Gabriele Cosmo
483 lines
16 KiB
C++
483 lines
16 KiB
C++
//
|
|
// ********************************************************************
|
|
// * License and Disclaimer *
|
|
// * *
|
|
// * The Geant4 software is copyright of the Copyright Holders of *
|
|
// * the Geant4 Collaboration. It is provided under the terms and *
|
|
// * conditions of the Geant4 Software License, included in the file *
|
|
// * LICENSE and available at http://cern.ch/geant4/license . These *
|
|
// * include a list of copyright holders. *
|
|
// * *
|
|
// * Neither the authors of this software system, nor their employing *
|
|
// * institutes,nor the agencies providing financial support for this *
|
|
// * work make any representation or warranty, express or implied, *
|
|
// * regarding this software system or assume any liability for its *
|
|
// * use. Please see the license in the file LICENSE and URL above *
|
|
// * for the full disclaimer and the limitation of liability. *
|
|
// * *
|
|
// * This code implementation is the result of the scientific and *
|
|
// * technical work of the GEANT4 collaboration. *
|
|
// * By using, copying, modifying or distributing the software (or *
|
|
// * any work based on the software) you agree to acknowledge its *
|
|
// * use in resulting scientific publications, and indicate your *
|
|
// * acceptance of all terms of the Geant4 Software license. *
|
|
// ********************************************************************
|
|
//
|
|
// $Id: G4PairProductionRelModel.cc,v 1.4 2010-10-26 09:06:04 vnivanch Exp $
|
|
// GEANT4 tag $Name: not supported by cvs2svn $
|
|
//
|
|
// -------------------------------------------------------------------
|
|
//
|
|
// GEANT4 Class file
|
|
//
|
|
//
|
|
// File name: G4PairProductionRelModel
|
|
//
|
|
// Author: Andreas Schaelicke
|
|
//
|
|
// Creation date: 02.04.2009
|
|
//
|
|
// Modifications:
|
|
//
|
|
// Class Description:
|
|
//
|
|
// Main References:
|
|
// J.W.Motz et.al., Rev. Mod. Phys. 41 (1969) 581.
|
|
// S.Klein, Rev. Mod. Phys. 71 (1999) 1501.
|
|
// T.Stanev et.al., Phys. Rev. D25 (1982) 1291.
|
|
// M.L.Ter-Mikaelian, High-energy Electromagnetic Processes in Condensed Media,
|
|
// Wiley, 1972.
|
|
//
|
|
// -------------------------------------------------------------------
|
|
//
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
|
|
|
|
#include "G4PairProductionRelModel.hh"
|
|
#include "G4Gamma.hh"
|
|
#include "G4Electron.hh"
|
|
#include "G4Positron.hh"
|
|
|
|
#include "G4ParticleChangeForGamma.hh"
|
|
#include "G4LossTableManager.hh"
|
|
|
|
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
|
|
|
|
using namespace std;
|
|
|
|
|
|
const G4double G4PairProductionRelModel::facFel = log(184.15);
|
|
const G4double G4PairProductionRelModel::facFinel = log(1194.); // 1440.
|
|
|
|
const G4double G4PairProductionRelModel::preS1 = 1./(184.15*184.15);
|
|
const G4double G4PairProductionRelModel::logTwo = log(2.);
|
|
|
|
const G4double G4PairProductionRelModel::xgi[]={ 0.0199, 0.1017, 0.2372, 0.4083,
|
|
0.5917, 0.7628, 0.8983, 0.9801 };
|
|
const G4double G4PairProductionRelModel::wgi[]={ 0.0506, 0.1112, 0.1569, 0.1813,
|
|
0.1813, 0.1569, 0.1112, 0.0506 };
|
|
const G4double G4PairProductionRelModel::Fel_light[] = {0., 5.31 , 4.79 , 4.74 , 4.71};
|
|
const G4double G4PairProductionRelModel::Finel_light[] = {0., 6.144 , 5.621 , 5.805 , 5.924};
|
|
|
|
|
|
|
|
G4PairProductionRelModel::G4PairProductionRelModel(const G4ParticleDefinition*,
|
|
const G4String& nam)
|
|
: G4VEmModel(nam),
|
|
fLPMconstant(fine_structure_const*electron_mass_c2*electron_mass_c2/(4.*pi*hbarc)*0.5),
|
|
fLPMflag(true),
|
|
lpmEnergy(0.),
|
|
use_completescreening(false)
|
|
{
|
|
fParticleChange = 0;
|
|
theGamma = G4Gamma::Gamma();
|
|
thePositron = G4Positron::Positron();
|
|
theElectron = G4Electron::Electron();
|
|
|
|
nist = G4NistManager::Instance();
|
|
|
|
currentZ = z13 = z23 = lnZ = Fel = Finel = fCoulomb = phiLPM = gLPM = xiLPM = 0;
|
|
|
|
}
|
|
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
|
|
|
|
G4PairProductionRelModel::~G4PairProductionRelModel()
|
|
{}
|
|
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
|
|
|
|
void G4PairProductionRelModel::Initialise(const G4ParticleDefinition* p,
|
|
const G4DataVector& cuts)
|
|
{
|
|
if(!fParticleChange) { fParticleChange = GetParticleChangeForGamma(); }
|
|
InitialiseElementSelectors(p, cuts);
|
|
}
|
|
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
|
|
|
|
G4double G4PairProductionRelModel::ComputeXSectionPerAtom(G4double totalEnergy, G4double Z)
|
|
{
|
|
G4double cross = 0.0;
|
|
|
|
// number of intervals and integration step
|
|
G4double vcut = electron_mass_c2/totalEnergy ;
|
|
|
|
// limits by the screening variable
|
|
G4double dmax = DeltaMax();
|
|
G4double dmin = min(DeltaMin(totalEnergy),dmax);
|
|
G4double vcut1 = 0.5 - 0.5*sqrt(1. - dmin/dmax) ;
|
|
vcut = max(vcut, vcut1);
|
|
|
|
|
|
G4double vmax = 0.5;
|
|
G4int n = 1; // needs optimisation
|
|
|
|
G4double delta = (vmax - vcut)*totalEnergy/G4double(n);
|
|
|
|
G4double e0 = vcut*totalEnergy;
|
|
G4double xs;
|
|
|
|
// simple integration
|
|
for(G4int l=0; l<n; l++,e0 += delta) {
|
|
for(G4int i=0; i<8; i++) {
|
|
|
|
G4double eg = (e0 + xgi[i]*delta);
|
|
if (fLPMflag && totalEnergy>100.*GeV)
|
|
xs = ComputeRelDXSectionPerAtom(eg,totalEnergy,Z);
|
|
else
|
|
xs = ComputeDXSectionPerAtom(eg,totalEnergy,Z);
|
|
cross += wgi[i]*xs;
|
|
|
|
}
|
|
}
|
|
|
|
cross *= delta*2.;
|
|
|
|
return cross;
|
|
}
|
|
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
|
|
|
|
G4double
|
|
G4PairProductionRelModel::ComputeDXSectionPerAtom(G4double eplusEnergy,
|
|
G4double totalEnergy,
|
|
G4double /*Z*/)
|
|
{
|
|
// most simple case - complete screening:
|
|
|
|
// dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k
|
|
// * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3) + 1/9 * y*(1-y) ]
|
|
// y = E+/k
|
|
G4double yp=eplusEnergy/totalEnergy;
|
|
G4double ym=1.-yp;
|
|
|
|
G4double cross = 0.;
|
|
if (use_completescreening)
|
|
cross = (yp*yp + ym*ym + 2./3.*ym*yp)*(Fel - fCoulomb) + 1./9.*yp*ym;
|
|
else {
|
|
G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym);
|
|
cross = (yp*yp + ym*ym)*(0.25*Phi1(delta) - lnZ/3. - fCoulomb)
|
|
+ 2./3.*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb);
|
|
}
|
|
return cross/totalEnergy;
|
|
|
|
}
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
|
|
|
|
G4double
|
|
G4PairProductionRelModel::ComputeRelDXSectionPerAtom(G4double eplusEnergy,
|
|
G4double totalEnergy,
|
|
G4double /*Z*/)
|
|
{
|
|
// most simple case - complete screening:
|
|
|
|
// dsig/dE+ = 4 * alpha * Z**2 * r0**2 / k
|
|
// * [ (y**2 + (1-y**2) + 2/3*y*(1-y) ) * ( log (183 * Z**-1/3) + 1/9 * y*(1-y) ]
|
|
// y = E+/k
|
|
G4double yp=eplusEnergy/totalEnergy;
|
|
G4double ym=1.-yp;
|
|
|
|
CalcLPMFunctions(totalEnergy,eplusEnergy); // gamma
|
|
|
|
G4double cross = 0.;
|
|
if (use_completescreening)
|
|
cross = xiLPM*(2./3.*phiLPM*(yp*yp + ym*ym) + gLPM)*(Fel - fCoulomb);
|
|
else {
|
|
G4double delta = 0.25*DeltaMin(totalEnergy)/(yp*ym);
|
|
cross = (1./3.*gLPM + 2./3.*phiLPM)*(yp*yp + ym*ym)
|
|
*(0.25*Phi1(delta) - lnZ/3. - fCoulomb)
|
|
+ 2./3.*gLPM*ym*yp*(0.25*Phi2(delta) - lnZ/3. - fCoulomb);
|
|
cross *= xiLPM;
|
|
}
|
|
return cross/totalEnergy;
|
|
|
|
}
|
|
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
|
|
|
|
void G4PairProductionRelModel::CalcLPMFunctions(G4double k, G4double eplus)
|
|
{
|
|
// *** calculate lpm variable s & sprime ***
|
|
// Klein eqs. (78) & (79)
|
|
G4double sprime = sqrt(0.125*k*lpmEnergy/(eplus*(k-eplus)));
|
|
|
|
G4double s1 = preS1*z23;
|
|
G4double logS1 = 2./3.*lnZ-2.*facFel;
|
|
G4double logTS1 = logTwo+logS1;
|
|
|
|
xiLPM = 2.;
|
|
|
|
if (sprime>1)
|
|
xiLPM = 1.;
|
|
else if (sprime>sqrt(2.)*s1) {
|
|
G4double h = log(sprime)/logTS1;
|
|
xiLPM = 1+h-0.08*(1-h)*(1-sqr(1-h))/logTS1;
|
|
}
|
|
|
|
G4double s = sprime/sqrt(xiLPM);
|
|
// G4cout<<"k="<<k<<" y="<<eplus/k<<G4endl;
|
|
// G4cout<<"s="<<s<<G4endl;
|
|
|
|
// *** calculate supression functions phi and G ***
|
|
// Klein eqs. (77)
|
|
G4double s2=s*s;
|
|
G4double s3=s*s2;
|
|
G4double s4=s2*s2;
|
|
|
|
if (s<0.1) {
|
|
// high suppression limit
|
|
phiLPM = 6.*s - 18.84955592153876*s2 + 39.47841760435743*s3
|
|
- 57.69873135166053*s4;
|
|
gLPM = 37.69911184307752*s2 - 236.8705056261446*s3 + 807.7822389*s4;
|
|
}
|
|
else if (s<1.9516) {
|
|
// intermediate suppression
|
|
// using eq.77 approxim. valid s<2.
|
|
phiLPM = 1.-exp(-6.*s*(1.+(3.-pi)*s)
|
|
+s3/(0.623+0.795*s+0.658*s2));
|
|
if (s<0.415827397755) {
|
|
// using eq.77 approxim. valid 0.07<s<2
|
|
G4double psiLPM = 1-exp(-4*s-8*s2/(1+3.936*s+4.97*s2-0.05*s3+7.50*s4));
|
|
gLPM = 3*psiLPM-2*phiLPM;
|
|
}
|
|
else {
|
|
// using alternative parametrisiation
|
|
G4double pre = -0.16072300849123999 + s*3.7550300067531581 + s2*-1.7981383069010097
|
|
+ s3*0.67282686077812381 + s4*-0.1207722909879257;
|
|
gLPM = tanh(pre);
|
|
}
|
|
}
|
|
else {
|
|
// low suppression limit valid s>2.
|
|
phiLPM = 1. - 0.0119048/s4;
|
|
gLPM = 1. - 0.0230655/s4;
|
|
}
|
|
|
|
// *** make sure suppression is smaller than 1 ***
|
|
// *** caused by Migdal approximation in xi ***
|
|
if (xiLPM*phiLPM>1. || s>0.57) xiLPM=1./phiLPM;
|
|
}
|
|
|
|
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
|
|
|
|
G4double
|
|
G4PairProductionRelModel::ComputeCrossSectionPerAtom(const G4ParticleDefinition*,
|
|
G4double gammaEnergy, G4double Z,
|
|
G4double, G4double, G4double)
|
|
{
|
|
// static const G4double gammaEnergyLimit = 1.5*MeV;
|
|
G4double crossSection = 0.0 ;
|
|
if ( Z < 0.9 ) return crossSection;
|
|
if ( gammaEnergy <= 2.0*electron_mass_c2 ) return crossSection;
|
|
|
|
SetCurrentElement(Z);
|
|
// choose calculator according to parameters and switches
|
|
// in the moment only one calculator:
|
|
crossSection=ComputeXSectionPerAtom(gammaEnergy,Z);
|
|
|
|
G4double xi = Finel/(Fel - fCoulomb); // inelastic contribution
|
|
crossSection*=4.*Z*(Z+xi)*fine_structure_const*classic_electr_radius*classic_electr_radius;
|
|
|
|
return crossSection;
|
|
}
|
|
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
|
|
|
|
void
|
|
G4PairProductionRelModel::SampleSecondaries(std::vector<G4DynamicParticle*>* fvect,
|
|
const G4MaterialCutsCouple* couple,
|
|
const G4DynamicParticle* aDynamicGamma,
|
|
G4double,
|
|
G4double)
|
|
// The secondaries e+e- energies are sampled using the Bethe - Heitler
|
|
// cross sections with Coulomb correction.
|
|
// A modified version of the random number techniques of Butcher & Messel
|
|
// is used (Nuc Phys 20(1960),15).
|
|
//
|
|
// GEANT4 internal units.
|
|
//
|
|
// Note 1 : Effects due to the breakdown of the Born approximation at
|
|
// low energy are ignored.
|
|
// Note 2 : The differential cross section implicitly takes account of
|
|
// pair creation in both nuclear and atomic electron fields.
|
|
// However triplet prodution is not generated.
|
|
{
|
|
const G4Material* aMaterial = couple->GetMaterial();
|
|
|
|
G4double GammaEnergy = aDynamicGamma->GetKineticEnergy();
|
|
G4ParticleMomentum GammaDirection = aDynamicGamma->GetMomentumDirection();
|
|
|
|
G4double epsil ;
|
|
G4double epsil0 = electron_mass_c2/GammaEnergy ;
|
|
if(epsil0 > 1.0) { return; }
|
|
|
|
// do it fast if GammaEnergy < 2. MeV
|
|
static const G4double Egsmall=2.*MeV;
|
|
|
|
// select randomly one element constituing the material
|
|
const G4Element* anElement = SelectRandomAtom(aMaterial, theGamma, GammaEnergy);
|
|
|
|
if (GammaEnergy < Egsmall) {
|
|
|
|
epsil = epsil0 + (0.5-epsil0)*G4UniformRand();
|
|
|
|
} else {
|
|
// now comes the case with GammaEnergy >= 2. MeV
|
|
|
|
// Extract Coulomb factor for this Element
|
|
G4double FZ = 8.*(anElement->GetIonisation()->GetlogZ3());
|
|
if (GammaEnergy > 50.*MeV) FZ += 8.*(anElement->GetfCoulomb());
|
|
|
|
// limits of the screening variable
|
|
G4double screenfac = 136.*epsil0/(anElement->GetIonisation()->GetZ3());
|
|
G4double screenmax = exp ((42.24 - FZ)/8.368) - 0.952 ;
|
|
G4double screenmin = min(4.*screenfac,screenmax);
|
|
|
|
// limits of the energy sampling
|
|
G4double epsil1 = 0.5 - 0.5*sqrt(1. - screenmin/screenmax) ;
|
|
G4double epsilmin = max(epsil0,epsil1) , epsilrange = 0.5 - epsilmin;
|
|
|
|
//
|
|
// sample the energy rate of the created electron (or positron)
|
|
//
|
|
//G4double epsil, screenvar, greject ;
|
|
G4double screenvar, greject ;
|
|
|
|
G4double F10 = ScreenFunction1(screenmin) - FZ;
|
|
G4double F20 = ScreenFunction2(screenmin) - FZ;
|
|
G4double NormF1 = max(F10*epsilrange*epsilrange,0.);
|
|
G4double NormF2 = max(1.5*F20,0.);
|
|
|
|
do {
|
|
if ( NormF1/(NormF1+NormF2) > G4UniformRand() ) {
|
|
epsil = 0.5 - epsilrange*pow(G4UniformRand(), 0.333333);
|
|
screenvar = screenfac/(epsil*(1-epsil));
|
|
if (fLPMflag && GammaEnergy>100.*GeV) {
|
|
CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil);
|
|
greject = xiLPM*((gLPM+2.*phiLPM)*Phi1(screenvar) - gLPM*Phi2(screenvar) - phiLPM*FZ)/F10;
|
|
}
|
|
else {
|
|
greject = (ScreenFunction1(screenvar) - FZ)/F10;
|
|
}
|
|
|
|
} else {
|
|
epsil = epsilmin + epsilrange*G4UniformRand();
|
|
screenvar = screenfac/(epsil*(1-epsil));
|
|
if (fLPMflag && GammaEnergy>100.*GeV) {
|
|
CalcLPMFunctions(GammaEnergy,GammaEnergy*epsil);
|
|
greject = xiLPM*((0.5*gLPM+phiLPM)*Phi1(screenvar) + 0.5*gLPM*Phi2(screenvar) - 0.5*(gLPM+phiLPM)*FZ)/F20;
|
|
}
|
|
else {
|
|
greject = (ScreenFunction2(screenvar) - FZ)/F20;
|
|
}
|
|
}
|
|
|
|
} while( greject < G4UniformRand() );
|
|
|
|
} // end of epsil sampling
|
|
|
|
//
|
|
// fixe charges randomly
|
|
//
|
|
|
|
G4double ElectTotEnergy, PositTotEnergy;
|
|
if (G4UniformRand() > 0.5) {
|
|
|
|
ElectTotEnergy = (1.-epsil)*GammaEnergy;
|
|
PositTotEnergy = epsil*GammaEnergy;
|
|
|
|
} else {
|
|
|
|
PositTotEnergy = (1.-epsil)*GammaEnergy;
|
|
ElectTotEnergy = epsil*GammaEnergy;
|
|
}
|
|
|
|
//
|
|
// scattered electron (positron) angles. ( Z - axis along the parent photon)
|
|
//
|
|
// universal distribution suggested by L. Urban
|
|
// (Geant3 manual (1993) Phys211),
|
|
// derived from Tsai distribution (Rev Mod Phys 49,421(1977))
|
|
|
|
G4double u;
|
|
const G4double a1 = 0.625 , a2 = 3.*a1 , d = 27. ;
|
|
|
|
if (9./(9.+d) >G4UniformRand()) u= - log(G4UniformRand()*G4UniformRand())/a1;
|
|
else u= - log(G4UniformRand()*G4UniformRand())/a2;
|
|
|
|
G4double TetEl = u*electron_mass_c2/ElectTotEnergy;
|
|
G4double TetPo = u*electron_mass_c2/PositTotEnergy;
|
|
G4double Phi = twopi * G4UniformRand();
|
|
G4double dxEl= sin(TetEl)*cos(Phi),dyEl= sin(TetEl)*sin(Phi),dzEl=cos(TetEl);
|
|
G4double dxPo=-sin(TetPo)*cos(Phi),dyPo=-sin(TetPo)*sin(Phi),dzPo=cos(TetPo);
|
|
|
|
//
|
|
// kinematic of the created pair
|
|
//
|
|
// the electron and positron are assumed to have a symetric
|
|
// angular distribution with respect to the Z axis along the parent photon.
|
|
|
|
G4double ElectKineEnergy = max(0.,ElectTotEnergy - electron_mass_c2);
|
|
|
|
G4ThreeVector ElectDirection (dxEl, dyEl, dzEl);
|
|
ElectDirection.rotateUz(GammaDirection);
|
|
|
|
// create G4DynamicParticle object for the particle1
|
|
G4DynamicParticle* aParticle1= new G4DynamicParticle(
|
|
theElectron,ElectDirection,ElectKineEnergy);
|
|
|
|
// the e+ is always created (even with Ekine=0) for further annihilation.
|
|
|
|
G4double PositKineEnergy = max(0.,PositTotEnergy - electron_mass_c2);
|
|
|
|
G4ThreeVector PositDirection (dxPo, dyPo, dzPo);
|
|
PositDirection.rotateUz(GammaDirection);
|
|
|
|
// create G4DynamicParticle object for the particle2
|
|
G4DynamicParticle* aParticle2= new G4DynamicParticle(
|
|
thePositron,PositDirection,PositKineEnergy);
|
|
|
|
// Fill output vector
|
|
fvect->push_back(aParticle1);
|
|
fvect->push_back(aParticle2);
|
|
|
|
// kill incident photon
|
|
fParticleChange->SetProposedKineticEnergy(0.);
|
|
fParticleChange->ProposeTrackStatus(fStopAndKill);
|
|
}
|
|
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
|
|
|
|
|
|
void G4PairProductionRelModel::SetupForMaterial(const G4ParticleDefinition*,
|
|
const G4Material* mat, G4double)
|
|
{
|
|
lpmEnergy = mat->GetRadlen()*fLPMconstant;
|
|
// G4cout<<" lpmEnergy="<<lpmEnergy<<G4endl;
|
|
}
|
|
|
|
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
|