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add proper p-wave (line,point) superfluid density calculation.

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suter_a 2020-12-28 15:13:45 +01:00
parent 12c2e5f7a4
commit 386217b1fe
5 changed files with 157 additions and 54 deletions
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89
src/external/BMWtools/BMWIntegrator.cpp vendored
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@ -47,7 +47,7 @@ std::vector<double> TPointPWaveGapIntegralCuhre::fPar;
* <p><b>return:</b>
* - value of the integral
*/
double TPointPWaveGapIntegralCuhre::IntegrateFunc()
double TPointPWaveGapIntegralCuhre::IntegrateFunc(int tag)
{
const unsigned int NCOMP(1);
const unsigned int NVEC(1);
@ -63,7 +63,13 @@ double TPointPWaveGapIntegralCuhre::IntegrateFunc()
int nregions, neval, fail;
double integral[NCOMP], error[NCOMP], prob[NCOMP];
Cuhre(fNDim, NCOMP, Integrand, USERDATA, NVEC,
if (tag == 0)
Cuhre(fNDim, NCOMP, Integrand_aa, USERDATA, NVEC,
EPSREL, EPSABS, VERBOSE | LAST, MINEVAL, MAXEVAL,
KEY, STATEFILE, SPIN,
&nregions, &neval, &fail, integral, error, prob);
else
Cuhre(fNDim, NCOMP, Integrand_cc, USERDATA, NVEC,
EPSREL, EPSABS, VERBOSE | LAST, MINEVAL, MAXEVAL,
KEY, STATEFILE, SPIN,
&nregions, &neval, &fail, integral, error, prob);
@ -74,6 +80,7 @@ double TPointPWaveGapIntegralCuhre::IntegrateFunc()
//-----------------------------------------------------------------------------
/**
* <p>Calculate the function value for the use with Cuhre---actual implementation of the function
* for p-wave point, aa==bb component
*
* <p><b>return:</b>
* - 0
@ -84,12 +91,35 @@ double TPointPWaveGapIntegralCuhre::IntegrateFunc()
* \param f function value
* \param userdata additional user parameters (required by the interface, NULL here)
*/
int TPointPWaveGapIntegralCuhre::Integrand(const int *ndim, const double x[],
const int *ncomp, double f[], void *userdata) // x = {E, theta}, fPar = {twokBT, Delta(T), Ec, thetac}
int TPointPWaveGapIntegralCuhre::Integrand_aa(const int *ndim, const double x[],
const int *ncomp, double f[], void *userdata) // x = {E, z}, fPar = {twokBT, Delta(T), Ec, zc}
{
double sinTheta = TMath::Sin(x[1]*fPar[3]);
double deltasq(TMath::Power(fPar[1]*sinTheta,2.0));
f[0] = sinTheta/TMath::Power(TMath::CosH(TMath::Sqrt(x[0]*x[0]*fPar[2]*fPar[2]+deltasq)/fPar[0]),2.0);
double z = x[1]*fPar[3];
double deltasq(pow(sqrt(1.0-z*z)*fPar[1],2.0));
f[0] = (1.0-z*z)/TMath::Power(TMath::CosH(TMath::Sqrt(x[0]*x[0]*fPar[2]*fPar[2]+deltasq)/fPar[0]),2.0);
return 0;
}
//-----------------------------------------------------------------------------
/**
* <p>Calculate the function value for the use with Cuhre---actual implementation of the function
* for p-wave point, cc component
*
* <p><b>return:</b>
* - 0
*
* \param ndim number of dimensions of the integral (2 here)
* \param x point where the function should be evaluated
* \param ncomp number of components of the integrand (1 here)
* \param f function value
* \param userdata additional user parameters (required by the interface, NULL here)
*/
int TPointPWaveGapIntegralCuhre::Integrand_cc(const int *ndim, const double x[],
const int *ncomp, double f[], void *userdata) // x = {E, z}, fPar = {twokBT, Delta(T), Ec, zc}
{
double z = x[1]*fPar[3];
double deltasq(pow(sqrt(1.0-z*z)*fPar[1],2.0));
f[0] = (z*z)/TMath::Power(TMath::CosH(TMath::Sqrt(x[0]*x[0]*fPar[2]*fPar[2]+deltasq)/fPar[0]),2.0);
return 0;
}
@ -104,7 +134,7 @@ std::vector<double> TLinePWaveGapIntegralCuhre::fPar;
* <p><b>return:</b>
* - value of the integral
*/
double TLinePWaveGapIntegralCuhre::IntegrateFunc()
double TLinePWaveGapIntegralCuhre::IntegrateFunc(int tag)
{
const unsigned int NCOMP(1);
const unsigned int NVEC(1);
@ -120,7 +150,13 @@ double TLinePWaveGapIntegralCuhre::IntegrateFunc()
int nregions, neval, fail;
double integral[NCOMP], error[NCOMP], prob[NCOMP];
Cuhre(fNDim, NCOMP, Integrand, USERDATA, NVEC,
if (tag == 0)
Cuhre(fNDim, NCOMP, Integrand_aa, USERDATA, NVEC,
EPSREL, EPSABS, VERBOSE | LAST, MINEVAL, MAXEVAL,
KEY, STATEFILE, SPIN,
&nregions, &neval, &fail, integral, error, prob);
else
Cuhre(fNDim, NCOMP, Integrand_cc, USERDATA, NVEC,
EPSREL, EPSABS, VERBOSE | LAST, MINEVAL, MAXEVAL,
KEY, STATEFILE, SPIN,
&nregions, &neval, &fail, integral, error, prob);
@ -131,6 +167,7 @@ double TLinePWaveGapIntegralCuhre::IntegrateFunc()
//-----------------------------------------------------------------------------
/**
* <p>Calculate the function value for the use with Cuhre---actual implementation of the function
* for p-wave line, aa==bb component
*
* <p><b>return:</b>
* - 0
@ -141,13 +178,35 @@ double TLinePWaveGapIntegralCuhre::IntegrateFunc()
* \param f function value
* \param userdata additional user parameters (required by the interface, NULL here)
*/
int TLinePWaveGapIntegralCuhre::Integrand(const int *ndim, const double x[],
const int *ncomp, double f[], void *userdata) // x = {E, theta}, fPar = {twokBT, Delta(T), Ec, thetac}
int TLinePWaveGapIntegralCuhre::Integrand_aa(const int *ndim, const double x[],
const int *ncomp, double f[], void *userdata) // x = {E, z}, fPar = {twokBT, Delta(T), Ec, zc}
{
double sinTheta = TMath::Sin(x[1]*fPar[3]);
double cosTheta = TMath::Cos(x[1]*fPar[3]);
double deltasq(TMath::Power(fPar[1]*cosTheta,2.0));
f[0] = sinTheta/TMath::Power(TMath::CosH(TMath::Sqrt(x[0]*x[0]*fPar[2]*fPar[2]+deltasq)/fPar[0]),2.0);
double z = x[1]*fPar[3];
double deltasq(pow(z*fPar[1],2.0));
f[0] = (1.0-z*z)/TMath::Power(TMath::CosH(TMath::Sqrt(x[0]*x[0]*fPar[2]*fPar[2]+deltasq)/fPar[0]),2.0);
return 0;
}
//-----------------------------------------------------------------------------
/**
* <p>Calculate the function value for the use with Cuhre---actual implementation of the function
* for p-wave line, cc component
*
* <p><b>return:</b>
* - 0
*
* \param ndim number of dimensions of the integral (2 here)
* \param x point where the function should be evaluated
* \param ncomp number of components of the integrand (1 here)
* \param f function value
* \param userdata additional user parameters (required by the interface, NULL here)
*/
int TLinePWaveGapIntegralCuhre::Integrand_cc(const int *ndim, const double x[],
const int *ncomp, double f[], void *userdata) // x = {E, z}, fPar = {twokBT, Delta(T), Ec, zc}
{
double z = x[1]*fPar[3];
double deltasq(pow(z*fPar[1],2.0));
f[0] = (z*z)/TMath::Power(TMath::CosH(TMath::Sqrt(x[0]*x[0]*fPar[2]*fPar[2]+deltasq)/fPar[0]),2.0);
return 0;
}

10
src/external/BMWtools/BMWIntegrator.h vendored
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@ -259,8 +259,9 @@ class TPointPWaveGapIntegralCuhre {
TPointPWaveGapIntegralCuhre() : fNDim(2) {}
~TPointPWaveGapIntegralCuhre() { fPar.clear(); }
void SetParameters(const std::vector<double> &par) { fPar=par; }
static int Integrand(const int*, const double[], const int*, double[], void*);
double IntegrateFunc();
static int Integrand_aa(const int*, const double[], const int*, double[], void*);
static int Integrand_cc(const int*, const double[], const int*, double[], void*);
double IntegrateFunc(int tag);
protected:
static std::vector<double> fPar; ///< parameters of the integrand
@ -278,8 +279,9 @@ class TLinePWaveGapIntegralCuhre {
TLinePWaveGapIntegralCuhre() : fNDim(2) {}
~TLinePWaveGapIntegralCuhre() { fPar.clear(); }
void SetParameters(const std::vector<double> &par) { fPar=par; }
static int Integrand(const int*, const double[], const int*, double[], void*);
double IntegrateFunc();
static int Integrand_aa(const int*, const double[], const int*, double[], void*);
static int Integrand_cc(const int*, const double[], const int*, double[], void*);
double IntegrateFunc(int tag);
protected:
static std::vector<double> fPar; ///< parameters of the integrand

BIN
src/external/libGapIntegrals/GapIntegrals.pdf vendored
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35
src/external/libGapIntegrals/GapIntegrals.tex vendored
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@ -170,18 +170,20 @@ The \gapint plug-in calculates $\tilde{I}(T)$ for the following $\Delta(\varphi)
otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.
\item[\textit{p}-wave (point) \cite{Pang2015}:]
\begin{equation}
\Delta(\theta, T) = \Delta(T) \sin(\theta)
\Delta(\theta, T) = \Delta(T) \sin(\theta) = \Delta(T) \cdot \sqrt{1-z^2}
\end{equation}
\musrfit theory line: \verb?userFcn libGapIntegrals TGapPointPWave 1 2 [3 4]?\\[1.5ex]
Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[c_0~(1),~a_{\rm G}~(1)]$. If $c_0$ and $a_{\rm G}$ are provided,
the temperature dependence according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.
\musrfit theory line: \verb?userFcn libGapIntegrals TGapPointPWave 1 2 [3 [4 5]]?\\[1.5ex]
Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, [ \verb?orientation_tag?, $[c_0~(1),~a_{\rm G}~(1)]$]. If $c_0$ and $a_{\rm G}$ are provided,
the temperature dependence according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized. \\
\verb?orientation_tag?: $0=\{aa,bb\}$, $1=cc$, and the default $2=$ average (see Eq.\ (\ref{eq:n_avg}))
\item[\textit{p}-wave (line) \cite{Ozaki1986}:]
\begin{equation}
\Delta(\theta, T) = \Delta(T) \cos(\theta)
\Delta(\theta, T) = \Delta(T) \cos(\theta) = \Delta(T) \cdot z
\end{equation}
\musrfit theory line: \verb?userFcn libGapIntegrals TGapLinePWave 1 2 [3 4]?\\[1.5ex]
Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, $[c_0~(1),~a_{\rm G}~(1)]$. If $c_0$ and $a_{\rm G}$ are provided,
the temperature dependence according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized.
\musrfit theory line: \verb?userFcn libGapIntegrals TGapLinePWave 1 2 [3 [4 5]]?\\[1.5ex]
Parameters: $T_{\mathrm c}~(\mathrm{K})$, $\Delta_0~(\mathrm{meV})$, [ \verb?orientation_tag?, $[c_0~(1),~a_{\rm G}~(1)]$]. If $c_0$ and $a_{\rm G}$ are provided,
the temperature dependence according to Eq.(\ref{eq:gapT_Prozorov}) will be used, otherwise Eq.(\ref{eq:gapT_Manzano}) will be utilized. \\
\verb?orientation_tag?: $0=\{aa,bb\}$, $1=cc$, and the default $2=$ average (see Eq.\ (\ref{eq:n_avg}))
\end{description}
\noindent It is also possible to calculate a power law temperature dependence (in the two fluid approximation $n=4$) and the dirty \textit{s}-wave expression.
@ -222,12 +224,12 @@ n_{aa \atop bb}(T) = 1 - \frac{1}{2\pi k_{\rm B} T} \int_0^{2\pi} \mathrm{d}\var
\begin{eqnarray}
n_{aa \atop bb}(T) &=& 1 - \frac{3}{4\pi k_{\rm B} T} \int_0^1 \mathrm{d}z\, (1-z^2) \int_0^{2\pi} \mathrm{d}\varphi\, {\cos^2(\varphi) \atop \sin^2(\varphi)} \cdot G(\Delta(z,\varphi), T) \label{eq:n_anisotrope_3D_aabb} \\
n_{cc}(T) &=& 1 - \frac{3}{2\pi k_{\rm B} T} \int_0^1 \mathrm{d}z\, z^2 \int_0^{2\pi} \mathrm{d}\varphi\, {\cos^2(\varphi) \atop \sin^2(\varphi)} \cdot G(\Delta(z,\varphi), T) \label{eq:n_anisotrope_3D_cc}
n_{cc}(T) &=& 1 - \frac{3}{2\pi k_{\rm B} T} \int_0^1 \mathrm{d}z\, z^2 \int_0^{2\pi} \mathrm{d}\varphi\, \cos^2(\varphi) \cdot G(\Delta(z,\varphi), T) \label{eq:n_anisotrope_3D_cc}
\end{eqnarray}
\noindent The ``powder averaged'' superfluid density is then defined as
\begin{equation}
\begin{equation}\label{eq:n_avg}
n_{\rm S} = \frac{1}{3}\cdot \left[ \sqrt{n_{aa} n_{bb}} + \sqrt{n_{aa} n_{cc}} + \sqrt{n_{bb} n_{cc}} \right]
\end{equation}
@ -252,7 +254,7 @@ n_{aa \atop bb}(T) = 1 - \frac{1}{2\pi k_{\rm B} T} \int_0^{2\pi} \mathrm{d}\var
\begin{eqnarray*}
n_{aa \atop bb}(T) &=& 1 - \frac{3}{4\pi k_{\rm B} T} \underbrace{\int_0^{\pi/2} \mathrm{d}\theta \, \sin^3(\theta)}_{= 2/3} \, \underbrace{\int_0^{2\pi} \mathrm{d}\varphi {\cos^2(\varphi) \atop \sin^2(\varphi)}}_{=\pi} \cdot G(\Delta, T) \\
&=& 1 - \frac{1}{2 k_{\rm B} T} \cdot G(\Delta, T). \\
n_{cc}(T) &=& 1 - \frac{3}{2\pi k_{\rm B} T} \underbrace{\int_0^{\pi/2} \mathrm{d}\theta \, \cos^2(\theta)\sin(\theta)}_{=1/3} \, \underbrace{\int_0^{2\pi} \mathrm{d}\varphi {\cos^2(\varphi) \atop \sin^2(\varphi)}}_{=\pi} \cdot G(\Delta, T) \\
n_{cc}(T) &=& 1 - \frac{3}{2\pi k_{\rm B} T} \underbrace{\int_0^{\pi/2} \mathrm{d}\theta \, \cos^2(\theta)\sin(\theta)}_{=1/3} \, \underbrace{\int_0^{2\pi} \mathrm{d}\varphi \cos^2(\varphi)}_{=\pi} \cdot G(\Delta, T) \\
&=& 1 - \frac{1}{2 k_{\rm B} T} \cdot G(\Delta, T).
\end{eqnarray*}
@ -260,6 +262,17 @@ n_{aa \atop bb}(T) = 1 - \frac{1}{2\pi k_{\rm B} T} \int_0^{2\pi} \mathrm{d}\var
$$ n_{\rm S}(T) = 1- \frac{1}{2 k_{\rm B} T} \cdot G(\Delta, T). $$
\subsubsection*{3D Fermi Surface Gap $\mathbf{\Delta \neq f(\bm\varphi)}$}
For this case the superfluid density integrals reduce to ($z=\cos(\theta)$)
\begin{eqnarray}
n_{aa \atop bb}(T) &=& 1 - \frac{3}{4 k_{\rm B} T} \int_0^1 \mathrm{d}z\, (1-z^2) \cdot G(\Delta(z, T),T) \\
n_{cc}(T) &=& 1 - \frac{3}{2 k_{\rm B} T} \int_0^1 \mathrm{d}z\, z^2 \cdot G(\Delta(z, T),T)
\end{eqnarray}
\subsection*{License}
The \gapint library is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation \cite{GPL}; either version 2 of the License, or (at your option) any later version.

63
src/external/libGapIntegrals/TGapIntegrals.cpp vendored
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@ -671,17 +671,23 @@ double TGapSWave::operator()(double t, const std::vector<double> &par) const {
*/
double TGapPointPWave::operator()(double t, const std::vector<double> &par) const {
// parameters: [0] Tc (K), [1] Delta0 (meV), [[2] c0 (1), [3] aG (1)]
// parameters: [0] Tc (K), [1] Delta0 (meV), [[2] orientation tag, [[3] c0 (1), [4] aG (1)]]
assert((par.size() == 2) || (par.size() == 4)); // 2 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205
// 4 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67
assert((par.size() >= 2) && (par.size() <= 5)); // 2 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205
// 4 or 5 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67
// and Erratum Supercond. Sci. Technol. 21 (2008) 082003
// c0 in the original context is c0 = (pi kB Tc) / Delta0
// orientation tag: 0=aa,bb; 1=cc; 2=(sqrt[aa bb] + sqrt[aa cc] + sqrt[bb cc])/3 (default)
if (t <= 0.0)
return 1.0;
else if (t >= par[0])
return 0.0;
// check if orientation tag is given
int orientation_tag(2);
if ((par.size()==3) || (par.size()==5))
orientation_tag = static_cast<int>(par[2]);
bool integralParChanged(false);
if (fPar.empty()) { // first time calling this routine
@ -715,19 +721,27 @@ double TGapPointPWave::operator()(double t, const std::vector<double> &par) cons
}
if (fCalcNeeded[vectorIndex]) {
double ds;
double ds, ds1;
std::vector<double> intPar; // parameters for the integral, T & Delta(T)
intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K
if (par.size() == 2) { // Carrington/Manzano
if ((par.size() == 2) || (par.size() == 3)) { // Carrington/Manzano
intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)));
} else { // Prozorov/Giannetta
intPar.push_back(par[1]*tanh(par[2]*sqrt(par[3]*(par[0]/t-1.0)))); // Delta0*tanh(c0*sqrt(aG*(Tc/T-1)))
}
intPar.push_back(4.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy
intPar.push_back(TMath::Pi()); // upper limit of theta-integration
intPar.push_back(1.0); // upper limit of theta-integration
fGapIntegral->SetParameters(intPar);
ds = 1.0-(intPar[2]*PI)/(2.0*intPar[0])*fGapIntegral->IntegrateFunc();
if (orientation_tag == 0) // aa,bb
ds = 1.0-(intPar[2]*3.0)/(2.0*intPar[0])*fGapIntegral->IntegrateFunc(0); // integral prefactor is by 2 lower [Eqs.(19,20)] since intPar[0]==2kB T!
else if (orientation_tag == 1) // cc
ds = 1.0-(intPar[2]*3.0)/(intPar[0])*fGapIntegral->IntegrateFunc(1); // integral prefactor is by 2 lower [Eqs.(19,20)] since intPar[0]==2kB T!
else { // average
ds = 1.0-(intPar[2]*3.0)/(2.0*intPar[0])*fGapIntegral->IntegrateFunc(0); // integral prefactor is by 2 lower [Eqs.(19,20)] since intPar[0]==2kB T!
ds1 = 1.0-(intPar[2]*3.0)/(intPar[0])*fGapIntegral->IntegrateFunc(1); // integral prefactor is by 2 lower [Eqs.(19,20)] since intPar[0]==2kB T!
ds = (ds + 2.0 * sqrt(ds*ds1))/3.0; // since aa==bb the avg looks like this
}
intPar.clear();
@ -745,27 +759,34 @@ double TGapPointPWave::operator()(double t, const std::vector<double> &par) cons
//--------------------------------------------------------------------
/**
* <p>prepare the needed parameters for the integration carried out in TLinePWaveGapIntegralCuhre.
* For details see also the Memo GapIntegrals.pdf, , especially Eq.(19) and (20).
* For details see also the Memo GapIntegrals.pdf, especially Eq.(19) and (20).
*/
double TGapLinePWave::operator()(double t, const std::vector<double> &par) const {
// parameters: [0] Tc (K), [1] Delta0 (meV), [[2] c0 (1), [3] aG (1)]
// parameters: [0] Tc (K), [1] Delta0 (meV), [[2] orientation tag, [[3] c0 (1), [4] aG (1)]]
assert((par.size() == 2) || (par.size() == 4)); // 2 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205
// 4 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67
assert((par.size() >= 2) && (par.size() <= 5)); // 2 parameters: see A.~Carrington and F.~Manzano, Physica~C~\textbf{385}~(2003)~205
// 4 or 5 parameters: see R. Prozorov and R. Giannetta, Supercond. Sci. Technol. 19 (2006) R41-R67
// and Erratum Supercond. Sci. Technol. 21 (2008) 082003
// c0 in the original context is c0 = (pi kB Tc) / Delta0
// orientation tag: 0=aa,bb; 1=cc; 2=(sqrt[aa bb] + sqrt[aa cc] + sqrt[bb cc])/3 (default)
if (t <= 0.0)
return 1.0;
else if (t >= par[0])
return 0.0;
// check if orientation tag is given
int orientation_tag(2);
if ((par.size()==3) || (par.size()==5))
orientation_tag = static_cast<int>(par[2]);
bool integralParChanged(false);
if (fPar.empty()) { // first time calling this routine
fPar = par;
integralParChanged = true;
} else { // check if Tc or Delta0 have changed
} else { // check if parameter have changed
for (unsigned int i(0); i<par.size(); i++) {
if (par[i] != fPar[i]) {
fPar[i] = par[i];
@ -793,19 +814,27 @@ double TGapLinePWave::operator()(double t, const std::vector<double> &par) const
}
if (fCalcNeeded[vectorIndex]) {
double ds;
double ds, ds1;
std::vector<double> intPar; // parameters for the integral, T & Delta(T)
intPar.push_back(0.172346648*t); // 2 kB T, kB in meV/K = 0.086173324 meV/K
if (par.size() == 2) { // Carrington/Manzano
if ((par.size() == 2) || (par.size() == 3)) { // Carrington/Manzano
intPar.push_back(par[1]*tanh(1.82*pow(1.018*(par[0]/t-1.0),0.51)));
} else { // Prozorov/Giannetta
intPar.push_back(par[1]*tanh(par[2]*sqrt(par[3]*(par[0]/t-1.0)))); // Delta0*tanh(c0*sqrt(aG*(Tc/T-1)))
intPar.push_back(par[1]*tanh(par[3]*sqrt(par[4]*(par[0]/t-1.0)))); // Delta0*tanh(c0*sqrt(aG*(Tc/T-1)))
}
intPar.push_back(4.0*(t+intPar[1])); // upper limit of energy-integration: cutoff energy
intPar.push_back(TMath::Pi()); // upper limit of theta-integration
intPar.push_back(1.0); // upper limit of z-integration
fGapIntegral->SetParameters(intPar);
ds = 1.0-(intPar[2]*PI)/(2.0*intPar[0])*fGapIntegral->IntegrateFunc();
if (orientation_tag == 0) // aa,bb
ds = 1.0-(intPar[2]*3.0)/(2.0*intPar[0])*fGapIntegral->IntegrateFunc(0); // integral prefactor is by 2 lower [Eqs.(19,20)] since intPar[0]==2kB T!
else if (orientation_tag == 1) // cc
ds = 1.0-(intPar[2]*3.0)/(intPar[0])*fGapIntegral->IntegrateFunc(1); // integral prefactor is by 2 lower [Eqs.(19,20)] since intPar[0]==2kB T!
else { // average
ds = 1.0-(intPar[2]*3.0)/(2.0*intPar[0])*fGapIntegral->IntegrateFunc(0); // integral prefactor is by 2 lower [Eqs.(19,20)] since intPar[0]==2kB T!
ds1 = 1.0-(intPar[2]*3.0)/(intPar[0])*fGapIntegral->IntegrateFunc(1); // integral prefactor is by 2 lower [Eqs.(19,20)] since intPar[0]==2kB T!
ds = (ds + 2.0 * sqrt(ds*ds1))/3.0; // since aa==bb the avg looks like this
}
intPar.clear();