LMU/musrfit
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Merged muonspin/musrfit into master

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Zaher Salman 2016-04-25 09:19:01 +02:00
commit 3b08cad70b
7 changed files with 206 additions and 153 deletions
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1
ChangeLog
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@ -4,6 +4,7 @@
changes since 0.17.0 changes since 0.17.0
=================================== ===================================
NEW 2016-04-22 Added the theory function muMinusExpTF for mu minus fits
NEW 2016-02-23 It is now possible to export the averaged data/Fourier NEW 2016-02-23 It is now possible to export the averaged data/Fourier
changes since 0.16.0 changes since 0.16.0

5
src/classes/PMsrHandler.cpp
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@ -5866,9 +5866,10 @@ void PMsrHandler::CheckMaxLikelihood()
{ {
if (!fStatistic.fChisq) { if (!fStatistic.fChisq) {
for (UInt_t i=0; i<fRuns.size(); i++) { for (UInt_t i=0; i<fRuns.size(); i++) {
if ((fRuns[i].GetFitType() != MSR_FITTYPE_SINGLE_HISTO) && (fGlobal.GetFitType() != MSR_FITTYPE_SINGLE_HISTO)) { if ((fRuns[i].GetFitType() != MSR_FITTYPE_SINGLE_HISTO) && (fGlobal.GetFitType() != MSR_FITTYPE_SINGLE_HISTO) &&
(fRuns[i].GetFitType() != MSR_FITTYPE_MU_MINUS) && (fGlobal.GetFitType() != MSR_FITTYPE_MU_MINUS)) {
cerr << endl << ">> PMsrHandler::CheckMaxLikelihood: **WARNING**: Maximum Log Likelihood Fit is only implemented"; cerr << endl << ">> PMsrHandler::CheckMaxLikelihood: **WARNING**: Maximum Log Likelihood Fit is only implemented";
cerr << endl << ">> for Single Histogram Fit. Will fall back to Chi Square Fit."; cerr << endl << ">> for Single Histogram and Mu Minus Fits. Will fall back to Chi Square Fit.";
cerr << endl << endl; cerr << endl << endl;
fStatistic.fChisq = true; fStatistic.fChisq = true;
break; break;

53
src/classes/PTheory.cpp
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@ -507,6 +507,10 @@ Double_t PTheory::Func(register Double_t t, const PDoubleVector& paramValues, co
return Polynom(t, paramValues, funcValues) * fMul->Func(t, paramValues, funcValues) + return Polynom(t, paramValues, funcValues) * fMul->Func(t, paramValues, funcValues) +
fAdd->Func(t, paramValues, funcValues); fAdd->Func(t, paramValues, funcValues);
break; break;
case THEORY_MU_MINUS_EXP:
return MuMinusExpTF(t, paramValues, funcValues) * fMul->Func(t, paramValues, funcValues) +
fAdd->Func(t, paramValues, funcValues);
break;
case THEORY_USER_FCN: case THEORY_USER_FCN:
return UserFcn(t, paramValues, funcValues) * fMul->Func(t, paramValues, funcValues) + return UserFcn(t, paramValues, funcValues) * fMul->Func(t, paramValues, funcValues) +
fAdd->Func(t, paramValues, funcValues); fAdd->Func(t, paramValues, funcValues);
@ -599,6 +603,9 @@ Double_t PTheory::Func(register Double_t t, const PDoubleVector& paramValues, co
case THEORY_DYNAMIC_TF_NK: case THEORY_DYNAMIC_TF_NK:
return DynamicNKTF (t, paramValues, funcValues) * fMul->Func(t, paramValues, funcValues); return DynamicNKTF (t, paramValues, funcValues) * fMul->Func(t, paramValues, funcValues);
break; break;
case THEORY_MU_MINUS_EXP:
return MuMinusExpTF(t, paramValues, funcValues) * fMul->Func(t, paramValues, funcValues);
break;
case THEORY_POLYNOM: case THEORY_POLYNOM:
return Polynom(t, paramValues, funcValues) * fMul->Func(t, paramValues, funcValues); return Polynom(t, paramValues, funcValues) * fMul->Func(t, paramValues, funcValues);
break; break;
@ -695,6 +702,9 @@ Double_t PTheory::Func(register Double_t t, const PDoubleVector& paramValues, co
case THEORY_DYNAMIC_TF_NK: case THEORY_DYNAMIC_TF_NK:
return DynamicNKTF (t, paramValues, funcValues) + fAdd->Func(t, paramValues, funcValues); return DynamicNKTF (t, paramValues, funcValues) + fAdd->Func(t, paramValues, funcValues);
break; break;
case THEORY_MU_MINUS_EXP:
return MuMinusExpTF(t, paramValues, funcValues) + fAdd->Func(t, paramValues, funcValues);
break;
case THEORY_POLYNOM: case THEORY_POLYNOM:
return Polynom(t, paramValues, funcValues) + fAdd->Func(t, paramValues, funcValues); return Polynom(t, paramValues, funcValues) + fAdd->Func(t, paramValues, funcValues);
break; break;
@ -789,6 +799,9 @@ Double_t PTheory::Func(register Double_t t, const PDoubleVector& paramValues, co
case THEORY_DYNAMIC_TF_NK: case THEORY_DYNAMIC_TF_NK:
return DynamicNKTF(t, paramValues, funcValues); return DynamicNKTF(t, paramValues, funcValues);
break; break;
case THEORY_MU_MINUS_EXP:
return MuMinusExpTF(t, paramValues, funcValues);
break;
case THEORY_POLYNOM: case THEORY_POLYNOM:
return Polynom(t, paramValues, funcValues); return Polynom(t, paramValues, funcValues);
break; break;
@ -2942,6 +2955,46 @@ Double_t PTheory::GetDynKTLFValue(const Double_t t) const
return fDynLFFuncValue[idx]+df; return fDynLFFuncValue[idx]+df;
} }
//--------------------------------------------------------------------------
/**
* <p> theory function: MuMinusExpTF
*
* \f[ = N_0 \exp(-t/tau) [1 + A \exp(-\lambda t) \cos(2\pi\nu t + \phi)] \f]
*
* <b>meaning of paramValues:</b> \f$t_{\rm shift}\f$, \f$N_0\f$, \f$\tau\f$, \f$A\f$, \f$\lambda\f$, \f$\phi\f$, \f$\nu\f$
*
* <b>return:</b> function value
*
* \param t time in \f$(\mu\mathrm{s})\f$, or x-axis value for non-muSR fit
* \param paramValues parameter values
* \param funcValues vector with the functions (i.e. functions of the parameters)
*/
Double_t PTheory::MuMinusExpTF(register Double_t t, const PDoubleVector& paramValues, const PDoubleVector& funcValues) const
{
// expected parameters: N0 tau A lambda phase frequency [tshift]
Double_t val[7];
assert(fParamNo.size() <= 7);
// check if FUNCTIONS are used
for (UInt_t i=0; i<fParamNo.size(); i++) {
if (fParamNo[i] < MSR_PARAM_FUN_OFFSET) { // parameter or resolved map
val[i] = paramValues[fParamNo[i]];
} else { // function
val[i] = funcValues[fParamNo[i]-MSR_PARAM_FUN_OFFSET];
}
}
Double_t tt;
if (fParamNo.size() == 6) // no tshift
tt = t;
else // tshift present
tt = t-val[6];
return val[0]*exp(-tt/val[1])*(1.0+val[2]*exp(-val[3]*tt)*cos(TWO_PI*val[5]*tt+DEG_TO_RAD*val[4]));
}
//-------------------------------------------------------------------------- //--------------------------------------------------------------------------
// END // END
//-------------------------------------------------------------------------- //--------------------------------------------------------------------------

12
src/include/PTheory.h
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@ -70,8 +70,9 @@
#define THEORY_STATIC_TF_NK 24 #define THEORY_STATIC_TF_NK 24
#define THEORY_DYNAMIC_ZF_NK 25 #define THEORY_DYNAMIC_ZF_NK 25
#define THEORY_DYNAMIC_TF_NK 26 #define THEORY_DYNAMIC_TF_NK 26
#define THEORY_POLYNOM 27 #define THEORY_MU_MINUS_EXP 27
#define THEORY_USER_FCN 28 #define THEORY_POLYNOM 28
#define THEORY_USER_FCN 29
// function parameter tags, i.e. how many parameters has a specific function // function parameter tags, i.e. how many parameters has a specific function
// if there is a comment with a (tshift), the number of parameters is increased by one // if there is a comment with a (tshift), the number of parameters is increased by one
@ -102,9 +103,10 @@
#define THEORY_PARAM_STATIC_TF_NK 4 // phase, frequency, damping D0, R_b=DGbG/D0 (tshift) #define THEORY_PARAM_STATIC_TF_NK 4 // phase, frequency, damping D0, R_b=DGbG/D0 (tshift)
#define THEORY_PARAM_DYNAMIC_ZF_NK 3 // damping D0, R_b=DGbG/D0, nu_c (tshift) #define THEORY_PARAM_DYNAMIC_ZF_NK 3 // damping D0, R_b=DGbG/D0, nu_c (tshift)
#define THEORY_PARAM_DYNAMIC_TF_NK 5 // phase, frequency, damping D0, R_b=DGbG/D0, nu_c (tshift) #define THEORY_PARAM_DYNAMIC_TF_NK 5 // phase, frequency, damping D0, R_b=DGbG/D0, nu_c (tshift)
#define THEORY_PARAM_MU_MINUS_EXP 6 // N0, tau, A, damping, phase, frequency (tshift)
// number of available user functions // number of available user functions
#define THEORY_MAX 29 #define THEORY_MAX 30
// maximal number of parameters. Needed in the contents of LF // maximal number of parameters. Needed in the contents of LF
#define THEORY_MAX_PARAM 10 #define THEORY_MAX_PARAM 10
@ -217,6 +219,9 @@ static PTheoDataBase fgTheoDataBase[THEORY_MAX] = {
{THEORY_DYNAMIC_TF_NK, THEORY_PARAM_DYNAMIC_TF_NK, false, {THEORY_DYNAMIC_TF_NK, THEORY_PARAM_DYNAMIC_TF_NK, false,
"dynamicNKTF", "dnktf", "(phase frequency damping_D0 R_b nu_c)", "(phase frequency damping_D0 R_b nu_c tshift)"}, "dynamicNKTF", "dnktf", "(phase frequency damping_D0 R_b nu_c)", "(phase frequency damping_D0 R_b nu_c tshift)"},
{THEORY_MU_MINUS_EXP, THEORY_PARAM_MU_MINUS_EXP, false,
"muMinusExpTF", "mmsetf", "(N0 tau A lambda phase nu)", "(N0 tau A lambda phase nu tshift)"},
{THEORY_POLYNOM, 0, false, {THEORY_POLYNOM, 0, false,
"polynom", "p", "(tshift p0 p1 ... pn)", "(tshift p0 p1 ... pn)"}, "polynom", "p", "(tshift p0 p1 ... pn)", "(tshift p0 p1 ... pn)"},
@ -272,6 +277,7 @@ class PTheory
virtual Double_t StaticNKTF(register Double_t t, const PDoubleVector& paramValues, const PDoubleVector& funcValues) const; virtual Double_t StaticNKTF(register Double_t t, const PDoubleVector& paramValues, const PDoubleVector& funcValues) const;
virtual Double_t DynamicNKZF(register Double_t t, const PDoubleVector& paramValues, const PDoubleVector& funcValues) const; virtual Double_t DynamicNKZF(register Double_t t, const PDoubleVector& paramValues, const PDoubleVector& funcValues) const;
virtual Double_t DynamicNKTF(register Double_t t, const PDoubleVector& paramValues, const PDoubleVector& funcValues) const; virtual Double_t DynamicNKTF(register Double_t t, const PDoubleVector& paramValues, const PDoubleVector& funcValues) const;
virtual Double_t MuMinusExpTF(register Double_t t, const PDoubleVector& paramValues, const PDoubleVector& funcValues) const;
virtual Double_t Polynom(register Double_t t, const PDoubleVector& paramValues, const PDoubleVector& funcValues) const; virtual Double_t Polynom(register Double_t t, const PDoubleVector& paramValues, const PDoubleVector& funcValues) const;
virtual Double_t UserFcn(register Double_t t, const PDoubleVector& paramValues, const PDoubleVector& funcValues) const; virtual Double_t UserFcn(register Double_t t, const PDoubleVector& paramValues, const PDoubleVector& funcValues) const;

256
src/tests/MuTransition/PSimulateMuTransition.cpp
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@ -3,9 +3,7 @@
PSimulateMuTransition.cpp PSimulateMuTransition.cpp
Author: Thomas Prokscha Author: Thomas Prokscha
Date: 25-Feb-2010 Date: 25-Feb-2010, 14-Apr-2016
$Id$
Use root macros runMuSimulation.C and testAnalysis.C to run the simulation Use root macros runMuSimulation.C and testAnalysis.C to run the simulation
and to get a quick look on the data. Data are saved to a root histogram file and to get a quick look on the data. Data are saved to a root histogram file
@ -13,26 +11,28 @@
analyze the simulated data. analyze the simulated data.
Description: Description:
Root class to simulate muon spin phase under successive Mu+/Mu0 charge-exchange Root class to simulate muon spin polarization under successive Mu+/Mu0 charge-exchange
processes by a Monte-Carlo method. Consider transverse field geometry, and assume or Mu0 spin-flip processes by a Monte-Carlo method. Consider transverse field geometry,
initial muon spin direction in x, and field applied along z. For PxMu(t) in and assume initial muon spin direction in x, and field applied along z. For PxMu(t) in
muonium use the equation 8.22 of the muSR book of Yaounc and Dalmas de Réotier, in muonium use the complex expression of
slightly modified form (see Senba, J. Phys. B 23, 1545 (1990)); note that PxMu(t) equation (4) in the paper of M. Senba, J. Phys. B 23, 1545 (1990), or
is given by a superposition of the four frequencies "nu_12", "nu_34", "nu_23", "nu_14". equation (7) in the paper of M. Senba, J. Phys. B 24, 3531 (1991);
These frequencies and the corresponding probabilities ("SetMuFractionState12" for note that PxMu(t) is given by a superposition of the four frequencies "nu_12", "nu_34",
transitions 12 and 34, "SetMuFractionState23" for states 23 and 14) can be calculated "nu_23", "nu_14". These frequencies and the corresponding probabilities ("SetMuFractionState12"
for transitions 12 and 34, "SetMuFractionState23" for states 23 and 14) can be calculated
for a given field with the root macro AnisotropicMu.C for a given field with the root macro AnisotropicMu.C
Parameters: Parameters:
1) Precession frequencies of "nu_12", "nu_34", "nu_23", "nu_14" 1) Precession frequencies of "nu_12", "nu_34", "nu_23", "nu_14"
2) fractions of nu_12, nu_34; and nu_23 and nu_14 2) fractions of nu_12, nu_34; and nu_23 and nu_14
3) total Mu0 fraction 3) total Mu0 fraction
4) electron-capture rate 4) Mu+ electron-capture rate
5) Mu ionization rate 5) Mu0 ionization rate
6) initial muon spin phase 6) Mu0 spin-flip rate
7) total muon decay asymmetry 7) initial muon spin phase
8) number of muon decays to be generated. 9) total muon decay asymmetry
9) debug flag: if TRUE print capture/ionization events on screen 9) number of muon decays to be generated.
10) debug flag: if TRUE print capture/ionization events on screen
Output: Output:
Two histograms ("forward" and "backward") are written to a root file. Two histograms ("forward" and "backward") are written to a root file.
@ -43,10 +43,13 @@
1) according to Mu+/Mu0 fraction begin either with a Mu+ state or Mu state 1) according to Mu+/Mu0 fraction begin either with a Mu+ state or Mu state
2) Mu+: determine next electron-capture time t_c. If t_c is larger than decay time t_d 2) Mu+: determine next electron-capture time t_c. If t_c is larger than decay time t_d
calculate muon spin precession for t_d; else calculate spin precession for t_c. calculate muon spin precession for t_d; else calculate spin precession for t_c.
3) Determine next ionization time t_i; calculate Px(t_i) in Muonium; calculate the 3) Determine next ionization time t_i; calculate Px(t_i) in Muonium; calculate the total
muon spin phase by acos(Px(t_i)). muon spin polarization Px(t_i)*Px(t_c).
4) get the next electron capture time, continue until t_d is reached; accumulate muon spin 4) get the next electron capture time, continue until t_d is reached, and calculate
phase. the resulting polarization.
The Mu0 spin-flip processes are calculated in GTSpinFlip(), using eq. (17) of
M. Senba, J. Phys. B 24, 3531 (1991).
***************************************************************************/ ***************************************************************************/
@ -111,8 +114,10 @@ PSimulateMuTransition::PSimulateMuTransition(UInt_t seed)
fMuonDecayTime = 0.; fMuonDecayTime = 0.;
fAsymmetry = 0.27; fAsymmetry = 0.27;
fMuFraction = 0.; fMuFraction = 0.;
fMuFractionState12 = 0.; fMuFractionState12 = 0.25;
fMuFractionState23 = 0.; fMuFractionState34 = 0.25;
fMuFractionState23 = 0.25;
fMuFractionState14 = 0.25;
fDebugFlag = kFALSE; fDebugFlag = kFALSE;
} }
@ -138,19 +143,27 @@ PSimulateMuTransition::~PSimulateMuTransition()
*/ */
void PSimulateMuTransition::PrintSettings() const void PSimulateMuTransition::PrintSettings() const
{ {
cout << endl << "Mu precession frequency 12 (MHz) = " << fMuPrecFreq12; cout << endl << "Mu0 precession frequency 12 (MHz) = " << fMuPrecFreq12;
cout << endl << "Mu precession frequency 34 (MHz) = " << fMuPrecFreq34; cout << endl << "Mu0 precession frequency 34 (MHz) = " << fMuPrecFreq34;
cout << endl << "Mu precession frequency 23 (MHz) = " << fMuPrecFreq23; cout << endl << "Mu0 precession frequency 23 (MHz) = " << fMuPrecFreq23;
cout << endl << "Mu precession frequency 14 (MHz) = " << fMuPrecFreq14; cout << endl << "Mu0 precession frequency 14 (MHz) = " << fMuPrecFreq14;
cout << endl << "Mu+ precession frequency (MHz) = " << fMuonGyroRatio * fBfield;
cout << endl << "B field (T) = " << fBfield; cout << endl << "B field (T) = " << fBfield;
cout << endl << "Mu+ electron capture rate (MHz) = " << fCaptureRate; cout << endl << "Mu+ electron capture rate (MHz) = " << fCaptureRate;
cout << endl << "Mu0 ionizatioan rate (MHz) = " << fIonizationRate; cout << endl << "Mu0 ionizatioan rate (MHz) = " << fIonizationRate;
cout << endl << "Mu0 spin-flip rate (MHz) = " << fSpinFlipRate; cout << endl << "Mu0 spin-flip rate (MHz) = " << fSpinFlipRate;
cout << endl << "!!! Note: if spin-flip rate > 0.001 only spin-flip process is considered!!!"; if (fSpinFlipRate > 0.001)
cout << endl << "!!! Note: spin-flip rate > 0.001 only spin-flip processes are considered!!!";
else{
cout << endl << "!!! spin-flip rate <= 0.001: only charge-exchange cycles are considered!!!";
cout << endl << "!!! if spin-flip rate > 0.001, only spin-flip processes are considered!!!";
}
cout << endl << "Decay asymmetry = " << fAsymmetry; cout << endl << "Decay asymmetry = " << fAsymmetry;
cout << endl << "Muonium fraction = " << fMuFraction; cout << endl << "Muonium fraction = " << fMuFraction;
cout << endl << "Muonium fraction state12 = " << fMuFractionState12; cout << endl << "Muonium fraction state12 = " << fMuFractionState12;
cout << endl << "Muonium fraction state34 = " << fMuFractionState34;
cout << endl << "Muonium fraction state23 = " << fMuFractionState23; cout << endl << "Muonium fraction state23 = " << fMuFractionState23;
cout << endl << "Muonium fraction state14 = " << fMuFractionState14;
cout << endl << "Number of particles to simulate = " << fNmuons; cout << endl << "Number of particles to simulate = " << fNmuons;
cout << endl << "Initial muon spin phase (degree) = " << fInitialPhase; cout << endl << "Initial muon spin phase (degree) = " << fInitialPhase;
cout << endl << "Debug flag = " << fDebugFlag; cout << endl << "Debug flag = " << fDebugFlag;
@ -181,23 +194,26 @@ void PSimulateMuTransition::SetSeed(UInt_t seed)
*/ */
void PSimulateMuTransition::Run(TH1F *histoForward, TH1F *histoBackward) void PSimulateMuTransition::Run(TH1F *histoForward, TH1F *histoBackward)
{ {
// Double_t muoniumPolX = 1.0; //polarization in x direction
Int_t i; Int_t i;
if (histoForward == 0 || histoBackward == 0) if (histoForward == 0 || histoBackward == 0)
return; return;
fMuonPrecFreq = fMuonGyroRatio * fBfield;
for (i = 0; i<fNmuons; i++){ for (i = 0; i<fNmuons; i++){
fMuonPhase = TMath::TwoPi() * fInitialPhase/360.; // transform to radians fMuonPhase = TMath::TwoPi() * fInitialPhase/360.; // transform to radians
fMuonDecayTime = NextEventTime(fMuonDecayRate); fMuonDecayTime = NextEventTime(fMuonDecayRate);
if (fSpinFlipRate > 0.001){// consider only Mu0 spin-flip in this case if (fSpinFlipRate > 0.001){// consider only Mu0 spin-flip in this case
fMuonPhase = TMath::ACos(GTSpinFlip(fMuonDecayTime)); fMuonPhase += TMath::ACos(GTSpinFlip(fMuonDecayTime));
} }
else{ else{
// initial muon state Mu+ or Mu0? // initial muon state Mu+ or Mu0?
if (fRandom->Rndm() <= 1.-fMuFraction) if (fRandom->Rndm() <= 1.-fMuFraction)
Event("Mu+"); fMuonPhase += TMath::ACos(Event("Mu+"));
else else
Event(""); fMuonPhase += TMath::ACos(Event("Mu0"));
} }
// fill 50% in "forward", and 50% in "backward" detector to get independent // fill 50% in "forward", and 50% in "backward" detector to get independent
// events in "forward" and "backward" histograms. This allows "normal" uSR // events in "forward" and "backward" histograms. This allows "normal" uSR
@ -233,28 +249,29 @@ Double_t PSimulateMuTransition::NextEventTime(const Double_t &EventRate)
//-------------------------------------------------------------------------- //--------------------------------------------------------------------------
// Phase (private) // Phase (private)
//-------------------------------------------------------------------------- //--------------------------------------------------------------------------
/** // /**
* <p>Determines phase of the muon spin /* * <p>Determines phase of the muon spin
* *
* \param time duration of precession (us); * \param time duration of precession (us);
* \param chargeState charge state of Mu ("Mu+" or "Mu0") * \param chargeState charge state of Mu ("Mu+" or "Mu0")
*/ */
Double_t PSimulateMuTransition::PrecessionPhase(const Double_t &time, const TString chargeState) // Double_t PSimulateMuTransition::PrecessionPhase(const Double_t &time, const TString chargeState)
{ // {
Double_t muonPhaseX; // Double_t muonPhaseX;
Double_t muoniumPolX = 0; // Double_t muoniumPolX = 0;
//
if (chargeState == "Mu+") // if (chargeState == "Mu+")
muonPhaseX = TMath::TwoPi()*fMuonPrecFreq*time; // muonPhaseX = TMath::TwoPi()*fMuonPrecFreq*time;
else if (chargeState == "Mu0"){ // else if (chargeState == "Mu0"){
muoniumPolX = GTFunction(time).Re(); // muoniumPolX = GTFunction(time).Re();
muonPhaseX = TMath::ACos(muoniumPolX); // if (fDebugFlag) cout << "muoniumPolX = " << muoniumPolX << endl;
} // muonPhaseX = TMath::ACos(muoniumPolX);
else // }
muonPhaseX = 0.; // else
// muonPhaseX = 0.;
return muonPhaseX; //
} // return muonPhaseX;
// }
//-------------------------------------------------------------------------- //--------------------------------------------------------------------------
// Mu0 transverse field polarization function (private) // Mu0 transverse field polarization function (private)
@ -264,29 +281,24 @@ Double_t PSimulateMuTransition::PrecessionPhase(const Double_t &time, const TStr
* *
* \param time (us); * \param time (us);
*/ */
TComplex PSimulateMuTransition::GTFunction(const Double_t &time) TComplex PSimulateMuTransition::GTFunction(const Double_t &time, const TString chargeState)
{ {
Double_t twoPi = TMath::TwoPi(); Double_t twoPi = TMath::TwoPi();
TComplex complexPol = 0; TComplex complexPol = 0;
complexPol =
0.5 * fMuFractionState12 * if (chargeState == "Mu+")
(TComplex::Exp(TComplex::I()*twoPi*fMuPrecFreq12*time) + complexPol = TComplex::Exp(-TComplex::I()*twoPi*fMuonPrecFreq*time);
TComplex::Exp(-TComplex::I()*twoPi*fMuPrecFreq34*time)) else{
+ complexPol =
0.5 * fMuFractionState23 * (fMuFractionState12 * TComplex::Exp(TComplex::I()*twoPi*fMuPrecFreq12*time) +
(TComplex::Exp(TComplex::I()*twoPi*fMuPrecFreq23*time) + fMuFractionState34 * TComplex::Exp(-TComplex::I()*twoPi*fMuPrecFreq34*time))
TComplex::Exp(TComplex::I()*twoPi*fMuPrecFreq14*time)); +
(fMuFractionState23 * TComplex::Exp(TComplex::I()*twoPi*fMuPrecFreq23*time) +
fMuFractionState14 * TComplex::Exp(TComplex::I()*twoPi*fMuPrecFreq14*time));
}
return complexPol; return complexPol;
// Double_t muoniumPolX = 0;
// muoniumPolX = 0.5 *
// (fMuFractionState12 * (TMath::Cos(twoPi*fMuPrecFreq12*time) + TMath::Cos(twoPi*fMuPrecFreq34*time)) +
// fMuFractionState23 * (TMath::Cos(twoPi*fMuPrecFreq23*time) + TMath::Cos(twoPi*fMuPrecFreq14*time)));
//
// return muoniumPolX;
} }
//-------------------------------------------------------------------------- //--------------------------------------------------------------------------
@ -308,18 +320,18 @@ Double_t PSimulateMuTransition::GTSpinFlip(const Double_t &time)
eventTime += NextEventTime(fSpinFlipRate); eventTime += NextEventTime(fSpinFlipRate);
if (eventTime >= time){ if (eventTime >= time){
muoniumPolX = GTFunction(time).Re(); muoniumPolX = GTFunction(time, "Mu0").Re();
} }
else{ else{
while (eventTime < time){ while (eventTime < time){
eventDiffTime = eventTime - lastEventTime; eventDiffTime = eventTime - lastEventTime;
complexPolX = complexPolX * GTFunction(eventDiffTime); complexPolX = complexPolX * GTFunction(eventDiffTime, "Mu0");
lastEventTime = eventTime; lastEventTime = eventTime;
eventTime += NextEventTime(fSpinFlipRate); eventTime += NextEventTime(fSpinFlipRate);
} }
// calculate for the last collision // calculate for the last collision
eventDiffTime = time - lastEventTime; eventDiffTime = time - lastEventTime;
complexPolX = complexPolX * GTFunction(eventDiffTime); complexPolX = complexPolX * GTFunction(eventDiffTime, "Mu0");
muoniumPolX = complexPolX.Re(); muoniumPolX = complexPolX.Re();
} }
@ -330,130 +342,100 @@ Double_t PSimulateMuTransition::GTSpinFlip(const Double_t &time)
// Event (private) // Event (private)
//-------------------------------------------------------------------------- //--------------------------------------------------------------------------
/** /**
* <p> Generates "muon event": simulate muon spin phase under charge-exchange with * <p> Generates "muon event": simulate muon spin polarization under charge-exchange with
* a neutral muonium state in transverse field, where the polarization evolution * a neutral muonium state in transverse field, where the polarization evolution
* PxMu(t) of the muon spin in muonium is determined by a superposition of the * PxMu(t) of the muon spin in muonium is determined by a superposition of the
* four "Mu transitions" nu_12, nu_34, nu_23, and nu_14. * four "Mu transitions" nu_12, nu_34, nu_23, and nu_14. Use complex polarization
* functions.
* 1) according to Mu+/Mu0 fraction begin either with a Mu+ state or Mu state * 1) according to Mu+/Mu0 fraction begin either with a Mu+ state or Mu state
* 2) Mu+: determine next electron-capture time t_c. If t_c is larger than decay time t_d * 2) Mu+: determine next electron-capture time t_c. If t_c is larger than decay time t_d
* calculate muon spin precession for t_d; else calculate spin precession for t_c. * calculate muon spin precession for t_d, Px(t_i); else calculate spin precession for t_c.
* 3) Determine next ionization time t_i; calculate Px(t_i) in Muonium; calculate the * 3) Determine next ionization time t_i+1; calculate Px(t_i+1) in Muonium. Polarization
* muon spin phase by acos(Px(t_i)). * after ionization process is given by Px(t_i+1)*Px(t_i).
* 4) get the next electron capture time, continue until t_d is reached. * 4) get the next electron capture time, continue until t_d is reached.
* *
* <p> For isotropic muonium, TF: * <p> For isotropic muonium, TF:
* nu_12 and nu_34 with equal probabilities, probability for both states fMuFractionState12 * nu_12 and nu_34 with equal probabilities, probability for both states fMuFractionState12
* ni_23 and nu_14 with equal probabilities, probability for both states fMuFractionState23 * ni_23 and nu_14 with equal probabilities, probability for both states fMuFractionState23
* *
* <p>Calculates Mu0 polarization in x direction during cyclic charge exchange.
* See M. Senba, J.Phys. B23, 1545 (1990), equations (9), (11)
* \param muonString if eq. "Mu+" begin with Mu+ precession * \param muonString if eq. "Mu+" begin with Mu+ precession
*/ */
void PSimulateMuTransition::Event(const TString muonString) Double_t PSimulateMuTransition::Event(const TString muonString)
{ {
TComplex complexPolX = 1.0;
Double_t muoniumPolX = 1.0; //initial polarization in x direction
Double_t eventTime, eventDiffTime, captureTime, ionizationTime; Double_t eventTime, eventDiffTime, captureTime, ionizationTime;
// Double_t muonPrecessionFreq, muoniumPrecessionFreq; // MHz
// Double_t rndm, frac1, frac2;
fMuonPrecFreq = fMuonGyroRatio * fBfield;
// charge-exchange loop until muon decay
eventTime = 0.; eventTime = 0.;
eventDiffTime = 0.; eventDiffTime = 0.;
if (fDebugFlag) cout << "Decay time = " << fMuonDecayTime << endl; if (fDebugFlag) cout << "Decay time = " << fMuonDecayTime << endl;
//cout << muonString << endl;
// charge-exchange loop until muon decays
while (1) { while (1) {
if (muonString == "Mu+"){ if (muonString == "Mu+"){// Mu+ initial state; get next electron capture time
// Mu+ initial state; get next electron capture time
captureTime = NextEventTime(fCaptureRate); captureTime = NextEventTime(fCaptureRate);
eventTime += captureTime; eventTime += captureTime;
if (fDebugFlag) cout << "Capture time = " << captureTime << " Phase = " << fMuonPhase << endl;
if (fDebugFlag) cout << "Capture time = " << captureTime << " PolX = " << complexPolX.Re() << endl;
if (eventTime < fMuonDecayTime) if (eventTime < fMuonDecayTime)
fMuonPhase += PrecessionPhase(captureTime, "Mu+"); complexPolX *= GTFunction(captureTime, "Mu+");
else{ //muon decays; handle precession prior to muon decay else{ //muon decays; handle precession prior to muon decay
eventDiffTime = fMuonDecayTime - (eventTime - captureTime); eventDiffTime = fMuonDecayTime - (eventTime - captureTime);
fMuonPhase += PrecessionPhase(eventDiffTime, "Mu+"); complexPolX *= GTFunction(eventDiffTime, "Mu+");
break; break;
} }
// now, we have Mu0; get next ionization time // now, we have Mu0; get next ionization time
ionizationTime = NextEventTime(fIonizationRate); ionizationTime = NextEventTime(fIonizationRate);
eventTime += ionizationTime; eventTime += ionizationTime;
// determine Mu state
// rndm = fRandom->Rndm();
// frac1 = 1. - fMuFractionState1 - fMuFractionState2; // non-precessing Mu states
// frac2 = 1. - fMuFractionState2;
// if ( rndm < frac1 )
// muoniumPrecessionFreq = 0.;
// else if (rndm >= frac1 && rndm <= frac2){
// if (fRandom->Rndm() <= 0.5)
// muoniumPrecessionFreq = fMuPrecFreq12;
// else
// muoniumPrecessionFreq = fMuPrecFreq34;
// }
// else{
// if (fRandom->Rndm() <= 0.5)
// muoniumPrecessionFreq = fMuPrecFreq23;
// else
// muoniumPrecessionFreq = fMuPrecFreq14;
// }
if (fDebugFlag) cout << "Ioniza. time = " << ionizationTime << " Phase = " << fMuonPhase << endl; if (fDebugFlag) cout << "Ioniza. time = " << ionizationTime << " PolX = " << complexPolX.Re() << endl;
if (eventTime < fMuonDecayTime) if (eventTime < fMuonDecayTime)
fMuonPhase += PrecessionPhase(ionizationTime, "Mu0"); complexPolX *= GTFunction(ionizationTime, "Mu0");
else{ //muon decays; handle precession prior to muon decay else{ //muon decays; handle precession prior to muon decay
eventDiffTime = fMuonDecayTime - (eventTime - ionizationTime); eventDiffTime = fMuonDecayTime - (eventTime - ionizationTime);
fMuonPhase += PrecessionPhase(eventDiffTime, "Mu0"); complexPolX *= GTFunction(eventDiffTime, "Mu0");
break; break;
} }
} }
else{ else{// Mu0 as initial state; get next ionization time
// Mu0 as initial state; get next ionization time
ionizationTime = NextEventTime(fIonizationRate); ionizationTime = NextEventTime(fIonizationRate);
eventTime += ionizationTime; eventTime += ionizationTime;
// determine Mu state
// rndm = fRandom->Rndm();
// frac1 = 1. - fMuFractionState1 - fMuFractionState2; // non-precessing Mu states
// frac2 = 1. - fMuFractionState2;
// if ( rndm < frac1 )
// muoniumPrecessionFreq = 0.;
// else if (rndm >= frac1 && rndm <= frac2){
// if (fRandom->Rndm() <= 0.5)
// muoniumPrecessionFreq = fMuPrecFreq12;
// else
// muoniumPrecessionFreq = fMuPrecFreq34;
// }
// else{
// if (fRandom->Rndm() <= 0.5)
// muoniumPrecessionFreq = fMuPrecFreq23;
// else
// muoniumPrecessionFreq = fMuPrecFreq14;
// }
if (fDebugFlag) if (fDebugFlag)
cout << "Mu Ioniza. time = " << ionizationTime << " Phase = " << fMuonPhase << endl; cout << "Mu Ioniza. time = " << ionizationTime << " PolX = " << complexPolX.Re() << endl;
if (eventTime < fMuonDecayTime) if (eventTime < fMuonDecayTime)
fMuonPhase += PrecessionPhase(ionizationTime, "Mu0"); complexPolX *= GTFunction(ionizationTime, "Mu0");
else{ //muon decays; handle precession prior to muon decay else{ //muon decays; handle precession prior to muon decay
eventDiffTime = fMuonDecayTime - (eventTime - ionizationTime); eventDiffTime = fMuonDecayTime - (eventTime - ionizationTime);
fMuonPhase += PrecessionPhase(eventDiffTime, "Mu0"); complexPolX *= GTFunction(eventDiffTime, "Mu0");
break; break;
} }
// Mu+ state; get next electron capture time // Mu+ state; get next electron capture time
captureTime = NextEventTime(fCaptureRate); captureTime = NextEventTime(fCaptureRate);
eventTime += captureTime; eventTime += captureTime;
if (fDebugFlag) cout << "Capture time = " << captureTime << " Phase = " << fMuonPhase << endl;
if (fDebugFlag) cout << "Capture time = " << captureTime << " PolX = " << complexPolX.Re() << endl;
if (eventTime < fMuonDecayTime) if (eventTime < fMuonDecayTime)
fMuonPhase += PrecessionPhase(captureTime, "Mu+"); complexPolX *= GTFunction(captureTime, "Mu+");
else{ //muon decays; handle precession prior to muon decay else{ //muon decays; handle precession prior to muon decay
eventDiffTime = fMuonDecayTime - (eventTime - captureTime); eventDiffTime = fMuonDecayTime - (eventTime - captureTime);
fMuonPhase += PrecessionPhase(eventDiffTime, "Mu+"); complexPolX *= GTFunction(eventDiffTime, "Mu+");
break; break;
} }
} }
} }
muoniumPolX = complexPolX.Re();
if (fDebugFlag) cout << " Final PolX = " << muoniumPolX << endl;
if (fDebugFlag) cout << " Final Phase = " << fMuonPhase << endl; return muoniumPolX;
//fMuonPhase = TMath::ACos(TMath::Cos(fMuonPhase))*360./TMath::TwoPi(); //transform back to [0, 180] degree interval
return;
} }

15
src/tests/MuTransition/PSimulateMuTransition.h
View File

@ -60,7 +60,9 @@ class PSimulateMuTransition : public TObject
virtual void SetDecayAsymmetry(Double_t value){ fAsymmetry = value; } //!< muon decay asymmetry virtual void SetDecayAsymmetry(Double_t value){ fAsymmetry = value; } //!< muon decay asymmetry
virtual void SetMuFraction(Double_t value){ fMuFraction = value; } //!< Muonium fraction virtual void SetMuFraction(Double_t value){ fMuFraction = value; } //!< Muonium fraction
virtual void SetMuFractionState12(Double_t value){ fMuFractionState12 = value; } virtual void SetMuFractionState12(Double_t value){ fMuFractionState12 = value; }
virtual void SetMuFractionState34(Double_t value){ fMuFractionState34 = value; }
virtual void SetMuFractionState23(Double_t value){ fMuFractionState23 = value; } virtual void SetMuFractionState23(Double_t value){ fMuFractionState23 = value; }
virtual void SetMuFractionState14(Double_t value){ fMuFractionState14 = value; }
virtual Bool_t IsValid() { return fValid; } virtual Bool_t IsValid() { return fValid; }
virtual void SetSeed(UInt_t seed); virtual void SetSeed(UInt_t seed);
@ -88,17 +90,18 @@ class PSimulateMuTransition : public TObject
Double_t fMuonPhase; //!< phase of muon spin Double_t fMuonPhase; //!< phase of muon spin
Double_t fAsymmetry; //!< muon decay asymmetry Double_t fAsymmetry; //!< muon decay asymmetry
Double_t fMuFraction; //!< total Mu fraction [0,1] Double_t fMuFraction; //!< total Mu fraction [0,1]
Double_t fMuFractionState12; //!< fraction of Mu in state 12, 34 Double_t fMuFractionState12; //!< fraction of Mu in state 12
Double_t fMuFractionState23; //!< fraction of Mu in state 23, 14 Double_t fMuFractionState34; //!< fraction of Mu in state 34
Double_t fMuFractionState23; //!< fraction of Mu in state 23
Double_t fMuFractionState14; //!< fraction of Mu in state 14
Int_t fNmuons; //!< number of muons to simulate Int_t fNmuons; //!< number of muons to simulate
Bool_t fDebugFlag; //!< debug flag Bool_t fDebugFlag; //!< debug flag
virtual Double_t NextEventTime(const Double_t &EventRate); virtual Double_t NextEventTime(const Double_t &EventRate);
// virtual Double_t PrecessionPhase(const Double_t &time, const Double_t &frequency); // virtual Double_t PrecessionPhase(const Double_t &time, const TString chargeState);
virtual Double_t PrecessionPhase(const Double_t &time, const TString chargeState); virtual TComplex GTFunction(const Double_t &time, const TString chargeState); //!< transverse field polarization function of Mu0 or Mu+
virtual TComplex GTFunction(const Double_t &time); //!< transverse field polarization function of Mu0
virtual Double_t GTSpinFlip(const Double_t &time); //!< transverse field polarization function after spin-flip collisions virtual Double_t GTSpinFlip(const Double_t &time); //!< transverse field polarization function after spin-flip collisions
virtual void Event(const TString muonString); virtual Double_t Event(const TString muonString);
ClassDef(PSimulateMuTransition, 0) ClassDef(PSimulateMuTransition, 0)
}; };

17
src/tests/MuTransition/runMuSimulation.C
View File

@ -65,10 +65,13 @@ void runMuSimulation()
Double_t Freq23 = 256.245; //Mu freq of the 23 transition Double_t Freq23 = 256.245; //Mu freq of the 23 transition
Double_t Freq14 = 356.245; //Mu freq of the 14 transition Double_t Freq14 = 356.245; //Mu freq of the 14 transition
Double_t MuFrac = 1.0; //total Mu fraction Double_t MuFrac = 1.0; //total Mu fraction
Double_t MuFrac12 = 2*0.487; //Mu in states 12 and 34 Double_t MuFrac12 = 0.487; //weight of transition 12
Double_t MuFrac23 = 2*0.013; //Mu in states 23 and 14 Double_t MuFrac34 = 0.487; //weight of transition 34
Double_t MuFrac23 = 0.013; //weight of transition 23
Double_t MuFrac14 = 0.013; //weight of transition 14
Int_t Nmuons = 5e6; //number of muons Int_t Nmuons = 5e6; //number of muons
Double_t Asym = 0.27; //muon decay asymmetry Double_t Asym = 0.27; //muon decay asymmetry
Int_t debugFlag = 0; //print debug information on screen
histogramFileName = TString("0"); histogramFileName = TString("0");
histogramFileName += runNo; histogramFileName += runNo;
@ -89,15 +92,17 @@ void runMuSimulation()
simulateMuTransition->SetMuPrecFreq23(Freq23); // MHz simulateMuTransition->SetMuPrecFreq23(Freq23); // MHz
simulateMuTransition->SetMuPrecFreq14(Freq14); // MHz simulateMuTransition->SetMuPrecFreq14(Freq14); // MHz
simulateMuTransition->SetMuFraction(MuFrac); // initial Mu fraction simulateMuTransition->SetMuFraction(MuFrac); // initial Mu fraction
simulateMuTransition->SetMuFractionState12(MuFrac12); // Mu in states 12, 34 simulateMuTransition->SetMuFractionState12(MuFrac12);
simulateMuTransition->SetMuFractionState23(MuFrac23); // Mu in states 23, 14 simulateMuTransition->SetMuFractionState34(MuFrac34);
simulateMuTransition->SetMuFractionState23(MuFrac23);
simulateMuTransition->SetMuFractionState14(MuFrac14);
simulateMuTransition->SetBfield(B/10000.); // Tesla simulateMuTransition->SetBfield(B/10000.); // Tesla
simulateMuTransition->SetCaptureRate(capRate); // MHz simulateMuTransition->SetCaptureRate(capRate); // MHz
simulateMuTransition->SetIonizationRate(ionRate); // MHz simulateMuTransition->SetIonizationRate(ionRate); // MHz
simulateMuTransition->SetSpinFlipRate(spinFlipRate); // MHz simulateMuTransition->SetSpinFlipRate(spinFlipRate); // MHz
simulateMuTransition->SetNmuons(Nmuons); simulateMuTransition->SetNmuons(Nmuons);
simulateMuTransition->SetDecayAsymmetry(Asym); simulateMuTransition->SetDecayAsymmetry(Asym);
simulateMuTransition->SetDebugFlag(kFALSE); // to print time and phase during charge-changing cycle simulateMuTransition->SetDebugFlag(debugFlag); // to print time and phase during charge-changing cycle
// feed run info header // feed run info header
gRunHeader = gROOT->GetRootFolder()->AddFolder("RunHeader", "MuTransition Simulation Header Info"); gRunHeader = gROOT->GetRootFolder()->AddFolder("RunHeader", "MuTransition Simulation Header Info");
@ -168,7 +173,9 @@ void runMuSimulation()
header->Set("Simulation/Mu0 Precession frequency 14", Freq14); header->Set("Simulation/Mu0 Precession frequency 14", Freq14);
header->Set("Simulation/Mu0 Fraction", MuFrac); header->Set("Simulation/Mu0 Fraction", MuFrac);
header->Set("Simulation/Mu0 Fraction 12", MuFrac12); header->Set("Simulation/Mu0 Fraction 12", MuFrac12);
header->Set("Simulation/Mu0 Fraction 34", MuFrac34);
header->Set("Simulation/Mu0 Fraction 23", MuFrac23); header->Set("Simulation/Mu0 Fraction 23", MuFrac23);
header->Set("Simulation/Mu0 Fraction 14", MuFrac14);
header->Set("Simulation/muon Capture Rate", capRate); header->Set("Simulation/muon Capture Rate", capRate);
header->Set("Simulation/Mu0 Ionization Rate", ionRate); header->Set("Simulation/Mu0 Ionization Rate", ionRate);
header->Set("Simulation/Mu0 Spin Flip Rate", spinFlipRate); header->Set("Simulation/Mu0 Spin Flip Rate", spinFlipRate);