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Cross-Referencing   Geant4
Geant4/processes/electromagnetic/standard/src/G4AllisonPositronAtRestModel.cc

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  //
  //
  // GEANT4 Class file
  //
  //
  // File name:     G4AllisonPositronAtRestModel
  //
  // Author:        Vladimir Ivanchenko
  // 
  // Creation date: 14 May 2024
  //
  // -------------------------------------------------------------------
  //
  
  #include "G4AllisonPositronAtRestModel.hh"
  #include "G4DynamicParticle.hh"
  #include "G4Material.hh"
  #include "Randomize.hh"
  #include "G4Gamma.hh"
  #include "G4RandomDirection.hh"
  #include "G4ThreeVector.hh"
  #include "G4PhysicalConstants.hh"
  #include "G4SystemOfUnits.hh"
  
  //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
  
  G4AllisonPositronAtRestModel::G4AllisonPositronAtRestModel()
    : G4VPositronAtRestModel("Allison")
  {}    
  
  //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
  
  void G4AllisonPositronAtRestModel::SampleSecondaries(
               std::vector<G4DynamicParticle*>& secParticles,
               G4double&, const G4Material* material) const
  {
    const G4double eGamma = CLHEP::electron_mass_c2;
  
    // In rest frame of positronium gammas are back to back
    const G4ThreeVector& dir1 = G4RandomDirection();
    const G4ThreeVector& dir2 = -dir1;
    auto aGamma1 = new G4DynamicParticle(G4Gamma::Gamma(),dir1,eGamma);
    auto aGamma2 = new G4DynamicParticle(G4Gamma::Gamma(),dir2,eGamma);
  
    // In rest frame the gammas are polarised perpendicular to each other - see
    // Pryce and Ward, Nature No 4065 (1947) p.435.
    // Snyder et al, Physical Review 73 (1948) p.440.
    G4ThreeVector pol1 = (G4RandomDirection().cross(dir1)).unit();
    G4ThreeVector pol2 = (pol1.cross(dir2)).unit();
  
    // A positron in matter slows down and combines with an atomic electron to
    // make a neutral atom called positronium, about half the size of a normal
    // atom. I expect that when the energy of the positron is small enough,
    // less than the binding energy of positronium (6.8 eV), it is
    // energetically favourable for an electron from the outer orbitals of a
    // nearby atom or molecule to transfer and bind to the positron, as in an
    // ionic bond, leaving behind a mildly ionised nearby atom/molecule. I
    // would expect the positronium to come away with a kinetic energy of a
    // few eV on average. In its para (spin 0) state it annihilates into two
    // photons, which in the rest frame of the positronium are collinear
    // (back-to-back) due to momentum conservation. Because of the motion of the
    // positronium, photons will be not quite back-to-back in the laboratory.
  
    // The positroniuim acquires an energy of order its binding energy and
    // doesn't have time to thermalise. Nevertheless, here we approximate its
    // energy distribution by a Maxwell-Boltzman with mean energy <KE>. In terms
    // of a more familiar concept of temperature, and the law of equipartition
    // of energy of translational motion, <KE>=3kT/2. Each component of velocity
    // has a distribution exp(-mv^2/2kT), which is a Gaussian of mean zero
    // and variance kT/m=2<KE>/3m, where m is the positronium mass.
  
    const G4double meanEnergyPerIonPair = material->GetIonisation()->GetMeanEnergyPerIonPair();
    const G4double& meanKE = meanEnergyPerIonPair;  // Just an alias
  
    if (meanKE > 0.) {  // Positronium has motion
     // Mass of positronium
     const G4double mass = 2.*CLHEP::electron_mass_c2;
     // Mean <KE>=3kT/2, as described above
     // const G4double T = 2.*meanKE/(3.*k_Boltzmann);
     // Component velocities: Gaussian, variance kT/m=2<KE>/3m.
     const G4double sigmav = std::sqrt(2.*meanKE/(3.*mass));
     // This is in units where c=1
     const G4double vx = G4RandGauss::shoot(0.,sigmav);
     const G4double vy = G4RandGauss::shoot(0.,sigmav);
     const G4double vz = G4RandGauss::shoot(0.,sigmav);
     const G4ThreeVector v(vx,vy,vz);  // In unit where c=1
     const G4ThreeVector& beta = v;    // so beta=v/c=v
     aGamma1->Set4Momentum(aGamma1->Get4Momentum().boost(beta));
     aGamma2->Set4Momentum(aGamma2->Get4Momentum().boost(beta));
 
     // Rotate polarisation vectors
     const G4ThreeVector& newDir1 = aGamma1->GetMomentumDirection();
     const G4ThreeVector& newDir2 = aGamma2->GetMomentumDirection();
     const G4ThreeVector& axis1 = dir1.cross(newDir1);  // No need to be unit
     const G4ThreeVector& axis2 = dir2.cross(newDir2);  // No need to be unit
     const G4double& angle1 = std::acos(dir1*newDir1);
     const G4double& angle2 = std::acos(dir2*newDir2);
     pol1.rotate(axis1, angle1);
     pol2.rotate(axis2, angle2);
   }
 
   // use constructors optimal for massless particle
   aGamma1->SetPolarization(pol1);
   aGamma2->SetPolarization(pol2);
 
   secParticles.push_back(aGamma1);
   secParticles.push_back(aGamma2);
 }
 
 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
 
 void G4AllisonPositronAtRestModel::PrintGeneratorInformation() const
 {
   G4cout << "\n" << G4endl;
   G4cout << "Allison AtRest positron 2-gamma annihilation model." << G4endl;
   G4cout << "Takes into account positronium motion in the media." << G4endl;
 } 
 
 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....