G4eplusTo3GammaOKVIModel.cc

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// -------------------------------------------------------------------
//
// GEANT4 Class file
//
//
// File name:   G4eplusTo3GammaOKVIModel
//
// Authors:  Andrei Alkin, Vladimir Ivanchenko, Omrame Kadri
//
// Creation date: 29.03.2018
//
// -------------------------------------------------------------------
//
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#include "G4eplusTo3GammaOKVIModel.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "G4EmParameters.hh"
#include "G4TrackStatus.hh"
#include "G4Electron.hh"
#include "G4Positron.hh"
#include "G4Gamma.hh"
#include "Randomize.hh"
#include "G4ParticleChangeForGamma.hh"
#include "G4Log.hh"
#include "G4Exp.hh"
 
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using namespace std;
 
G4eplusTo3GammaOKVIModel::G4eplusTo3GammaOKVIModel(const G4ParticleDefinition*,
                                                   const G4String& nam)
  : G4VEmModel(nam), fDelta(0.001)
{
  theGamma = G4Gamma::Gamma();
}
 
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G4eplusTo3GammaOKVIModel::~G4eplusTo3GammaOKVIModel() = default;
 
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void G4eplusTo3GammaOKVIModel::Initialise(const G4ParticleDefinition*,
                      const G4DataVector&)
{}
 
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// (A.A.) F_{ijk} calculation method
G4double G4eplusTo3GammaOKVIModel::ComputeF(G4double fr1, G4double fr2, 
                                            G4double fr3, G4double kinEnergy) 
{
  G4double ekin   = std::max(eV,kinEnergy);
  G4double tau    = ekin/electron_mass_c2;
  G4double gam    = tau + 1.0;
  G4double gamma2 = gam*gam;
  G4double bg2    = tau * (tau+2.0);
  G4double bg     = sqrt(bg2);
 
  G4double rho = (gamma2+4.*gam+1.)*G4Log(gam+bg)/(gamma2-1.) 
    - (gam+3.)/(sqrt(gam*gam - 1.)) + 1.;   
  G4double border;
 
  if(ekin < 500*MeV) { 
    border = 1. - (electron_mass_c2)/(2*(ekin + electron_mass_c2)); 
  } else { 
    border = 1. - (100*electron_mass_c2)/(2*(ekin + electron_mass_c2)); 
  }
 
  border = std::min(border, 0.9999);
 
  if (fr1>border)  { fr1 = border; }
  if (fr2>border)  { fr2 = border; }
  if (fr3>border)  { fr3 = border; }
 
  G4double  fr1s = fr1*fr1; // "s" for "squared" 
  G4double  fr2s = fr2*fr2;
  G4double  fr3s = fr3*fr3; 
 
  G4double  aa = (1.-fr1)*(1.-fr2);
  G4double  ab = fr3s + (fr1-fr2)*(fr1-fr2);
  G4double  add= ((1.-fr1)*(1.-fr1) + (1.-fr2)*(1.-fr2))/(fr3s*aa);
 
  G4double  fres = -rho*(1./fr1s + 1./fr2s) 
    + (ab/(2.*(fr1*fr2*aa)))*(G4Log(2.*gam*aa/(fr1*fr2))) 
    + (ab/(2.*fr1*fr2*(1-fr3)))*G4Log(2.*gam*(1.-fr3)/(fr1*fr2)) - add;
 
  return fres;
}
 
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// (A.A.) F_{ijk} calculation method
G4double G4eplusTo3GammaOKVIModel::ComputeF0(G4double fr1, G4double fr2, 
                                             G4double fr3) 
{
  G4double tau    = 0.0;
  G4double gam    = tau + 1.0;
  G4double gamma2 = gam*gam;
  G4double bg2    = tau * (tau+2.0);
  G4double bg     = sqrt(bg2);
 
  G4double rho = (gamma2+4.*gam+1.)*G4Log(gam+bg)/(gamma2-1.) 
    - (gam+3.)/(sqrt(gam*gam - 1.)) + 1.;   
  G4double border = 0.5;
 
  if (fr1>border)  { fr1 = border; }
  if (fr2>border)  { fr2 = border; }
  if (fr3>border)  { fr3 = border; }
 
  G4double  fr1s = fr1*fr1; // "s" for "squared" 
  G4double  fr2s = fr2*fr2;
  G4double  fr3s = fr3*fr3; 
 
  G4double  aa = (1.-fr1)*(1.-fr2);
  G4double  ab = fr3s + (fr1-fr2)*(fr1-fr2);
  G4double  add= ((1.-fr1)*(1.-fr1) + (1.-fr2)*(1.-fr2))/(fr3s*aa);
 
  G4double  fres = -rho*(1./fr1s + 1./fr2s) 
    + (ab/(2.*(fr1*fr2*aa)))*(G4Log(2.*gam*aa/(fr1*fr2))) 
    + (ab/(2.*fr1*fr2*(1-fr3)))*G4Log(2.*gam*(1.-fr3)/(fr1*fr2)) - add;
 
  return fres;
}
 
//(A.A.) diff x-sections for maximum search and rejection
G4double G4eplusTo3GammaOKVIModel::ComputeFS(G4double fr1, 
         G4double fr2, G4double fr3, G4double kinEnergy) 
{
  G4double ekin  = std::max(eV,kinEnergy);   
  G4double tau   = ekin/electron_mass_c2;
  G4double gam   = tau + 1.0;  
 
  G4double fsum = fr1*fr1*(ComputeF(fr1,fr2,fr3,ekin) + 
               ComputeF(fr3,fr1,fr2,ekin) + 
               ComputeF(fr2,fr3,fr1,ekin));
 
  G4double dcross = fsum/((3*fr1*fr1*(gam+1.)));
 
  return dcross;
}
 
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G4double 
G4eplusTo3GammaOKVIModel::ComputeCrossSectionPerElectron(G4double kinEnergy)
{
  // Calculates the cross section per electron of annihilation into 3 photons
  // from the Heilter formula.
 
  G4double ekin   = std::max(CLHEP::eV, kinEnergy);   
  G4double tau    = ekin/CLHEP::electron_mass_c2;
  G4double gam    = tau + 1.0;
  G4double gamma2 = gam*gam;
  G4double bg2    = tau * (tau+2.0);
  G4double bg     = sqrt(bg2);
  
  G4double rho = (gamma2+4*gam+1.)*G4Log(gam+bg)/(gamma2-1.) 
    - (gam+3.)/(sqrt(gam*gam - 1.));
 
  G4double cross = alpha_rcl2*(4.2 - (2.*G4Log(fDelta)+1.)*rho*rho)/(gam+1.);
  return cross;  
}
 
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G4double G4eplusTo3GammaOKVIModel::ComputeCrossSectionPerAtom(
                                    const G4ParticleDefinition*,
                                    G4double kineticEnergy, G4double Z,
                    G4double, G4double, G4double)
{
  G4double cross = Z*ComputeCrossSectionPerElectron(kineticEnergy);
  return cross;  
}
 
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G4double G4eplusTo3GammaOKVIModel::CrossSectionPerVolume(
                    const G4Material* material,
                    const G4ParticleDefinition*,
                          G4double kineticEnergy,
                          G4double, G4double)
{
  // Calculates the cross section per volume of annihilation into two photons
  
  G4double eDensity = material->GetElectronDensity();
  G4double cross = eDensity*ComputeCrossSectionPerElectron(kineticEnergy);
  return cross;
}
 
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// Polarisation of gamma according to M.H.L.Pryce and J.C.Ward, 
// Nature 4065 (1947) 435.
 
void 
G4eplusTo3GammaOKVIModel::SampleSecondaries(vector<G4DynamicParticle*>* vdp,
                        const G4MaterialCutsCouple*,
                        const G4DynamicParticle* dp,
                        G4double, G4double)
{
  // let us perform sampling in C.M.S. reference frame of e- at rest and e+ on fly
  G4double posiKinEnergy = dp->GetKineticEnergy();
  G4LorentzVector lv(dp->GetMomentum(),
             posiKinEnergy + 2*CLHEP::electron_mass_c2);
  G4double eGammaCMS = 0.5 * lv.mag();
 
  // the limit value fDelta is defined by a class, which call this method
  // thickness of border defined by C.M.S. energy
  G4double border =
    1.0 - std::min(std::max(CLHEP::electron_mass_c2/eGammaCMS, fDelta), 0.1);
 
  CLHEP::HepRandomEngine* rndmEngine = G4Random::getTheEngine();
   
  G4ThreeVector posiDirection = dp->GetMomentumDirection();
 
  // (A.A.) LIMITS FOR 1st GAMMA
  G4double xmin = 0.01;
  G4double xmax = 0.667;   // CHANGE to 3/2 
  
  G4double d1, d0, x1, x2, dmax, x2min;
 
  // (A.A.) sampling of x1 x2 x3 (whole cycle of rejection)
  do {
    x1 = 1./((1./xmin) - ((1./xmin)-(1./xmax))*rndmEngine->flat()); 
    dmax = ComputeFS(eGammaCMS, x1, 1.-x1, border);
    x2min = 1. - x1;
    x2 = 1 - rndmEngine->flat()*(1. - x2min);
    d1 = dmax*rndmEngine->flat();
    d0 = ComputeFS(eGammaCMS, x1, x2, 2.-x1-x2);
  }  
  while(d0 < d1);
 
  G4double x3 = 2 - x1 - x2;
  //
  // angles between Gammas  
  //
  G4double psi13 = 2*std::asin(std::sqrt(std::abs((x1+x3-1.)/(x1*x3))));
  G4double psi12 = 2*std::asin(std::sqrt(std::abs((x1+x2-1.)/(x1*x2))));
  //
  // kinematic of the created pair
  //
  G4double phot1Energy = x1*eGammaCMS;      
  G4double phot2Energy = x2*eGammaCMS;
  G4double phot3Energy = x3*eGammaCMS;
    
  // DIRECTIONS
    
  // The azimuthal angles of q1 and q3 with respect to some plane 
  // through the beam axis are generated at random. 
 
  G4ThreeVector phot1Direction(0, 0, 1);
  G4ThreeVector phot2Direction(0, std::sin(psi12), std::cos(psi12));
  G4ThreeVector phot3Direction(0, std::sin(psi13), std::cos(psi13));
 
  G4LorentzVector lv1(phot1Energy*phot1Direction, phot1Energy);
  G4LorentzVector lv2(phot2Energy*phot2Direction, phot2Energy);
  G4LorentzVector lv3(phot3Energy*phot3Direction, phot3Energy);
 
  auto boostV = lv.boostVector();
  lv1.boost(boostV);
  lv2.boost(boostV);
  lv3.boost(boostV);
 
  auto aGamma1 = new G4DynamicParticle (theGamma, lv1.vect());
  auto aGamma2 = new G4DynamicParticle (theGamma, lv2.vect());
  auto aGamma3 = new G4DynamicParticle (theGamma, lv3.vect());
    
  //!!! POLARIZATION - not yet implemented
 
  vdp->push_back(aGamma1);
  vdp->push_back(aGamma2);
  vdp->push_back(aGamma3);
}
 
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