii)/(n_fi-1);
} }
void final_state::read_angles(FILE *fin, char *my_file)
{
FILE *fang; int i, nang;
if(!strcmpC(my_file,"inline")) fang=fin;
else fang=open_file(foutput,my_file,"r");
nang=read_int(fang);
free_mesh();
if(nang>1) {
delete [] th; delete [] th_out; delete [] transmission; delete [] fi;
n_th=nang;
th=new numero [n_th];
th_out=new numero [n_th];
transmission=new numero [n_th];
n_fi=nang;
fi=new numero [n_fi];
for(i=0; i<nang; i++) {
th[i]=th_out[i]=read_numero(fang);
transmission[i]=1;
fi[i]=read_numero(fang);
}
}
if(strcmpC(my_file,"inline")) fclose(fang);
}
void final_state::init_refraction(numero refraction)
{
int i;
for(i=0; i<n_th; i++)
if(refraction==0) th[i]=th_out[i];
else {
th[i]=asin(sin(th_out[i])/sqrt(1+refraction));
if(th_out[i]>pi/2) th[i]=pi-th[i];
}
init_transmission(refraction);
}
void final_state::init_transmission(numero refraction)
{
int i;
for(i=0; i<n_th; i++)
if(refraction!=0)
transmission[i]=cos(th_out[i])/cos(th[i]) / (1+refraction);
else transmission[i]=1;
}
void final_state::init_Ylm(void)
{
int i,j,m;
if(n_th*n_fi) {
free_Ylm();
Ylm0_th_flag=n_th;
Ylm0_fi_flag=n_fi;
Ylm0_th=new array [n_th];
Ylm0_fi=new array [n_fi];
for(i=0; i<n_th; i++) {
Ylm0_th[i].alloc(lp12[lmax_eff]);
init_Ylm(th[i],0,Ylm0_th[i].a);
}
for(j=0; j<n_fi; j++) {
Ylm0_fi[j].alloc(2*lmax_eff+1);
for(m=-lmax_eff; m<=lmax_eff; m++)
Ylm0_fi[j].a[m+lmax_eff]=exp(i_c*(m*fi[j]));
} } }
void final_state::init_Ylm(numero th_, numero fi_, complex *Ylm_)
{
int l,m,lm;
numero cth=cos(th_);
for(l=lm=0; l<=lmax_eff; l++)
for(m=-l; m<=l; m++,lm++) Ylm_[lm]=Ylmmu(l,m,cth,fi_);
}
complex *final_state::Ylm(int i, int j)
{
int l,m,lm;
complex *Ylm_;
Ylm_=new complex [lp12[lmax_eff]];
for(l=lm=0; l<=lmax_eff; l++)
for(m=-l; m<=l; m++,lm++) Ylm_[lm]=Ylm0_th[i].a[lm] *
Ylm0_fi[j].a[m+lmax_eff];
return Ylm_;
}
vector final_state::Ylm(complex *Ylm_)
{
numero *tr,*ti;
vector temp;
int l,m,lm;
temp.alloc(lmax_eff,1);
for(l=lm=0, tr=temp.re, ti=temp.im; l<=lmax_eff; l++)
for(m=-l; m<=l; m++, lm++, tr++, ti++) {
*tr=real(Ylm_[lm]);
*ti=imag(Ylm_[lm]);
}
return temp;
}
void final_state::init_mesh(int n_1_, int n_2_)
{
free(); n_1=n_1_; n_2=n_2_;
x=new numero [n_1*n_2];
y=new numero [n_1*n_2];
z=new numero [n_1*n_2];
}
void final_state::init_mesh(numero x0, numero y0, numero z0,
numero x1, numero y1, numero z1,
numero x2, numero y2, numero z2,
int n_1_, int n_2_)
{
init_mesh(n_1_,n_2_);
numero h1,h2; int i,j;
if(n_1>1) h1=1/(n_1-1.0); else h1=0;
if(n_2>1) h2=1/(n_2-1.0); else h2=0;
mesh_flag=1;
for(i=0; i<n_1; i++)
for(j=0; j<n_2; j++) {
x[i*n_2+j]=x0+i*(x1-x0)*h1+j*(x2-x1)*h2;
y[i*n_2+j]=y0+i*(y1-y0)*h1+j*(y2-y1)*h2;
z[i*n_2+j]=z0+i*(z1-z0)*h1+j*(z2-z1)*h2;
} }
void final_state::init_mesh(numero r,
numero th1, numero th2,
numero fi1, numero fi2, int n_1_, int n_2_)
{
init_mesh(n_1_,n_2_);
numero tth,ffi, cth,sth, h1,h2;
if(n_1>1) h1=1/(n_1-1.0); else h1=0;
if(n_2>1) h2=1/(n_2-1.0); else h2=0;
int i,j;
mesh_flag=2;
for(i=0; i<n_1; i++) {
tth=th1+i*(th2-th1)*h1;
cth=cos(tth); sth=sin(tth);
for(j=0; j<n_2; j++) {
ffi=fi1+i*(fi2-fi1)*h2;
x[i*n_2+j]=r*sth*cos(ffi)+coord.x0;
y[i*n_2+j]=r*sth*sin(ffi)+coord.y0;
z[i*n_2+j]=r*cth+coord.z0;
} } }
void final_state::free(void)
{
if(n_th>0) {
n_th=0; delete [] th; delete [] th_out; delete [] transmission;
}
if(n_fi>0) {n_fi=0; delete [] fi;}
free_mesh();
free_Ylm();
}
void final_state::free_Ylm(void)
{
int i;
if(Ylm0_th_flag) {
for(i=0; i<Ylm0_th_flag; i++) Ylm0_th[i].free();
delete [] Ylm0_th; Ylm0_th_flag=0;
}
if(Ylm0_fi_flag) {
for(i=0; i<Ylm0_fi_flag; i++) Ylm0_fi[i].free();
delete [] Ylm0_fi; Ylm0_fi_flag=0;
} }
void final_state::free_mesh(void)
{
if(mesh_flag>0) {
delete [] x; delete [] y; delete [] z;
mesh_flag=n_1=n_2=0;
} }
#ifdef jga_erf
#else
#define jga_erf 1
numero gammln(numero xx)
{
numero stp=2.5066282746310005,
x=xx-1,tmp,ser=1.000000000190015,
cof[6];
int j;
cof[0]=76.18009172947146; cof[1]=-86.50532032941677;
cof[2]=24.01409824083091; cof[3]=-1.231739572450155;
cof[4]=0.1208650973866179e-2; cof[5]=-0.5395239384953e-5;
x=xx;
tmp=x+5.5;
tmp=(x+0.5)*log(tmp)-tmp;
for(j=0; j<6; j++) {x++; ser+=cof[j]/x;}
return tmp+log(stp*ser/xx);
}
numero gamma(numero x)
{
if(x<0) return gamma(x+1)/x;
return exp(gammln(x));
}
numero gser(numero a, numero x, int p)
{
int n, itmax=101;
numero sum,del,ap, eps=3.0e-7, gln=gammln(a);
if(x<=0) {
if(x<0) printf("Error in gser: x<0\n");
return 0;
} else {
ap=a; sum=1/a; del=sum;
for(n=1; n<itmax; n++) {
ap++;
del=del*x/ap;
sum+=del;
if(ABS(del)<ABS(sum)*eps) n=itmax+1;
}
if(n<=itmax) printf("Error in gser: a too large, itmax too small\n");
if(p) return sum*exp(-x+a*log(x)-gln);
else return exp(gln)-sum*exp(-x+a*log(x));
} }
numero gcf(numero a, numero x, int p)
{
int n, itmax=101;
numero gold,g,fac,b1,b0,anf,ana,an,a1,a0, eps=3.0e-7, gln=gammln(a);
gold=0; a0=1; a1=x; b0=0; b1=1; fac=1;
for(n=1; n<itmax; n++) {
an=1*n; ana=an-a; a0=(a1+a0*ana)*fac;
b0=(b1+b0*ana)*fac; anf=an*fac;
a1=x*a0+anf*a1; b1=x*b0+anf*b1;
if(a1!=0) {
fac=1/a1; g=b1*fac;
if(ABS((g-gold)/g)<eps) n=itmax+1;
gold=g;
} }
if(n<=itmax) printf("Error in gcf: a too large, itmax too small\n");
if(p) return exp(-x+a*log(x)-gln)*g;
else return exp(-x+a*log(x))*g;
}
numero gammp(numero a, numero x)
{
if(x<0 || a<=0) {printf("Error in gammp: invalid arguments\n"); return 0;}
if(x<a+1) return gser(a,x,1);
else return 1-gcf(a,x,1);
}
numero gammq(numero a, numero x)
{
if(x<0 || a<=0) {printf("Error in gammq: invalid arguments\n"); return 0;}
if(x<a+1) return 1-gser(a,x,1);
else return gcf(a,x,1);
}
numero gamma(numero a, numero x)
{
if(a<0) return (gamma(a+1,x)-pow(x,a)*exp(-x))/a;
if(x==0) return gamma(a);
if(x<0) {printf("Error in gammq: invalid arguments\n"); return 0;}
if(x<a+1) return gser(a,x,0);
else return gcf(a,x,0);
}
numero erf(numero x)
{
if(x<0) return -gammp(0.5,sqr(x));
else return gammp(0.5,sqr(x));
}
numero erfc(numero x)
{
if(x<0) return 1+gammp(0.5,sqr(x));
else return gammq(0.5,sqr(x));
}
#ifdef jga_complex
complex erf(complex xx)
{
if(imag(xx)<0) return -erf(-xx); else
if(imag(xx)==0) return complex(erf(real(xx)),0);
numero x=real(xx), y=imag(xx), ex,xy,x2,_2x, cxy,sxy, ey, ch,sh, fn,gn;
complex val,z; val=0;
int n,n2,nmax=10;
x2=x*x; ex=exp(-x2); xy=2*x*y; cxy=cos(xy); sxy=sin(xy); _2x=2*x;
for(n=1; n<=nmax; n++) {
n2=n*n; ey=exp(n*y); ch=(ey+1/ey)/2; sh=(ey-1/ey)/2;
fn = _2x*(1-ch*cxy) + n*sh*sxy;
gn = _2x* ch*sxy + n*sh*cxy;
val=val+(exp(-n2/4.0)/(n2+4*x2))*complex(fn,gn);
}
if(x!=0) z=complex(1-cxy,sxy)/_2x; else z=complex(0,y);
return erf(x) + (ex/pi) * (z + 2*val);
}
complex erfc(complex x) {return 1.0-erf(x);}
complex erfw_asymptotic(complex z)
{
complex z2=z*z;
if(real(z)>6 || imag(z)>6)
return i_c*z*(0.5124242/(z2-0.2752551)+0.05176536/(z2-2.724745));
else return i_c*z*(0.4613135/(z2-0.1901635)+0.09999216/(z2-1.7844927)
+ 0.002883894/(z2-5.5253437));
}
complex erfw_series(complex z, int n)
{
complex fct1, fct2, ff=-z*z, val;
int i;
fct1=1;
fct2=i_c*z/(sqrt(pi)/2); val=fct1+fct2;
for(i=1; i<=n; i++) {
fct1=fct1*ff/(i+0.0);
fct2=fct2*ff/(i+0.5);
val+=fct1+fct2;
}
return val;
}
complex erfw(complex z)
{
numero x=real(z), y=imag(z);
if(y<0) return 2*exp(-z*z) - erfw(-z);
if(x<0) return conj(erfw(complex(-x,y)));
if(x>3.9 || y>3) return erfw_asymptotic(z);
return erfw_series(z, 100);
}
complex erfw(complex z, complex b)
{
numero x=real(z), y=imag(z);
complex b2=b*b;
complex eb2=exp(-b2);
if(y<0) return 2*exp(-z*z-b2) - eb2 * erfw(-z);
if(x<0) return eb2 * conj(erfw(complex(-x,y)));
if(x>3.9 || y>3) return eb2 * erfw_asymptotic(z);
return eb2 * erfw_series(z, 100);
}
complex gamma1_2(int n, complex x)
{
if(n==0) return sqrt(pi)*exp(-x)*erfw(euler(sqrt(mod(x)),(arg(x)+pi)/2));
if(n<0) return (gamma1_2(n+1,x)-pow(x,n+0.5)*exp(-x))/(n+0.5);
return (n-0.5)*gamma1_2(n-1,x)+pow(x,n-0.5)*exp(-x);
}
#endif
#endif
#ifdef jga_Kambe
#else
#define jga_Kambe 1
class Kambe {
numero a0,b0;
numero ax,ay, bx,by;
numero Gax,Gay, Gbx,Gby;
numero th0,phi0;
numero qx,qy,qz;
complex k;
numero att;
numero eps;
numero a,a_2;
int D3lm(void);
#define integl_ij 40401
complex integl(int ll, complex kRj);
void integl_clear(void);
int *integl_flag[integl_ij], integl_l, integl_i;
complex *integl_data[integl_ij];
numero integl_x0, integl_y0;
complex Almz(int l_, int m_,
numero x, numero y, numero z, numero z1_, int flag_);
void tested_sum(complex coef, int ij, int index);
void perimeter(complex coef,
int ij0, int ij1, int index);
numero x0,y0,z0, z1, area;
int l,m, i,j,s, n,lm, flag;
complex k2, sum, qzc;
public:
int ijmin, ijstep;
Kambe(void) {ijmin=5; ijstep=3; integl_l=-1; x0=y0=0;}
void free(void);
void integl_alloc(int ll);
void init(complex k_, numero th0_, numero phi0_, numero eps_);
void init(complex k_, numero eps_) {init(k_,pi,0,eps_);}
void lattice(numero a0_, numero b0_, numero al, numero be);
void lattice(numero a0_) {lattice(a0_,a0_,0,pi/2);}
void attenuation(numero att_) {att=att_;}
void q(numero qx_, numero qy_, numero qz_) {qx=qx_; qy=qy_; qz=qz_;}
complex Alm(int l, int m, numero x, numero y, numero z);
complex Blm(int l, int m, numero x, numero y, numero z, numero z1_);
complex Blm_NaCl1(int l, int m, int n_);
complex Blm_NaCl2(int l, int m, int n_);
complex Clm(int l, int m, numero x, numero y, numero z, numero z1_);
complex Alm(int l, int m, numero x, numero y, numero z,
numero qx_, numero qy_, numero qz_);
complex Almj(int l, int m, numero x, numero y, numero z, int j_);
void report(void)
{
printf("q=(%g,%g,%g) att=%g\n", qx,qy,qz, att);
printf("k=(%g,%g)\n", real(k), imag(k));
printf("a=(%g,%g) b=(%g,%g)\n", ax,ay, bx,by);
} };
void Kambe::lattice(numero a0_, numero b0_, numero al, numero be)
{
a0=a0_; b0=b0_;
ax=a0*cos(al); bx=b0*cos(al+be);
ay=a0*sin(al); by=b0*sin(al+be);
area=ax*by-ay*bx;
Gax= 2*pi * by/area;
Gay=-2*pi * bx/area;
Gbx=-2*pi * ay/area;
Gby= 2*pi * ax/area;
area=ABS(area);
}
void Kambe::init(complex k_, numero th0_, numero phi0_, numero eps_)
{
init_ffact(); free();
k=k_; k2=k*k;
th0=th0_; phi0=phi0_;
eps=eps_;
a=mod2(k)*area/(32*pi);
if(a>8) a=8;
a_2=sqrt(a);
att=imag(k)/ABS(cos(th0));
qx=real(k)*sin(th0)*cos(phi0);
qy=real(k)*sin(th0)*sin(phi0);
qz=real(k)*cos(th0);
}
void Kambe::free(void)
{
int ij;
if(integl_l>=0)
for(ij=0; ij<integl_ij; ij++) {
delete [] integl_flag[ij]; delete [] integl_data[ij];
}
integl_l=-1;
}
complex Kambe::Alm(int l_, int m_, numero x, numero y, numero z)
{
complex coef_D1lm, coef_D2lm;
l=l_; m=m_; x0=x; y0=y; z0=z;
if(mod(k*z0)>1e-10) return Almz(l,m,x0,y0,z0,0,0);
if(!l && !m && x0==0 && y0==0) sum=i_c*k/sqrt(4*pi);
else sum=0;
if((l+m)%2==0) {
lm=(l-ABS(m))/2;
coef_D1lm=-1/(k*area) * i_l(1-m)/pow(2.0,l+0.0)
* sqrt((2*l+1)*fact[l+m]*fact[l-m]);
coef_D2lm=-k/(4*pi)*(sign_1l(l+(l+m)/2)/pow(2.0,l+0.0))
* sqrt((2*l+1)*fact[l-m]*fact[l+m])
/ (fact[(l-m)/2]*fact[(l+m)/2]);
D3lm();
perimeter(coef_D1lm, 0, ijmin, 1);
if(mod(k*(integl_x0-x0))+mod(k*(integl_x0-x0))>1e-9) integl_clear();
if(x0!=0 || y0!=0) perimeter(coef_D2lm, 0,ijmin, 2);
else perimeter(coef_D2lm, 1,ijmin, 2);
tested_sum(coef_D1lm, ijmin, 1);
tested_sum(coef_D2lm, ijmin, 2);
}
return -4*pi * exp(i_c*(qx*x0+qy*y0)) * sum;
}
complex Kambe::Blm(int l_, int m_, numero x, numero y, numero z, numero z1_)
{
complex val=0;
z1_=ABS(z1_);
if(mod(k*z1_)<=1e-10) on_error("Kambe::Blm","z1=0");
while(z>=0 || mod(k*z)<=1e-10) {val+=Alm(l_,m_,x,y,z); z-=z1_;}
return val + Almz(l_,m_,x,y,z,-z1_,1);
}
complex Kambe::Blm_NaCl1(int l_, int m_, int n_)
{
return (Blm(l_,m_, a0/2, 0, (n_/2)*a0, a0)
+ Blm(l_,m_, 0, a0/2, (n_/2)*a0, a0)
+ Blm(l_,m_, 0, 0, -a0/2+((n_+1)/2)*a0, a0)
+ Blm(l_,m_, a0/2, a0/2, -a0/2+((n_+1)/2)*a0, a0))
* exp(-n_*(a0/2)*att);
}
complex Kambe::Blm_NaCl2(int l_, int m_, int n_)
{
return (Blm(l_,m_, a0/2, 0, -a0/2+((n_+1)/2)*a0, a0)
+ Blm(l_,m_, 0, a0/2, -a0/2+((n_+1)/2)*a0, a0)
+ Blm(l_,m_, 0, 0, (n_/2)*a0, a0)
+ Blm(l_,m_, a0/2, a0/2, (n_/2)*a0, a0))
* exp(-n_*(a0/2)*att);
}
complex Kambe::Clm(int l_, int m_, numero x, numero y, numero z, numero z1_)
{
numero att_=att;
complex val;
z1_=ABS(z1_);
if(mod(k*z1_)<=1e-10) on_error("Kambe::Clm","z1=0");
while(z>=z1_) z-=z1_;
while(z<=-z1_) z+=z1_;
attenuation(0);
val= Almz(l_,m_,x,y,z+z1_,z1_,1)
+ Almz(l_,m_,x,y,z-z1_,-z1_,1)
+ Alm (l_,m_,x,y,z);
attenuation(att_);
return val;
}
complex Kambe::Alm(int l_, int m_, numero x, numero y, numero z,
numero qx_, numero qy_, numero qz_)
{
numero qqx=qx, qqy=qy, qqz=qz; qx=qx_; qy=qy_; qz=qz_;
complex val=Alm(l,m,x,y,z); qx=qqx; qy=qqy; qz=qqz;
return val;
}
complex Kambe::Almj(int l_, int m_, numero x, numero y, numero z, int j_)
{
numero h=real(k)/10000;
if(j_==0) return -i_c*( Alm(l,m,x,y,z,qx+h,qy,qz)
-Alm(l,m,x,y,z,qx-h,qy,qz))/(2*h); else
if(j_==1) return -i_c*( Alm(l,m,x,y,z,qx,qy+h,qz)
-Alm(l,m,x,y,z,qx,qy-h,qz))/(2*h); else
if(j_==2) return -i_c*( Alm(l,m,x,y,z,qx,qy,qz+h)
-Alm(l,m,x,y,z,qx,qy,qz-h))/(2*h);
return 0;
}
void Kambe::integl_clear(void)
{
int ij,ll;
if(integl_l>=0) for(ij=0; ij<integl_ij; ij++)
for(ll=-1; ll<=integl_l; ll++) integl_flag[ij][ll+1]=0;
integl_x0=x0; integl_y0=y0; integl_i=0;
}
void Kambe::integl_alloc(int ll)
{
int ij; integl_l=ll;
for(ij=0; ij<integl_ij; ij++) {
integl_flag[ij]=new int [integl_l+2];
integl_data[ij]=new complex [integl_l+2];
}
integl_clear();
}
complex Kambe::integl(int ll, complex kRj)
{
if(integl_i<integl_ij && ll<=integl_l)
if(integl_flag[integl_i][ll+1]) return integl_data[integl_i][ll+1];
complex kR2a=sqr(kRj)/(4*a), val;
if(ll==-1) val= sqrt(pi) * exp(a) / (2*i_c)
* ( erfw( a_2+i_c*kRj/(2*a_2), kRj/(2*a_2))
- erfw(-a_2+i_c*kRj/(2*a_2), kRj/(2*a_2))); else
if(ll== 0) val= sqrt(pi)/(kRj/2.0) * exp(a) / 2.0
* ( erfw( a_2+i_c*kRj/(2*a_2), kRj/(2*a_2))
+ erfw(-a_2+i_c*kRj/(2*a_2), kRj/(2*a_2))); else
if(ll>0) val= ((ll-0.5)*integl(ll-1,kRj)
- integl(ll-2,kRj)
+ exp(a-kR2a)/pow(a,ll-0.5))/(a*kR2a); else
val= (ll+1.5)*integl(ll+1,kRj)
- integl(ll+2,kRj) * a*kR2a
+ exp(a-kR2a)/pow(a,ll+1.5);
if(integl_i<integl_ij && ll<=integl_l) {
integl_flag[integl_i][ll+1]=1; integl_data[integl_i][ll+1]=val;
}
return val;
}
int Kambe::D3lm(void)
{
if(l || m || x0!=0 || y0!=0) return 0;
numero ea=exp(a);
sum += k/(2*pi) * (ea/a_2 + i_c*sqrt(pi)*(erfw(a_2)*ea-1.0));
return 0;
}
complex Kambe::Almz(int l_, int m_,
numero x, numero y, numero z, numero z1_, int flag_)
{
x0=x; y0=y; z0=z; l=l_; m=m_;
z1=z1_; flag=flag_;
if(z0*z1<=0 && flag) on_error("Kambe::Almz","z0*z1<=0");
s=(z0>0)?1:-1;
qzc=qz-i_c*att;
sum=0;
perimeter(1, 0, 4*ijmin, 3);
tested_sum(1, 4*ijmin, 3);
return (4*pi) * 2*pi/area * sign_1l(l+m) * i_l(l) * sum;
}
void Kambe::tested_sum(complex coef, int ij, int index)
{
complex sum0; ij++;
do {
sum0=sum;
perimeter(coef, ij,ij+ijstep-1,index); ij+=ijstep;
} while(mod((sum-sum0)/sum)>eps);
}
void Kambe::perimeter(complex coef, int ij0, int ij1, int index)
{
complex partial_sum=0, sum1, fct1,fct2, Gam,cth, qGz,qGz2, kR;
numero Rx,Ry, rRx,rRy,rR, Gx,Gy, qGx,qGy, qG2, phi;
for(i=-ij1; i<=ij1; i++)
for(j=-ij1; j<=ij1; j++) {
if(ABS(i)<ij0) if(j==-ij0+1) j=ij0;
if(index==1) {
Gx=i*Gax+j*Gbx; Gy=i*Gay+j*Gby;
qGx=qx+Gx; qGy=qy+Gy;
qG2=sqr(qGx)+sqr(qGy);
if(qG2!=0 || m==0) {
qGz2=k2-qG2; qGz=sqrt(qGz2);
fct1=pow(sqrt(qG2)/k,ABS(m))*pow(qGz/k,lm+lm-1.0);
fct2=qG2/qGz2;
for(n=lm,sum1=0; n>=0; n--) {
sum1 += fct1 / (fact[n]*fact[(l-m)/2-n]*fact[(l+m)/2-n])
* gamma1_2(-n,-a*qGz2/k2-i_c*1e-15);
fct1=fct1*fct2;
}
if(qGx==0 && qGy==0) phi=0; else phi=atan2(qGy,qGx);
partial_sum += exp(-i_c*(qGx*x0+qGy*y0+m*phi)) * sum1;
} } else
if(index==2) {
Rx=i*ax+j*bx; Ry=i*ay+j*by;
rRx=x0+Rx; rRy=y0+Ry;
rR=sqrt(sqr(rRx)+sqr(rRy)); kR=k*rR;
sum1=pow(kR/2.0,l) * integl(l,kR); integl_i++;
if(rRx==0 && rRy==0) phi=0; else phi=atan2(-rRy,-rRx);
partial_sum += exp(-i_c*(qx*Rx+qy*Ry+m*phi)) * sum1;
} else
if(index==3) {
Gx=i*Gax+j*Gbx; Gy=i*Gay+j*Gby;
qGx=-qx+Gx; qGy=-qy+Gy;
qG2=sqr(qGx)+sqr(qGy);
Gam=sqrt(qG2-k2-complex(0,1e-15));
if(qGx==0 && qGy==0) phi=0; else phi=atan2(qGy,qGx);
cth=s*i_c*Gam/k;
sum1= exp(-Gam*ABS(z0) + i_c*(Gx*x0+Gy*y0+qzc*z0))/Gam
* Ylmmu(l,-m,cth,phi);
if(flag) sum1=sum1/(1.0-exp((-s*Gam+i_c*qzc)*z1));
partial_sum+=sum1;
} }
sum +=coef*partial_sum;
}
#endif
void green::init(complex k, numero dd, numero tth, numero ffi, int periodic)
{
int c,l,m,cp,lp,mp,lpp,mpp, i;
numero *Gr,*Gi, cth, jl,yl, *cg, krd,kid;
complex *hL; hL=new complex [sqr(2*lmax_eff+1)];
complex hh, kd, val;
Kambe a;
if(scat.Gab_cg_flag==0) {
for(l=i=0; l<=lmax_eff; l++)
for(m=-l; m<=l; m++)
for(lp=0; lp<=lmax_eff; lp++)
for(mp=-lp; mp<=lp; mp++)
for(lpp=ABS(l-lp); lpp<=l+lp; lpp+=2) i++;
scat.Gab_cg=new numero [i];
cg=scat.Gab_cg;
for(l=0; l<=lmax_eff; l++)
for(m=-l; m<=l; m++)
for(lp=0; lp<=lmax_eff; lp++)
for(mp=-lp; mp<=lp; mp++)
for(lpp=ABS(l-lp); lpp<=l+lp; lpp+=2) {
mpp=m-mp;
*cg=Gaunt(lp,lpp,l,mp,mpp);
cg++;
}
scat.Gab_cg_flag=1;
}
d=dd; th=tth; fi=ffi; cth=cos(tth);
kd=k*d; krd=real(kd); kid=imag(kd);
re=new numero [sqr(lp12[lmax_eff])]; Gr=re;
im=new numero [sqr(lp12[lmax_eff])]; Gi=im;
if(periodic==0)
for(l=0; l<=2*lmax_eff; l++) {
if(scat.attenuation_type==0) hh=besselilh(l,kd);
else {
besseljy(l,krd,jl,yl);
hh=i_l(l) * (i_c*jl-yl) * exp(-kid);
}
hh=4*pi*hh;
for(m=-l; m<=l; m++) hL[l*l+l+m]= hh*conj(Ylmmu(l,m,cth,fi));
}
else {
a.lattice(3.61/a0_au);
a.init(k, 30*pi/180,50*pi/180, 0.0001);
a.attenuation(0);
for(l=0; l<=2*lmax_eff; l++)
for(m=-l; m<=l; m++)
hL[l*l+l+m]=a.Alm(l,m,d*sin(th)*cos(fi),d*sin(th)*sin(fi),d*cth) / k;
}
cg=scat.Gab_cg;
for(c=0; c<1; c++)
for(l=0; l<=lmax_eff; l++)
for(m=-l; m<=l; m++)
for(cp=0; cp<1; cp++)
for(lp=0; lp<=lmax_eff; lp++)
for(mp=-lp; mp<=lp; mp++, Gr++, Gi++) {
val=0;
mpp=m-mp;
for(lpp=ABS(l-lp); lpp<=l+lp; lpp+=2) {
val += hL[lpp*lpp+lpp+mpp] * (*cg);
cg++;
}
*Gr=real(val);
*Gi=imag(val);
}
delete [] hL;
}
void green::prod(vector &a)
{
int c,l,m,cp,lp,mp;
numero *Gr,*Gi,*ar,*ai,*br,*bi;
vector b;
b.copy(a); a.free(); a.alloc(lmax_eff,b.n_c);
Gr=re; Gi=im; ar=a.re; ai=a.im;
for(c=0; c<a.n_c; c++)
for(l=0; l<=lmax_eff; l++)
for(m=-l; m<=l; m++, ar++, ai++)
for(cp=0, br=b.re, bi=b.im; cp<a.n_c; cp++)
for(lp=0; lp<=lmax_eff; lp++)
for(mp=-lp; mp<=lp; mp++, Gr++, Gi++) if(lp<=b.lmax) {
*ar += (*Gr)*(*br) - (*Gi)*(*bi);
*ai += (*Gr)*(*bi) + (*Gi)*(*br);
br++; bi++;
}
b.free();
}
int electron_bin::init_wf_LEED(int spin_)
{
int a,l,m,lm, dim=lp12[lmax_eff];
complex ekRa,psi, *Ylm;
vector gg;
numero kr=real(scat.k);
numero fi0=calc.e_ffi;
numero th0=calc.e_tth;
k0x=kr*sin(th0)*cos(fi0);
k0y=kr*sin(th0)*sin(fi0);
k0z=kr*cos(th0);
Ylm=new complex [dim];
final.init_Ylm(th0,fi0,Ylm);
for(a=0; a<coord.n; a++) if(coord.is_emitter(a)) {
if(spin_==0) gg.alloc(lmax_eff,1);
else gg.alloc(lmax_eff,2);
ekRa= 4*pi *
exp( i_c * ( k0x*(coord.x[a]-coord.x0)
+ k0y*(coord.y[a]-coord.y0)
+ k0z*(coord.z[a]-coord.z0))
- (coord.zs-coord.z[a])*imag(scat.k)/ABS(cos(th0)));
for(l=lm=0; l<=lmax_eff; l++)
for(m=-l; m<=l; m++, lm++) {
psi=ekRa*conj(Ylm[lm]);
if(spin_==1 || spin_==0) {
gg.re[lm] =real(psi);
gg.im[lm] =imag(psi);
} else {
gg.re[lm+dim]=real(psi);
gg.im[lm+dim]=imag(psi);
} }
scat.R_1TR(gg, a);
iter.o.g[a].copy(gg); gg.free();
} else if(spin_==0) iter.o.g[a].alloc(-1,1);
else iter.o.g[a].alloc(-1,2);
delete [] Ylm;
for(a=0; a<coord.n; a++) iter.n.g[a].copy(iter.o.g[a]);
return 1;
}
void electron_bin::surface_lattice(numero a, numero b, numero al, numero be)
{
leed_a=a; leed_b=b;
ax=a*cos(al); bx=b*cos(al+be);
ay=a*sin(al); by=b*sin(al+be);
numero a_b=ax*by-ay*bx;
Gax= 2*pi * by/a_b;
Gay=-2*pi * bx/a_b;
Gbx=-2*pi * ay/a_b;
Gby= 2*pi * ax/a_b;
area=ABS(a_b);
}
void electron_bin::init_leed_emitters(void)
{
int i;
numero ra,rb;
numero ab=ax*bx+ay*by;
numero c1,c2;
numero den=sqr(leed_a*leed_b)-sqr(ab);
coord.free_emitters();
coord.sort(-1);
for(i=0; i<coord.n; i++) {
ra= (coord.x[i]-leed_x)*ax
+(coord.y[i]-leed_y)*ay;
rb= (coord.x[i]-leed_x)*bx
+(coord.y[i]-leed_y)*by;
c1=leed_a*(ra*sqr(leed_b)-rb*ab)/den;
c2=leed_b*(rb*sqr(leed_a)-ra*ab)/den;
if(-coord.eps_d<c1 && c1<leed_a-coord.eps_d &&
-coord.eps_d<c2 && c2<leed_b-coord.eps_d) coord.add_emitter(i);
} }
numero electron_bin::intensity(complex *wf)
{
numero val=0;
int c;
if(spin_flag) val=mod2(wf[0]);
else for(c=0; c<n_c; c++) val+=mod2(wf[c]);
return val;
}
void electron_bin::wf_far(int i, int j, complex *wf)
{
complex *Ylm; Ylm=final.Ylm(i,j);
wf_far(final.th[i], final.fi[j], Ylm, wf);
delete [] Ylm;
}
void electron_bin::wf_far(numero th, numero fi, complex *Ylm, complex *wf)
{
int a, c;
numero kfx,kfy,kfz, ilam, kr=real(scat.k);
complex *wft, ekRa;
kfx= kr*sin(th)*cos(fi);
kfy= kr*sin(th)*sin(fi);
kfz= kr*cos(th);
ilam=imag(scat.k)/ABS(cos(th));
wft=new complex [n_c];
for(c=0; c<n_c; c++) wf[c]=0;
for (a=0; a<coord.n; a++) {
ekRa= exp( -i_c * ( kfx*(coord.x[a]-coord.x0)
+ kfy*(coord.y[a]-coord.y0)
+ kfz*(coord.z[a]-coord.z0))
-(coord.zs-coord.z[a])*ilam*(1-molecule) );
wf_far(iter.n.g[a], Ylm, wft);
for(c=0; c<n_c; c++) wf[c]+=wft[c]*ekRa;
}
for(c=0; c<n_c; c++) wf[c]=wf[c]/kr;
delete [] wft;
}
void electron_bin::wf_far(vector &a, complex *Ylm, complex *wf)
{
int l,m,lm, c; numero *ar,*ai;
if((th_spin!=0 || fi_spin!=0) && a.n_c==2)
a.spin_rotation(0, th_spin, pi-fi_spin);
for(c=0; c<a.n_c; c++) {
ar=a.re+(c*lp12[a.lmax]);
ai=a.im+(c*lp12[a.lmax]); wf[c]=0;
for(l=lm=0; l<=a.lmax; l++)
for(m=-l; m<=l; m++, ar++, ai++, lm++) {
wf[c]+=complex((*ar),(*ai)) * Ylm[lm];
} }
if((th_spin!=0 || fi_spin!=0) && a.n_c==2)
a.spin_rotation(fi_spin-pi, -th_spin, 0);
}
void electron_bin::wf_near(int i, int j, complex *wf)
{
int a, c;
complex *wft;
wft=new complex [n_c];
for(c=0; c<n_c; c++) wf[c]=0;
for (a=0; a<coord.n; a++) {
}
delete [] wft;
}
void electron_bin::wf_LEED(complex *wf)
{
int c;
numero kf;
numero fi;
numero kfx= k0x + leed_i*Gax + leed_j*Gbx;
numero kfy= k0y + leed_i*Gay + leed_j*Gby;
numero kfz2=sqr(real(scat.k))-sqr(kfx)-sqr(kfy);
if(kfz2<=0) {for(c=0; c<n_c; c++) wf[c]=0; leed_th=0;}
else {
cartesian_to_spherical(kfx,kfy,sqrt(kfz2), kf,leed_th,fi);
complex *Ylm; Ylm=new complex [lp12[lmax_eff]];
final.init_Ylm(leed_th,fi,Ylm);
wf_far(leed_th, fi, Ylm, wf);
delete [] Ylm;
} }
void electron_bin::init_wf_PD(int jm, int mjms, complex *eps)
{
int i;
for(i=0; i<coord.n; i++) if(i!=emitter) iter.o.g[i].alloc(-1,n_c);
if(manual_flag) init_wf_manual();
else {
if(rmat==NULL && CR_flag) {
scat.get_scatterer(coord.atom[emitter]);
rrm[0]=rmat_el_CR(l0+1);
rrm[1]=rmat_el_CR(l0-1);
} else
if(rmat==NULL) {
scat.get_scatterer(coord.atom[emitter]);
rrm[0]=rmat_el_MT(l0+1);
rrm[1]=rmat_el_MT(l0-1);
} else
if(excitation==0) {
rrm[0]=rmat[0].val(real(scat.k));
rrm[1]=rmat[1].val(real(scat.k)); if(l0==0) rrm[1]=0;
} else
if(excitation==1) {
rrm[0]=rmat[0].val(real(scat.k));
rrm[1]=rmat[1].val(real(scat.k));
rrm[2]=rmat[2].val(real(scat.k));
rrm[3]=rmat[3].val(real(scat.k)); if(l0==0) rrm[1]=rrm[3]=0;
}
if(ljmj) init_wf_ljmj(jm,mjms,eps);
else init_wf_lmms(jm,mjms,eps);
}
for(i=0; i<coord.n; i++)
if(i!=emitter) iter.n.g[i].alloc(-1,n_c);
else iter.n.g[i].copy(iter.o.g[i]);
}
void electron_bin::init_rmat_MT(void)
{
numero E=-sqr(scat.a->atZ+0.0)/sqr(n0), cc=c_au; c_au*=1000;
free_rmat_MT();
Rho_dbound(scat.a->atZ, P0,Q0, E, n0,-l0-1); c_au=cc;
}
complex electron_bin::rmat_el_MT(int l)
{
if(l<0) return 0;
Salvat Dirac;
spline integral;
numero r, f,g, rr,ps, cc=c_au; c_au*=1000;
int i;
Dirac.vint(scat.a->rad, scat.a->re, scat.a->n_rad, scat.a->atZ);
Dirac.dfree(sqr(real(scat.k))/2, ps, -l-1);
integral.alloc(P0.n);
for(i=0; i<P0.n; i++) {
r=P0.x[i];
Dirac.wf(r,f,g);
integral.put(i, r, P0.y[i]*f);
}
integral.init();
rr=integral.integ(P0.a, P0.b, 1);
if(0) {
printf("--> %g %g %g %d\n", integral.integ(P0.a, P0.b, 1),
integral.integ(P0.a, P0.b, 2), ps, l);
Dirac.dfree(sqr(real(scat.k))/2, ps, -2-1);
integral.alloc(P0.n);
for(i=0; i<P0.n; i++) {
r=P0.x[i];
Dirac.wf(r,f,g);
integral.put(i, r, P0.y[i]*f);
}
integral.init();
printf("--> %g %g %g %d\n", integral.integ(P0.a, P0.b, 1),
integral.integ(P0.a, P0.b, 2), ps, l+1);
}
Dirac.free(); integral.free(); c_au=cc;
return euler(rr,ps);
}
numero electron_bin::CR_wf(numero r)
{
numero val=0, red;
int n;
if(l0==0) red=0.75; else
if(l0==1) red=0.7; else
red=1;
for(n=0; n<CR_nterms; n++)
val+=CR_C[n]/sqrt(fact[2*CR_n[n]])
* pow(r,CR_n[n]-1.0)
* pow(2*CR_xhi[n],CR_n[n]+0.5)
* exp(-CR_xhi[n]*r/red);
return val;
}
complex electron_bin::rmat_el_CR(int l)
{
if(l<0) return 0;
Salvat Dirac;
spline integral;
numero r, f,g, rr,ps, cc=c_au; c_au*=1000;
int i, nr=100;
numero rmax=10;
Dirac.vint(scat.a->rad, scat.a->re, scat.a->n_rad, scat.a->atZ);
Dirac.dfree(sqr(real(scat.k))/2, ps, -l-1);
integral.alloc(nr);
for(i=0; i<nr; i++) {
r=(i+0.5)*rmax/nr;
Dirac.wf(r,f,g);
integral.put(i, r, CR_wf(r)*f);
}
integral.init();
rr=integral.integ(integral.a, integral.b, 2);
Dirac.free(); integral.free(); c_au=cc;
return euler(rr,ps);
}
complex electron_bin::ang_mat_el(int m0_, int l, int m, complex *eps)
{
numero gg[3];
complex val;
if(m0_-1==m) gg[0]=Gaunt(l0,1,l,m0_,-1,m); else gg[0]=0;
if(m0_ ==m) gg[1]=Gaunt(l0,1,l,m0_, 0,m); else gg[1]=0;
if(m0_+1==m) gg[2]=Gaunt(l0,1,l,m0_, 1,m); else gg[2]=0;
return sqrt(4*pi/3) * (gg[0]*eps[0] + gg[1]*eps[1] + gg[2]*eps[2]);
}
void electron_bin::init_wf_lmms(int m0_, int ms0_, complex *eps)
{
int i,l,m,c;
complex val, rm;
iter.o.g[emitter].alloc(l0+1,n_c);
for(c=i=0; c<n_c; c++)
for(l=0; l<=iter.o.g[emitter].lmax; l++)
for(m=-l; m<=l; m++, i++) {
iter.o.g[emitter].re[i]=iter.o.g[emitter].im[i]=0;
if((l==l0+1) || (l==l0-1))
if(excitation==1 || n_c==1 || (ms0_==1 && c==0) || (ms0_==-1 && c==1)) {
if(l>l0) if(excitation==1) rm=rrm[2*c]; else rm=rrm[0];
else if(excitation==1) rm=rrm[2*c+1]; else rm=rrm[1];
rm=real(scat.k)*sqrt(4*pi) * i_l(-l) * rm;
if(n_c==1) rm=rm*sqrt(2);
val=rm*ang_mat_el(m0_,l,m, eps);
iter.o.g[emitter].re[i]= real(val);
iter.o.g[emitter].im[i]= imag(val);
} } }
void electron_bin::init_wf_ljmj(int j0_, int mj0_, complex *eps)
{
int i,l,m,m0_, dim;
numero cgu = CGspin1_2(2*l0,j0_, 1,mj0_),
cgd = CGspin1_2(2*l0,j0_,-1,mj0_);
complex val, rm;
if(2*l0-1!=j0_ && 2*l0+1 != j0_)
on_error(foutput,"scan pd","unphysical (l0,j0) combination");
iter.o.g[emitter].alloc(l0+1,n_c);
dim=lp12[iter.o.g[emitter].lmax];
for(l=i=0; l<=iter.o.g[emitter].lmax; l++)
for(m=-l; m<=l; m++, i++) {
iter.o.g[emitter].re[i]=iter.o.g[emitter].im[i]=0;
iter.o.g[emitter].re[i+dim]=iter.o.g[emitter].im[i+dim]=0;
if((l==l0+1)||(l==l0-1)) {
if(l>l0) rm=rrm[0]; else rm=rrm[1];
rm=real(scat.k)*sqrt(4*pi) * i_l(-l) * rm;
m0_=(mj0_-1)/2;
val=rm*ang_mat_el(m0_,l,m, eps);
iter.o.g[emitter].re[i] = cgu * real(val);
iter.o.g[emitter].im[i] = cgu * imag(val);
m0_=(mj0_+1)/2;
val=rm*ang_mat_el(m0_,l,m, eps);
iter.o.g[emitter].re[i+dim]= cgd * real(val);
iter.o.g[emitter].im[i+dim]= cgd * imag(val);
} } }
void electron_bin::init_wf_manual(void)
{
int i,c,l,m;
vector gg;
iter.o.g[emitter].alloc(lmax_manual,n_c);
for(c=i=0; c<n_c; c++)
for(l=0; l<=iter.o.g[emitter].lmax; l++)
for(m=-l; m<=l; m++, i++) {
iter.o.g[emitter].re[i] = real(manual[i]);
iter.o.g[emitter].im[i] = imag(manual[i]);
} }
void electron_bin::read_rmat(FILE *fin)
{
FILE *frmat; int i,j,n_k, f; numero k, x,y,R;
char units1[str_length_units];
char index2[str_length_comments];
char my_file[str_length_files];
free_rmat();
read_name(fin,my_file);
if(!strcmpC(my_file,"inline")) frmat=fin;
else frmat=open_file(foutput,my_file,"r");
n_k=read_int(frmat);
if(n_k>1) read_name(frmat,units1);
read_name(frmat,index2);
if(!strcmpC(index2,"regular1")) {excitation=0; n_rmat=2; f=1;} else
if(!strcmpC(index2,"regular2")) {excitation=0; n_rmat=2; f=0;} else
if(!strcmpC(index2,"ex1")) {excitation=1; n_rmat=4; f=1;} else
if(!strcmpC(index2,"ex2")) {excitation=1; n_rmat=4; f=0;} else
on_error(foutput,"read_rmat","wrong argument:",index2);
if(excitation==1) ljmj=0;
l0=read_int(frmat);
rmat=new splinec [n_rmat];
for(i=0; i<n_rmat; i++)
{rmat[i].n=0; rmat[i].alloc(n_k,interpolation_type);}
for(j=0; j<n_k; j++) {
if(n_k>1) {k=read_numero(frmat); k=units_k(units1,k);}
for(i=0; i<n_rmat; i++) {
x=read_numero(frmat); y=read_numero(frmat);
if(f) {R=x; x=R*cos(y); y=R*sin(y);}
if(n_k>1) rmat[i].put(j,k,complex(x,y));
else rmat[i].init(complex(x,y),0);
} }
if(n_k>1) for(i=0; i<n_rmat; i++) rmat[i].init();
if(strcmpC(my_file,"inline")) fclose(frmat);
}
void electron_bin::free_rmat(void)
{
int i;
if(rmat!=NULL) {
for(i=0; i<n_rmat; i++) rmat[i].free();
delete [] rmat; rmat=NULL;
} }
int electron_bin::scan_PD(char *name)
{
int k,n, emit_s, initial,pol, sct,emit_MT;
int ljmj_old=ljmj, ms0_old=ms0;
if(manual_flag==1 && (calc.mode_sample>0 || calc.mode_beta>0))
on_error(foutput,"scan pd",
"cannot use wf manual with this type of mobility");
if(manual_flag==1 && manual==NULL)
on_error(foutput,"scan pd", "empty list wf manual coefficients");
if(manual_flag) n_c=n_c_manual; else
if(scat.get_n_c()==2) n_c=2; else
if(rmat!=NULL && excitation==1) n_c=2; else
if(ljmj && (j0<1000 || mj0<1000)) n_c=2; else
n_c=1;
if(n_c==1) {ms0=1; ljmj=0;}
scat.set_lmax();
int jmmin,jmmax,jmstep,jmcomp, mjmsmin,mjmsmax,mjmsstep,mjmscomp,
jm,
mjms;
if(manual_flag) {
jmmin=1; jmmax=1; jmstep=1; jmcomp=1;
mjmsmin=1; mjmsmax=1; mjmsstep=1; mjmscomp=1;
} else
if(ljmj==0) {
jmmin=-l0; jmmax=l0; jmstep=1; jmcomp=m0;
mjmsmin=-1; mjmsmax=1; mjmsstep=2; mjmscomp=ms0;
} else {
jmmin=2*l0-1; jmmax=2*l0+1; jmstep=2; jmcomp=j0;
mjmsmin=-j0; mjmsmax=j0; mjmsstep=2; mjmscomp=mj0;
}
calc.n_c=n_c; calc.select_wf=0;
calc.init_final_dist();
calc.init(name, "scan PD");
for(k=0; k<calc.n_k; k++) {
scat.set_k(k);
final.init_Ylm();
calc.alloc(coord.n_emit*((jmmax-jmmin)/jmstep+1)
*((mjmsmax-mjmsmin)/mjmsstep+1));
for(n=initial=0; n<coord.n_emit; n++) {
coord.sort(coord.emit[n]);
emitter=coord.emit[n];
emit_s=coord.atom[emitter];
scat.get_scatterer(emit_s);
if(manual_flag==0 && rmat==NULL) {
if(scat.a->select!=3)
on_error(foutput,"scan pd", "undefined radial mat. elem.");
if(CR_flag==0) init_rmat_MT();
}
if(scat.a->select==3) {
emit_MT=1;
sct=1000; while(scat.get_scatterer(sct,0)==0) sct++;
coord.atom[emitter]=sct;
scat.add_screened_scatterer(sct, emit_s);
} else {emit_MT=0; coord.atom[emitter]=coord.emit_s[n];}
iter.alloc();
if(iter.method==3) scat.get_exact(n_c,lmax_eff);
for(jm=jmmin; jm<=jmmax; jm+=jmstep)
if(jmcomp>1000 || jm==jmcomp) {
for(mjms=mjmsmin; mjms<=mjmsmax; mjms+=mjmsstep)
if(mjmscomp>1000 || mjms==mjmscomp)
for(pol=0; pol<calc.mode_eps; pol++, initial++) {
if(manual_flag==0) calc.set_polarization(pol);
if(calc.wf_fin==NULL) init_wf_PD(jm, mjms, calc.eps);
calc.evaluation(initial);
iter.clear();
} }
if(iter.method==3) scat.free_exact();
iter.free();
coord.atom[emitter]=emit_s;
if(emit_MT) scat.free_scatterer(sct);
}
scat.free_Green_functions();
scat.free_t_matrix();
calc.write(k);
final.free_Ylm();
}
calc.free();
scat.free_rotations();
free_lmax();
free_rmat_MT(); ljmj=ljmj_old; ms0=ms0_old;
return 0;
}
int electron_bin::scan_MS(char *name, int nwf)
{
numero *kk; kk=copy(calc.kk,calc.n_k); delete [] calc.kk;
int iwf, n_k=calc.n_k; calc.n_k=1; calc.kk=new numero [1];
char k_units[str_length_units];
strcpy(k_units, calc.k_units); strcpy(calc.k_units, "E(eV)");
calc.n_c=wf_ns; calc.select_wf=0; calc.ms=1;
calc.init_final_dist();
calc.init(name, "scan MS");
for(iwf=0; iwf<nwf; iwf++) {
calc.alloc(1);
iter.alloc();
if(iter.method==3) scat.get_exact(wf_ns,lmax_eff);
calc.evaluation(0);
iter.clear();
if(iter.method==3) scat.free_exact();
iter.free();
scat.free_Green_functions();
scat.free_t_matrix();
calc.write(0);
final.free_Ylm();
scat.free_rotations();
free_lmax();
}
calc.free();
coord.free();
calc.kk=copy(kk,n_k); delete [] kk; calc.n_k=n_k; calc.ms=0;
strcpy(calc.k_units, k_units); strcpy(calc.wf_in,"none");
return 0;
}
int electron_bin::scan_DLEED(char *name)
{
int k;
n_c=1;
scat.set_lmax();
coord.sort(-1);
calc.n_c=n_c; calc.select_wf=0;
calc.init_final_dist();
calc.init(name, "scan DLEED");
iter.alloc();
for(k=0; k<calc.n_k; k++) {
scat.set_k(k);
final.init_transmission(0);
final.init_Ylm();
calc.alloc(1);
if(calc.wf_fin==NULL) init_wf_LEED(0);
if(iter.method==3) scat.get_exact(n_c, lmax_eff);
calc.evaluation(0);
if(iter.method==3) scat.free_exact();
iter.clear();
scat.free_Green_functions();
scat.free_t_matrix();
calc.write(k);
final.free_Ylm();
}
calc.free();
iter.free();
scat.free_rotations();
free_lmax();
return 0;
}
int electron_bin::scan_LEED(char *name)
{
int k;
n_c=1;
scat.set_lmax();
coord.sort(-1);
calc.n_c=n_c; calc.select_wf=-2;
calc.init_final_f(1);
calc.init(name, "scan LEED");
iter.alloc();
for(k=0; k<calc.n_k; k++) {
scat.set_k(k);
final.init_transmission(0);
calc.alloc(1);
if(calc.wf_fin==NULL) init_wf_LEED(0);
if(iter.method==3) scat.get_exact(n_c,lmax_eff);
calc.evaluation(0);
if(iter.method==3) scat.free_exact();
iter.clear();
scat.free_Green_functions();
scat.free_t_matrix();
calc.write(k);
}
calc.free();
iter.free();
scat.free_rotations();
free_lmax();
return 0;
}
void electron_bin::program(char *my_file)
{
FILE *fprog=NULL, *ftmp=NULL;
char command[str_length_comments];
char light[str_length_comments];
char units[str_length_units];
char name[str_length_files];
numero al,be,del, a1,a2, xx,yy,zz, th,fi, tt,ff, val1,val2;
int *o, e1,e2, i,j,k,l,m,n;
complex *kc;
char c;
numero x0,y0,z0, x1,y1,z1, x2,y2,z2, r, th1,th2, fi1,fi2;
int n_1, n_2;
if(!strcmpC(my_file,"inline")) fprog=stdin; else
if((fprog=fopen(my_file,"r"))==NULL)
fprog=open_file(foutput,strcat(my_file,".ms"),"r");
for(read_name(fprog, command);
strcmpC(command,"end") &&
strcmpC(command,"quit") &&
strcmpC(command,"exit");
read_name(fprog, command)) {
if(command[0]=='"') {
i=strlen(command);
if(i>1) {
for(j=1; j<i-1; j++) {
c=command[j];
if(c=='\\') {
c=command[++j];
if(c=='\\' || c=='"') fprintf(foutput,"%c",c); else
if(c=='n') fprintf(foutput,"\n");
} else fprintf(foutput,"%c",c);
}
if(j==i) fscanf(fprog,"%c",&c); else c=command[i-1];
} else fscanf(fprog,"%c",&c);
while (c!='"') {
if(c=='\\') {
fscanf(fprog,"%c",&c);
if(c=='\\' || c=='"') fprintf(foutput,"%c",c); else
if(c=='n') fprintf(foutput,"\n");
} else fprintf(foutput,"%c",c);
fscanf(fprog,"%c",&c);
} } else
if((i=algebra_locate(command,'='))>0) {
command[i]=0;
algebra_define(command,command+i+1);
} else
if(!strcmpC(command,"add")) {
read_name(fprog,name);
if(!strcmpC(name,"cluster")) {
read_name(fprog,name);
i=coord.read_atomic_type(fprog);
read_name(fprog,units); val1=units_conversion_factor(units);
xx=val1*alread_numero(fprog);
yy=val1*alread_numero(fprog);
zz=val1*alread_numero(fprog);
if(!strcmpC(name,"atom")) {
if(coord.oriented) {
th=pi/180*alread_numero(fprog); fi=pi/180*alread_numero(fprog);}
else th=fi=0;
coord.add_atom(xx,yy,zz, th,fi, i);
} else
if(!strcmpC(name,"half-layer")) {
a1=val1*alread_numero(fprog); a2=val1*alread_numero(fprog);
al=pi/180*alread_numero(fprog); del=pi/180*alread_numero(fprog);
ff=pi/180*alread_numero(fprog);
if(coord.oriented) {
th=pi/180*alread_numero(fprog); fi=pi/180*alread_numero(fprog);}
else th=fi=0;
coord.add_half_layer(xx,yy,zz, a1,a2, al,del, ff, th,fi, i);
} else
if(!strcmpC(name,"layer")) {
a1=val1*alread_numero(fprog); a2=val1*alread_numero(fprog);
al=pi/180*alread_numero(fprog); del=pi/180*alread_numero(fprog);
if(coord.oriented) {
th=pi/180*alread_numero(fprog); fi=pi/180*alread_numero(fprog);}
else th=fi=0;
coord.add_layer(xx,yy,zz, a1,a2, al,del, th,fi, i);
} else
if(!strcmpC(name,"row")) {
a1=val1*alread_numero(fprog);
tt=pi/180*alread_numero(fprog); ff=pi/180*alread_numero(fprog);
if(coord.oriented) {
th=pi/180*alread_numero(fprog); fi=pi/180*alread_numero(fprog);}
else th=fi=0;
coord.add_row(xx,yy,zz, a1, tt,ff, th,fi, i);
} else
if(!strcmpC(name,"surface")) {
a1=val1*alread_numero(fprog);
read_name(fprog,name);
if(!strcmpC(name,"hcp0001")) a2=val1*alread_numero(fprog); else a2=0;
if(coord.oriented) {
th=pi/180*alread_numero(fprog); fi=pi/180*alread_numero(fprog);}
else th=fi=0;
coord.add_surface(xx,yy,zz, a1,a2, name, th,fi, i);
} else
on_warning(foutput,"(input) add cluster","command ignored:", name);
} else on_error(foutput,"(input) add","wrong keyword:", name);
} else
if(!strcmpC(command,"attenuation-type"))
scat.attenuation_type=alread_int(fprog); else
if(!strcmpC(command,"beamline")) {
read_name(fprog,command);
if(!strcmpC(command,"ALS-7.0.1")) i=1;
if(!strcmpC(command,"Aebi")) i=2;
if(i==2) {
calc.beamline_th=pi/180*alread_numero(fprog);
calc.beamline_fi=pi/180*alread_numero(fprog);
}
calc.init_beamline(i);
} else
if(!strcmpC(command,"beta")) calc.beta=pi/180*alread_numero(fprog); else
if(!strcmpC(command,"clear")) {
read_name(fprog,command);
if(!strcmpC(command,"cluster"))
{coord.free(); scat.free_rotations();} else
if(!strcmpC(command,"emitters"))
coord.free_emitters(); else
if(!strcmpC(command,"imfp"))
{scat.iimfp.free(); scat.iimfp.n=0;} else
if(!strcmpC(command,"rmat"))
free_rmat(); else
if(!strcmpC(command,"scatterer"))
scat.free_scatterer(alread_int(fprog)); else
if(!strcmpC(command,"scatterers"))
scat.free_scatterers(); else
on_warning(foutput,"(input) clear","command ignored:", command);
} else
if(!strcmpC(command,"cluster")) {
read_name(fprog,name);
if(!strcmpC(name,"input")) {
read_name(fprog,name);
coord.read(fprog,name);
} else
if(!strcmpC(name,"output")) {
read_name(fprog,units); read_name(fprog,name);
coord.sort(-1);
coord.write(name,units);
} else
if(!strcmpC(name,"natoms")) {
coord.nnn=alread_int(fprog); coord.set_n();
} else
if(!strcmpC(name,"reference-point")) {
read_name(fprog,units);
coord.x0=units_conversion_factor(units)*alread_numero(fprog);
coord.y0=units_conversion_factor(units)*alread_numero(fprog);
coord.z0=units_conversion_factor(units)*alread_numero(fprog);
} else
if(!strcmpC(name,"Rmax")) {
read_name(fprog,units);
coord.Rmax=units_conversion_factor(units)*alread_numero(fprog);
} else
if(!strcmpC(name,"surface")) {
read_name(fprog,units);
if(!strcmpC(units,"on")) coord.surface=1; else
if(!strcmpC(units,"off")) coord.surface=0; else
coord.zs=units_conversion_factor(units)*alread_numero(fprog);
} else on_error(foutput,"(input) cluster","wrong keyword:", name);
} else
if(!strcmpC(command,"Debye-temperature")) {
read_name(fprog,name);
l=element_properties(name);
if(l==0) l=alread_int(name);
val1=alread_numero(fprog); if(val1<1) val1=1;
scat.T_Debye[l]=val1;
} else
if(!strcmpC(command,"displace")) {
read_name(fprog,name);
if(!strcmpC(name,"cluster")) {
read_name(fprog,units);
xx=units_conversion_factor(units)*alread_numero(fprog);
yy=units_conversion_factor(units)*alread_numero(fprog);
zz=units_conversion_factor(units)*alread_numero(fprog);
coord.displace(xx,yy,zz);
} else
on_warning(foutput,"(input) displace","command ignored:", name);
} else
if(!strcmpC(command,"dmax")) {
read_name(fprog,units);
scat.dmax=units_conversion_factor(units)*alread_numero(fprog);
} else
if(!strcmpC(command,"emission")) {
read_name(fprog, command);
if(!strcmpC(command,"energy")) {
read_name(fprog, units);
val1=alread_numero(fprog);
val2=alread_numero(fprog);
n=alread_int(fprog);
calc.init_k(val1,val2,n,units);
} else
if(!strcmpC(command,"angle")) {
read_name(fprog, command);
if(!strcmpC(command,"theta")) {
val1=pi/180*alread_numero(fprog);
val2=pi/180*alread_numero(fprog);
n=alread_int(fprog);
final.init_th(val1,val2,n);
} else
if(!strcmpC(command,"phi")) {
val1=pi/180*alread_numero(fprog);
val2=pi/180*alread_numero(fprog);
n=alread_int(fprog);
final.init_phi(val1,val2,n);
} else
if(!strcmpC(command,"normal")) {
final.init_th(0,0,1); final.init_phi(0,0,1);
} else
if(!strcmpC(command,"window")) {
calc.thave=pi/180*alread_numero(fprog);
}
else on_error(foutput,"(input) emission angle",
"theta/phi/normal expected instead of", command);
} else on_error(foutput,"(input) emission",
"energy/angle expected instead of", command);
} else
if(!strcmpC(command,"emitters")) {
read_name(fprog,name);
if(!strcmpC(name,"all")) {
e1=alread_int(fprog);
e2=alread_int(fprog);
coord.all_emitters(e1,e2);
} else
if(!strcmpC(name,"plane")) {
read_name(fprog,units);
xx=units_k(units, alread_numero(fprog));
yy=units_k(units, alread_numero(fprog));
zz=units_k(units, alread_numero(fprog));
th=pi/180*alread_numero(fprog);
fi=pi/180*alread_numero(fprog);
coord.add_emitter_plane(xx,yy,zz,th,fi);
} else
if(!strcmpC(name,"column")) {
read_name(fprog,units);
xx=units_k(units, alread_numero(fprog));
yy=units_k(units, alread_numero(fprog));
coord.add_emitter_column(xx,yy);
} else {
n=alread_int(name); read_name(fprog,units);
for(i=0; i<n; i++) {
if(units[0]=='l') {
xx=units_k(units, alread_numero(fprog));
yy=units_k(units, alread_numero(fprog));
zz=units_k(units, alread_numero(fprog));
val1=0.05/a0_au;
if(val1<coord.eps_d) val1=coord.eps_d;
e1=coord.get_atom(xx,yy,zz, val1);
if(e1==-1) on_error(foutput,"(input) emitters",
"cluster position not found");
} else if(i==0) e1=alread_int(units)-1;
else e1=alread_int(fprog)-1;
e2=alread_int(fprog);
coord.add_emitter(e1,e2);
} } } else
if(!strcmpC(command,"fixed")) {
read_name(fprog,name);
calc.init_mode_sample(0);
calc.init_mode_beta(0);
} else
if(!strcmpC(command,"giant-matrix-output")) {
read_name(fprog,scat.aa_output);
scat.aa_output_flag=1;
iter.method= 3;
} else
if(!strcmpC(command,"imfp")) {
scat.iimfp.free(); scat.iimfp.n=0;
read_name(fprog,name);
if(!strcmpC(name,"TPP-2M")) {
scat.TPP_rho=alread_numero(fprog);
scat.TPP_Nv=alread_numero(fprog);
scat.TPP_Ep=alread_numero(fprog);
scat.TPP_Eg=alread_numero(fprog);
if(scat.TPP_rho<=0 || scat.TPP_Nv<=0
|| scat.TPP_Ep<=0 || scat.TPP_Eg<0)
on_error(foutput,"(input) imfp TPP-2M", "wrong parameters");
scat.iimfp_flag=1;
} else if(!strcmpC(name,"SD-UC")) {
scat.iimfp_flag=3;
} else {
scat.read_imfp(fprog,name);
scat.iimfp_flag=0;
} } else
if(!strcmpC(command,"incidence")) {
read_name(fprog, light);
if(!strcmpC(light,"normal")) calc.init_incidence(0,0);
else {
val1=pi/180*alread_numero(light);
val2=pi/180*alread_numero(fprog);
calc.init_incidence(val1,val2);
} } else
if((!strcmpC(command,"include")) || (!strcmpC(command,"insert"))) {
read_name(fprog,name);
program(name);
} else
if(!strcmpC(command,"initial")) {
read_name(fprog,command);
CR_flag=0;
if(!strcmpC(command,"lmms")) ljmj=0; else
if(!strcmpC(command,"ljmj")) ljmj=1; else
if(!strcmpC(command,"n0")) n0 =alread_int(fprog); else
if(!strcmpC(command,"l0")) l0 =alread_int(fprog); else
if(!strcmpC(command,"m0")) m0 =alread_int(fprog); else
if(!strcmpC(command,"j0")) j0 =alread_int(fprog); else
if(!strcmpC(command,"ms0")) ms0=alread_int(fprog); else
if(!strcmpC(command,"mj0")) mj0=alread_int(fprog); else
if(!strcmpC(command,"state")) {
read_name(fprog,command);
if(!strcmpC(command,"C-R")) {
CR_nterms=alread_int(fprog); CR_flag=1;
for(j=0; j<CR_nterms; j++) {
CR_n[j]=alread_int(fprog);
CR_xhi[j]=alread_numero(fprog);
CR_C[j]=alread_numero(fprog);
}
} else {
j=element_orbital(command, n,k);
if(j==-1)
on_error(foutput,"(input) initial state", "wrong state:",command);
n0=n;
if(k<0) l0=-k-1; else l0=k;
if(j<1000) if(k<0) j0=2*l0+1; else j0=2*l0-1;
}
} else on_error(foutput,"(input) initial", "wrong keyword:",command);
} else
if(!strcmpC(command,"interpolation")) {
read_name(fprog,command);
if(!strcmpC(command,"spline")) interpolation_type=0; else
if(!strcmpC(command,"linear")) interpolation_type=1; else
on_warning(foutput,"(input) interpolation",
"command ignored:",command);
} else
if(!strcmpC(command,"iteration")) {
read_name(fprog,command);
if(!strcmpC(command,"recursive")) iter.method=-1; else
if(!strcmpC(command,"recursion")) iter.method=-1; else
if(!strcmpC(command,"Haydock")) iter.method=-1; else
if(!strcmpC(command,"Jacobi")) iter.method= 0; else
if(!strcmpC(command,"Gauss")) iter.method= 1; else
if(!strcmpC(command,"SR")) iter.method= 2; else
if(!strcmpC(command,"exact")) iter.method= 3; else
on_warning(foutput,"(input) iteration","command ignored:",command);
if(!strcmpC(command,"SR")) iter.eta=alread_numero(fprog);
} else
if(!strcmpC(command,"leed")) {
read_name(fprog,command);
if(!strcmpC(command,"beam")) {
leed_i=alread_int(fprog);
leed_j=alread_int(fprog);
} else
if(!strcmpC(command,"emitters"))
init_leed_emitters();
else
if(!strcmpC(command,"lattice")) {
read_name(fprog,units);
a1=units_k(units, alread_numero(fprog));
a2=units_k(units, alread_numero(fprog));
al=pi/180*alread_numero(fprog);
be=pi/180*alread_numero(fprog);
surface_lattice(a1,a2,al,be);
} else
if(!strcmpC(command,"origin")) {
read_name(fprog,units);
leed_x=units_k(units, alread_numero(fprog));
leed_y=units_k(units, alread_numero(fprog));
} } else
if(!strcmpC(command,"lmax")) lmax_max=alread_int(fprog); else
if(!strcmpC(command,"mesh1")) {
read_name(fprog,units);
x0=units_k(units,alread_numero(fprog));
y0=units_k(units,alread_numero(fprog));
z0=units_k(units,alread_numero(fprog));
x1=units_k(units,alread_numero(fprog));
y1=units_k(units,alread_numero(fprog));
z1=units_k(units,alread_numero(fprog));
x2=units_k(units,alread_numero(fprog));
y2=units_k(units,alread_numero(fprog));
z2=units_k(units,alread_numero(fprog));
n_1=alread_int(fprog);
n_2=alread_int(fprog);
final.init_mesh(x0,y0,z0, x1,y1,z1, x2,y2,z2, n_1,n_2);
} else
if(!strcmpC(command,"mesh2")) {
read_name(fprog,units);
r=units_k(units,alread_numero(fprog));
th1=pi/180*alread_numero(fprog);
th2=pi/180*alread_numero(fprog);
fi1=pi/180*alread_numero(fprog);
fi2=pi/180*alread_numero(fprog);
n_1=alread_int(fprog);
n_2=alread_int(fprog);
final.init_mesh(r, th1,th2, fi1,fi2, n_1,n_2);
} else
if(!strcmpC(command,"momenta")) {
read_name(fprog, units);
n=alread_int(fprog);
kc=new complex [n];
for(i=0; i<n; i++) {
val1=units_k(units,alread_numero(fprog));
val2=units_k(units,alread_numero(fprog));
kc[i]=complex(val1,val2);
}
calc.init_k(kc,n,units);
} else
if(!strcmpC(command,"molecule")) {
molecule=1;
} else
if(!strcmpC(command,"movable")) {
read_name(fprog,name);
calc.init_mode_sample(1);
calc.init_mode_beta(1);
} else
if(!strcmpC(command,"muffin-tin")) scat.set_muffin_tin_potentials();
else
if(!strcmpC(command,"orders")) {
n=alread_int(fprog); o=new int [n];
for(i=0; i<n; i++) o[i]=alread_int(fprog);
calc.init_orders(n,o);
} else
if(!strcmpC(command,"orientation")) {
read_name(fprog,name);
if(!strcmpC(name,"on")) coord.oriented=1; else
if(!strcmpC(name,"off")) coord.oriented=0; else {
a1=pi/180*alread_numero(name);
a2=pi/180*alread_numero(fprog);
for(i=0; i<coord.nn; i++) {coord.th[i]=a1; coord.fi[i]=a2;}
} } else
if(!strcmpC(command,"output")) {
close_file(foutput);
read_name(fprog,name);
foutput=open_file(foutput,name,"a");
} else
if(!strcmpC(command,"periodic")) {
read_name(fprog,command);
if(!strcmpC(command,"off")) scat.separation= 1; else
if(!strcmpC(command,"on")) scat.separation=-1; else
if(!strcmpC(command,"test")) scat.separation= 0; else
on_error(foutput,"(input) periodic","wrong keyword:",command);
} else
if(!strcmpC(command,"polarization")) {
read_name(fprog, light);
if(!strcmpC(light,"LPx")) calc.init_polarization(0, 0); else
if(!strcmpC(light,"LPy")) calc.init_polarization(pi/2, 0); else
if(!strcmpC(light,"LCP")) calc.init_polarization(pi/4, pi/2); else
if(!strcmpC(light,"RCP")) calc.init_polarization(pi/4,-pi/2); else
if(!strcmpC(light,"direction")) {
val1=pi/2-pi/180*alread_numero(fprog);
val2=pi +pi/180*alread_numero(fprog);
normalize_angles(val1,val2);
calc.init_incidence(val1,val2);
calc.init_polarization(0,0);
} else {
val1=pi/180*alread_numero(light);
val2=pi/180*alread_numero(fprog);
calc.init_polarization(val1,val2);
} } else
if(!strcmpC(command,"remove")) {
read_name(fprog,name);
if(!strcmpC(name,"cluster")) {
read_name(fprog,name);
if(!strcmpC(name,"non-emitters"))
coord.delete_non_emitters();
else {
read_name(fprog,units); val1=units_conversion_factor(units);
xx=val1*alread_numero(fprog); yy=val1*alread_numero(fprog);
zz=val1*alread_numero(fprog);
if(!strcmpC(name,"atom"))
coord.delete_atom(xx,yy,zz);
else
if(!strcmpC(name,"layer")) {
a1=val1*alread_numero(fprog); a2=val1*alread_numero(fprog);
al=pi/180*alread_numero(fprog); del=pi/180*alread_numero(fprog);
coord.delete_layer(xx,yy,zz, a1,a2, al,del);
} else
if(!strcmpC(name,"row")) {
a1=val1*alread_numero(fprog);
tt=pi/180*alread_numero(fprog); ff=pi/180*alread_numero(fprog);
coord.delete_row(xx,yy,zz, a1, tt,ff);
} else on_warning(foutput,"(input) remove cluster",
"command ignored:", name);
}
} else on_error(foutput,"(input) remove","wrong keyword:", name);
} else
if(!strcmpC(command,"report")) {
read_name(fprog,command);
if(!strcmpC(command,"emitters")) coord.report_emitters(); else
if(!strcmpC(command,"links")) scat.report_links(); else
if(!strcmpC(command,"lmax"))
fprintf(foutput,"--- lmax = %d\n", size_of_lmax); else
if(!strcmpC(command,"natoms"))
fprintf(foutput,
"--- the cluster consists of %d atoms (%d selected, %d used)\n",
coord.nn, coord.set_n(), calc.n_atoms_last); else
if(!strcmpC(command,"scatterer"))
scat.scan_scatterer(alread_int(fprog),"none",-1); else
if(!strcmpC(command,"size")) report_size(); else
on_warning(foutput,"(input) report","command ignored:",command);
} else
if(!strcmpC(command,"rmat")) {
read_rmat(fprog);
CR_flag=0;
} else
if(!strcmpC(command,"rotate")) {
read_name(fprog,name);
if(!strcmpC(name,"cluster")) {
read_name(fprog,name);
if(name[0]=='x') coord.rotate(0, pi/180*alread_numero(fprog));
if(name[0]=='y') coord.rotate(1, pi/180*alread_numero(fprog));
if(name[0]=='z') coord.rotate(2, pi/180*alread_numero(fprog));
} else
on_warning(foutput,"(input) rotate","command ignored:", name);
} else
if(!strcmpC(command,"scan")) {
read_name(fprog,command);
if(!strcmpC(command,"integrated")) {
calc.integ=2;
read_name(fprog,command);
} else
if(!strcmpC(command,"half-integrated")) {
calc.integ=1;
read_name(fprog,command);
} else calc.integ=0;
i=-1;
if(!strcmpC(command,"pd")) i=0; else
if(!strcmpC(command,"ms")) i=1; else
if(!strcmpC(command,"dleed")) i=2; else
if(!strcmpC(command,"leed")) i=3;
if(!strcmpC(command,"scatterer")) { i=5;
l=alread_int(fprog);
read_name(fprog, name); j=0;
if(!strcmpC(name,"phase-shifts")) {j=2; read_name(fprog, name);}
if(!strcmpC(name,"potential")) {j=3; read_name(fprog, name);}
} else
if(!strcmpC(command,"imfp")) { i=6;
read_name(fprog, name);
} else {
if(i==1) n=alread_int(fprog);
read_name(fprog, name);
if(!strcmpC(name,"amplitude")) {
read_name(fprog,name);
calc.n_intensities=0;
} else calc.n_intensities=1;
}
if(i==0) scan_PD(name); else
if(i==1) scan_MS(name, n); else
if(i==2) scan_DLEED(name); else
if(i==3) scan_LEED(name); else
if(i==5) scat.scan_scatterer(l,name,j); else
if(i==6) scat.scan_imfp(name); else
on_error(foutput,"(input) scan","wrong keyword",command);
scat.aa_output_flag=0;
} else
if(!strcmpC(command,"scatterer")) {
j=alread_int(fprog);
read_name(fprog,command);
if(!strcmpC(command,"mass")) {
scat.get_scatterer(j);
read_name(fprog,name);
if(element_properties(name)) scat.a->mass=element_mass*amu_au;
else scat.a->mass=alread_numero(name);
} else
if(!strcmpC(command,"sphere")) {
scat.add_scatterer(j);
read_name(fprog,units);
scat.a->a=units_conversion_factor(units)*alread_numero(fprog);
read_name(fprog,units);
scat.a->V=units_conversion_factor(units)*alread_numero(fprog);
scat.a->select=-1;
scat.a->lmax=infinite_int;
scat.a->n_c=1;
} else {
scat.add_scatterer(j);
scat.a->read(fprog, command);
} } else
if(!strcmpC(command,"scattering-so")) scat.scattering_so=alread_int(fprog);
else
if(!strcmpC(command,"screening-length")) {
read_name(fprog,units);
scat.screening_length=units_conversion_factor(units)
* alread_numero(fprog);
if(scat.screening_length<=0) scat.screening_length=1e-10;
} else
if(!strcmpC(command,"semi-movable")) {
read_name(fprog,name);
calc.init_mode_sample(1);
calc.init_mode_beta(0);
} else
if(!strcmpC(command,"spin")) {
read_name(fprog,command);
if(!strcmpC(command,"on")) spin_flag=1; else
if(!strcmpC(command,"off")) spin_flag=0; else {
th_spin=pi/180*alread_numero(command);
fi_spin=pi/180*alread_numero(fprog);
} } else
if(!strcmpC(command,"temperature")) {
scat.T=alread_numero(fprog);
val1=alread_numero(fprog); if(val1<1) val1=1;
for(i=0; i<n_Debye_temperature_elements; i++)
scat.T_Debye[i]=val1;
} else
if(!strcmpC(command,"temperature-T"))
scat.T=alread_numero(fprog);
else
if(!strcmpC(command,"time")) time_print(foutput); else
if(!strcmpC(command,"tmat")) {
l=alread_int(fprog);
read_name(fprog,name);
calc.scan_tmat(name, l);
} else
if(!strcmpC(command,"tolerance")) {
read_name(fprog,command);
if(!strcmpC(command,"angles"))
coord.eps_th=pi/180*alread_numero(fprog); else
if(!strcmpC(command,"distances"))
coord.eps_d=alread_numero(fprog); else
if(!strcmpC(command,"tmat"))
scat.epsilon=alread_numero(fprog); else
on_error(foutput,"(input) precision","wrong keyword",command);
} else
if(!strcmpC(command,"V0")) {
read_name(fprog,command);
scat.V0=alread_numero(fprog) * units_conversion_factor(command);
} else
if(!strcmpC(command,"verbose")) {
read_name(fprog,name);
if(!strcmpC(name,"on")) calc.verbose=1; else calc.verbose=0;
} else
if(!strcmpC(command,"Vi")) {
scat.iimfp.free(); scat.iimfp.n=0; scat.iimfp_flag=2;
read_name(fprog, units);
scat.Vi=alread_numero(fprog) * units_conversion_factor(units);
} else
if(!strcmpC(command,"wf")) {
read_name(fprog,command);
if(!strcmpC(command,"input")) {
wf_ns=alread_int(fprog); read_name(fprog,calc.wf_in);} else
if(!strcmpC(command,"output")) read_name(fprog,calc.wf_out); else
if(!strcmpC(command,"manual")) {
read_name(fprog,name);
if(!strcmpC(name,"on")) manual_flag=1; else
if(!strcmpC(name,"off")) manual_flag=0; else {
if(manual!=NULL) {delete [] manual; manual=NULL;}
n_c_manual=alread_int(name);
lmax_manual=alread_int(fprog);
manual=new complex [n_c_manual*sqr(lmax_manual+1)];
for(n=i=0; n<n_c_manual; n++)
for(l=0; l<=lmax_manual; l++)
for(m=-l; m<=l; m++, i++) {
a1=alread_numero(fprog);
a2=alread_numero(fprog); manual[i]=complex(a1,a2);
} } }
} else
on_warning(foutput,"input file","command ignored:",command);
}
close_file(fprog);
close_file(foutput); foutput=stdout;
}
void copyright(void)
{
printf(
"---------------------------------------------------------------------\n");
printf("EDAC: Electron Diffraction in Atomic Clusters\n");
printf("\n");
printf("Copyright (c) 1997-2000 F. Javier Garcia de Abajo\n");
printf("Lawrence Berkeley National Laboratory (LBNL)\n");
printf("\n");
printf("Please cite the following article ");
printf("when EDAC is used in published work:\n");
printf("\n");
printf("--- Application to the case of PD and LEED:\n");
printf(" F. J. Garcia de Abajo, M. A. Van Hove, and C. S. Fadley,\n");
printf(" Phys. Rev. B. 63, 075404 (2001)\n");
printf(
"---------------------------------------------------------------------\n");
printf("\n");
}
#endif
int main(int argc, char **argv)
{
int i,j=1;
particle_type=electrones;
if(argc<=2) copyright(); else
if(strcmp(argv[1],"-t")) copyright(); else j++;
init_fact();
if(argc==1) { printf("Inline mode\n\n");
electron.program("inline");
} else
for(i=j; i<argc; i++) electron.program(argv[i]);
fprintf(foutput,"That's all, folks!\n");
return 0;
}
int run_script(char *scriptfile)
{
particle_type=electrones;
init_fact();
electron.program(scriptfile);
return 0;
}
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