G4KleinNishinaModel.cc

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// $Id$
//
// -------------------------------------------------------------------
//
// GEANT4 Class file
//
//
// File name:     G4KleinNishinaModel
//
// Author:        Vladimir Ivanchenko on base of G4KleinNishinaCompton
//
// Creation date: 13.06.2010
//
// Modifications:
//
// Class Description:
//
// -------------------------------------------------------------------
//
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#include "G4KleinNishinaModel.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "G4Electron.hh"
#include "G4Gamma.hh"
#include "Randomize.hh"
#include "G4RandomDirection.hh"
#include "G4DataVector.hh"
#include "G4ParticleChangeForGamma.hh"
#include "G4VAtomDeexcitation.hh"
#include "G4AtomicShells.hh"
#include "G4LossTableManager.hh"

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using namespace std;

G4KleinNishinaModel::G4KleinNishinaModel(const G4String& nam)
  : G4VEmModel(nam)
{
  theGamma = G4Gamma::Gamma();
  theElectron = G4Electron::Electron();
  lowestGammaEnergy = 1.0*eV;
  limitFactor       = 4;
  fProbabilities.resize(9,0.0);
  SetDeexcitationFlag(true);
  fParticleChange = 0;
  fAtomDeexcitation = 0;
}

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G4KleinNishinaModel::~G4KleinNishinaModel()
{}

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void G4KleinNishinaModel::Initialise(const G4ParticleDefinition* p,
                                     const G4DataVector& cuts)
{
  fAtomDeexcitation = G4LossTableManager::Instance()->AtomDeexcitation();
  InitialiseElementSelectors(p, cuts);
  if(!fParticleChange) { fParticleChange = GetParticleChangeForGamma(); }
}

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G4double 
G4KleinNishinaModel::ComputeCrossSectionPerAtom(const G4ParticleDefinition*,
                                                G4double GammaEnergy,
                                                G4double Z, G4double,
                                                G4double, G4double)
{
  G4double xSection = 0.0 ;
  if ( Z < 0.9999 || GammaEnergy < 0.1*keV) { return xSection; }

  static const G4double a = 20.0 , b = 230.0 , c = 440.0;
  
  static const G4double
    d1= 2.7965e-1*barn, d2=-1.8300e-1*barn, d3= 6.7527   *barn, d4=-1.9798e+1*barn,
    e1= 1.9756e-5*barn, e2=-1.0205e-2*barn, e3=-7.3913e-2*barn, e4= 2.7079e-2*barn,
    f1=-3.9178e-7*barn, f2= 6.8241e-5*barn, f3= 6.0480e-5*barn, f4= 3.0274e-4*barn;
     
  G4double p1Z = Z*(d1 + e1*Z + f1*Z*Z), p2Z = Z*(d2 + e2*Z + f2*Z*Z),
           p3Z = Z*(d3 + e3*Z + f3*Z*Z), p4Z = Z*(d4 + e4*Z + f4*Z*Z);

  G4double T0  = 15.0*keV; 
  if (Z < 1.5) { T0 = 40.0*keV; } 

  G4double X   = max(GammaEnergy, T0) / electron_mass_c2;
  xSection = p1Z*std::log(1.+2.*X)/X
               + (p2Z + p3Z*X + p4Z*X*X)/(1. + a*X + b*X*X + c*X*X*X);
                
  //  modification for low energy. (special case for Hydrogen)
  if (GammaEnergy < T0) {
    G4double dT0 = keV;
    X = (T0+dT0) / electron_mass_c2 ;
    G4double sigma = p1Z*log(1.+2*X)/X
                    + (p2Z + p3Z*X + p4Z*X*X)/(1. + a*X + b*X*X + c*X*X*X);
    G4double   c1 = -T0*(sigma-xSection)/(xSection*dT0);             
    G4double   c2 = 0.150; 
    if (Z > 1.5) { c2 = 0.375-0.0556*log(Z); }
    G4double    y = log(GammaEnergy/T0);
    xSection *= exp(-y*(c1+c2*y));          
  }

  if(xSection < 0.0) { xSection = 0.0; }
  //  G4cout << "e= " << GammaEnergy << " Z= " << Z 
  //  << " cross= " << xSection << G4endl;
  return xSection;
}

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void G4KleinNishinaModel::SampleSecondaries(
                             std::vector<G4DynamicParticle*>* fvect,
                             const G4MaterialCutsCouple* couple,
                             const G4DynamicParticle* aDynamicGamma,
                             G4double,
                             G4double)
{
  // primary gamma
  G4double energy = aDynamicGamma->GetKineticEnergy();
  G4ThreeVector direction = aDynamicGamma->GetMomentumDirection();

  // select atom
  const G4Element* elm = SelectRandomAtom(couple, theGamma, energy);

  // select shell first
  G4int nShells = elm->GetNbOfAtomicShells();
  if(nShells > (G4int)fProbabilities.size()) { fProbabilities.resize(nShells); }
  G4double totprob = 0.0;
  G4int i;
  for(i=0; i<nShells; ++i) {
    //G4double bindingEnergy = elm->GetAtomicShell(i);
    totprob += elm->GetNbOfShellElectrons(i);
    //totprob += elm->GetNbOfShellElectrons(i)/(bindingEnergy*bindingEnergy);
    fProbabilities[i] = totprob; 
  }
  //if(totprob == 0.0) { return; }

  // Loop on sampling
  //  const G4int nlooplim = 100;
  //G4int nloop = 0;

  G4double bindingEnergy, ePotEnergy, eKinEnergy;
  G4double gamEnergy0, gamEnergy1;

  //static const G4double eminus2 =  1.0 - exp(-2.0);

  do {
    //++nloop;
    G4double xprob = totprob*G4UniformRand();

    // select shell
    for(i=0; i<nShells; ++i) { if(xprob <= fProbabilities[i]) { break; } }
   
    bindingEnergy = elm->GetAtomicShell(i);
    //    ePotEnergy    = bindingEnergy;
    //    gamEnergy0 = energy;
    lv1.set(0.0,0.0,energy,energy);

    //G4cout << "nShells= " << nShells << " i= " << i 
    //   << " Egamma= " << energy << " Ebind= " << bindingEnergy
    //   << " Elim= " << limitEnergy 
    //   << G4endl;

    // for rest frame of the electron
    G4double x = -log(G4UniformRand());
    eKinEnergy = bindingEnergy*x;
    ePotEnergy = bindingEnergy*(1.0 + x);

    // for rest frame of the electron
    G4double eTotMomentum = sqrt(eKinEnergy*(eKinEnergy + 2*electron_mass_c2));
    G4double phi = G4UniformRand()*twopi;
    G4double costet = 2*G4UniformRand() - 1;
    G4double sintet = sqrt((1 - costet)*(1 + costet));
    lv2.set(eTotMomentum*sintet*cos(phi),eTotMomentum*sintet*sin(phi),
            eTotMomentum*costet,eKinEnergy + electron_mass_c2);
    bst = lv2.boostVector();
    lv1.boost(-bst);

    gamEnergy0 = lv1.e();
   
    // In the rest frame of the electron
    // The scattered gamma energy is sampled according to Klein-Nishina formula
    // The random number techniques of Butcher & Messel are used 
    // (Nuc Phys 20(1960),15). 
    G4double E0_m = gamEnergy0/electron_mass_c2;

    //
    // sample the energy rate of the scattered gamma 
    //

    G4double epsilon, epsilonsq, onecost, sint2, greject ;

    G4double eps0       = 1./(1 + 2*E0_m);
    G4double epsilon0sq = eps0*eps0;
    G4double alpha1     = - log(eps0);
    G4double alpha2     = 0.5*(1 - epsilon0sq);

    do {
      if ( alpha1/(alpha1+alpha2) > G4UniformRand() ) {
        epsilon   = exp(-alpha1*G4UniformRand());   // epsilon0**r
        epsilonsq = epsilon*epsilon; 

      } else {
        epsilonsq = epsilon0sq + (1.- epsilon0sq)*G4UniformRand();
        epsilon   = sqrt(epsilonsq);
      }

      onecost = (1.- epsilon)/(epsilon*E0_m);
      sint2   = onecost*(2.-onecost);
      greject = 1. - epsilon*sint2/(1.+ epsilonsq);

    } while (greject < G4UniformRand());
    gamEnergy1 = epsilon*gamEnergy0;
 
    // before scattering total 4-momentum in e- system
    lv2.set(0.0,0.0,0.0,electron_mass_c2);
    lv2 += lv1;
 
    //
    // scattered gamma angles. ( Z - axis along the parent gamma)
    //
    if(sint2 < 0.0) { sint2 = 0.0; }
    costet = 1. - onecost; 
    sintet = sqrt(sint2);
    phi  = twopi * G4UniformRand();

    // e- recoil
    //
    // in  rest frame of the electron
    G4ThreeVector gamDir = lv1.vect().unit();
    G4ThreeVector v = G4ThreeVector(sintet*cos(phi),sintet*sin(phi),costet);
    v.rotateUz(gamDir);
    lv1.set(gamEnergy1*v.x(),gamEnergy1*v.y(),gamEnergy1*v.z(),gamEnergy1);
    lv2 -= lv1;
    //G4cout<<"Egam= "<<lv1.e()<<" Ee= "<< lv2.e()-electron_mass_c2 << G4endl;
    lv2.boost(bst);
    eKinEnergy = lv2.e() - electron_mass_c2 - ePotEnergy;   
    //G4cout << "eKinEnergy= " << eKinEnergy << G4endl;

  } while ( eKinEnergy < 0.0 );

  //
  // update G4VParticleChange for the scattered gamma
  //
   
  lv1.boost(bst);
  gamEnergy1 = lv1.e();
  if(gamEnergy1 > lowestGammaEnergy) {
    G4ThreeVector gamDirection1 = lv1.vect().unit();
    gamDirection1.rotateUz(direction);
    fParticleChange->ProposeMomentumDirection(gamDirection1);
  } else { 
    fParticleChange->ProposeTrackStatus(fStopAndKill);
    gamEnergy1 = 0.0;
  }
  fParticleChange->SetProposedKineticEnergy(gamEnergy1);

  //
  // kinematic of the scattered electron
  //

  if(eKinEnergy > lowestGammaEnergy) {
    G4ThreeVector eDirection = lv2.vect().unit();
    eDirection.rotateUz(direction);
    G4DynamicParticle* dp = 
      new G4DynamicParticle(theElectron,eDirection,eKinEnergy);
    fvect->push_back(dp);
  } else { eKinEnergy = 0.0; }

  G4double edep = energy - gamEnergy1 - eKinEnergy;
  
  // sample deexcitation
  //
  if(fAtomDeexcitation) {
    G4int index = couple->GetIndex();
    if(fAtomDeexcitation->CheckDeexcitationActiveRegion(index)) {
      G4int Z = G4lrint(elm->GetZ());
      G4AtomicShellEnumerator as = G4AtomicShellEnumerator(i);
      const G4AtomicShell* shell = fAtomDeexcitation->GetAtomicShell(Z, as);
      size_t nbefore = fvect->size();
      fAtomDeexcitation->GenerateParticles(fvect, shell, Z, index);
      size_t nafter = fvect->size();
      if(nafter > nbefore) {
        for (size_t j=nbefore; j<nafter; ++j) {
          edep -= ((*fvect)[j])->GetKineticEnergy();
        } 
      }
    }
  }
  // energy balance
  if(edep < 0.0) { edep = 0.0; }
  fParticleChange->ProposeLocalEnergyDeposit(edep);
}

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