G4PairProductionRelModel.cc

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// $Id$
//
// -------------------------------------------------------------------
//
// 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.
//
// -------------------------------------------------------------------
//
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#include "G4PairProductionRelModel.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "G4Gamma.hh"
#include "G4Electron.hh"
#include "G4Positron.hh"
 
#include "G4ParticleChangeForGamma.hh"
#include "G4LossTableManager.hh"
 
 
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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;
 
}
 
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G4PairProductionRelModel::~G4PairProductionRelModel()
{}
 
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void G4PairProductionRelModel::Initialise(const G4ParticleDefinition* p,
                      const G4DataVector& cuts)
{
  if(!fParticleChange) { fParticleChange = GetParticleChangeForGamma(); }
  InitialiseElementSelectors(p, cuts);
}
 
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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;
}
 
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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;
 
}
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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;
 
}
 
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void  
G4PairProductionRelModel::CalcLPMFunctions(G4double k, G4double eplusEnergy)
{
  // *** calculate lpm variable s & sprime ***
  // Klein eqs. (78) & (79)
  G4double sprime = sqrt(0.125*k*lpmEnergy/(eplusEnergy*(k-eplusEnergy)));
 
  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 s0 = sprime/sqrt(xiLPM); 
  //   G4cout<<"k="<<k<<" y="<<eplusEnergy/k<<G4endl;
  //   G4cout<<"s0="<<s0<<G4endl;
  
  // *** calculate supression functions phi and G ***
  // Klein eqs. (77)
  G4double s2=s0*s0;
  G4double s3=s0*s2;
  G4double s4=s2*s2;
 
  if (s0<0.1) {
    // high suppression limit
    phiLPM = 6.*s0 - 18.84955592153876*s2 + 39.47841760435743*s3 
      - 57.69873135166053*s4;
    gLPM = 37.69911184307752*s2 - 236.8705056261446*s3 + 807.7822389*s4;
  }
  else if (s0<1.9516) {
    // intermediate suppression
    // using eq.77 approxim. valid s0<2.      
    phiLPM = 1.-exp(-6.*s0*(1.+(3.-pi)*s0)
        +s3/(0.623+0.795*s0+0.658*s2));
    if (s0<0.415827397755) {
      // using eq.77 approxim. valid 0.07<s<2
      G4double psiLPM = 1-exp(-4*s0-8*s2/(1+3.936*s0+4.97*s2-0.05*s3+7.50*s4));
      gLPM = 3*psiLPM-2*phiLPM;
    }
    else {
      // using alternative parametrisiation
      G4double pre = -0.16072300849123999 + s0*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. || s0>0.57)  xiLPM=1./phiLPM;
}
 
 
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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;
}
 
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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....