G4PolarizedAnnihilationCrossSection.cc

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// -------------------------------------------------------------------
// $Id: G4PolarizedAnnihilationCrossSection.cc 68046 2013-03-13 14:31:38Z gcosmo $
// -------------------------------------------------------------------
//
// GEANT4 Class file
//
//
// File name:     G4PolarizedAnnihilationCrossSection
//
// Author:        Andreas Schaelicke
//
// Creation date: 22.03.2006
//
// Modifications:
//   24-03-06 included cross section as given in W.McMaster, Nuovo Cimento 7, 1960, 395
//   27-07-06 new calculation by P.Starovoitov
//   15.10.07 introduced a more general framework for cross sections (AS)
//   16.10.07 some minor corrections in formula longPart
//
// Class Description:
//   * calculates the differential cross section in e+e- -> gamma gamma
//

#include "G4PolarizedAnnihilationCrossSection.hh"
#include "G4PhysicalConstants.hh"

G4PolarizedAnnihilationCrossSection::G4PolarizedAnnihilationCrossSection() :
  polxx(0.), polyy(0.), polzz(0.), polxz(0.), polzx(0.), polxy(0.), 
  polyx(0.), polyz(0.), polzy(0.),
  re2(1.), diffXSFactor(1.), totalXSFactor(1.),
  phi0(0.)
{
  re2 = classic_electr_radius * classic_electr_radius;
  phi2 = G4ThreeVector(0., 0., 0.);
  phi3 = G4ThreeVector(0., 0., 0.);
  dice = 0.;
  polXS= 0.;
  unpXS = 0.;
  ISPxx=ISPyy=ISPzz=ISPnd=0.;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4PolarizedAnnihilationCrossSection::~G4PolarizedAnnihilationCrossSection()
{
}

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void G4PolarizedAnnihilationCrossSection::TotalXS()
{
  // total cross section is sum of
  //  + unpol xsec  "sigma0"
  //  + longitudinal polarised cross section "sigma_zz" times pol_3(e-)*pol_3(e+)
  //  + transverse contribution "(sigma_xx+sigma_yy)/2" times pol_T(e-)*pol_T(e+)
  //     (Note: if both beams are transversely polarised, i.e. pol_T(e-)!=0 and 
  //      pol_T(e+)!=0, and sigma_xx!=sigma_yy, then the diff. cross section will
  //      exhibit a azimuthal asymmetry even if pol_T(e-)*pol_T(e+)==0)


}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

void G4PolarizedAnnihilationCrossSection::Initialize(
                          G4double eps,
                          G4double gam,
                          G4double , // phi
                    const G4StokesVector & pol0, // positron polarization
                    const G4StokesVector & pol1, // electron polarization
                          G4int flag)
{

  diffXSFactor=re2/(gam - 1.);
  DefineCoefficients(pol0,pol1);
  //  
  // prepare dicing
  //
  dice = 0.;
  G4double symmXS = 0.125*((-1./sqr(gam + 1.))/sqr(eps) + 
                           ((sqr(gam) + 4.*gam - 1.)/sqr(gam + 1.))/eps - 1.);
  //
  //
  //
  G4ThreeVector epsVector(1./sqr(eps), 1./eps, 1.);
  G4ThreeVector oneEpsVector(1./sqr(1. - eps), 1./(1.-eps), 1.);
  G4ThreeVector sumEpsVector(epsVector + oneEpsVector);
  G4ThreeVector difEpsVector(epsVector - oneEpsVector);
  G4ThreeVector calcVector(0., 0., 0.);
  //
  // temporary variables
  //
  G4double helpVar2 = 0., helpVar1 = 0.;
  //
  // unpolarised contribution
  //
  helpVar1 = (gam*gam + 4.*gam + 1.)/sqr(gam + 1.);
  helpVar2 = -1./sqr(gam + 1.);
  calcVector = G4ThreeVector(helpVar2, helpVar1, -1.);
  unpXS = 0.125 * calcVector * sumEpsVector;

  // initial particles polarised contribution
  helpVar2 = 1./sqr(gam + 1.);
  helpVar1 = -(gam*gam + 4.*gam + 1.)/sqr(gam + 1.);
  calcVector = G4ThreeVector(helpVar2, helpVar1, 0.5*(gam + 3.));
  ISPxx = 0.25*(calcVector * sumEpsVector)/(gam - 1.);

  helpVar1 = 1./sqr(gam + 1.);
  calcVector = G4ThreeVector(-helpVar1, 2.*gam*helpVar1, -1.);
  ISPyy = 0.125 * calcVector * sumEpsVector;

  helpVar1 = 1./(gam - 1.);
  helpVar2 = 1./sqr(gam + 1.);
  calcVector = G4ThreeVector(-(gam*gam + 1.)*helpVar2,(gam*gam*(gam + 1.) + 7.*gam + 3.)*helpVar2, -(gam + 3.));
  ISPzz = 0.125*helpVar1*(calcVector * sumEpsVector);

  helpVar1 = std::sqrt(std::fabs(eps*(1. - eps)*2.*(gam + 1.) - 1.));
  calcVector = G4ThreeVector(-1./(gam*gam - 1.), 2./(gam - 1.), 0.);
  ISPnd = 0.125*(calcVector * difEpsVector) * helpVar1;

  polXS = 0.;  
  polXS += ISPxx*polxx;
  polXS += ISPyy*polyy;
  polXS += ISPzz*polzz;
  polXS += ISPnd*(polzx + polxz);
  phi0 = unpXS + polXS;
  dice = symmXS;
  //  if(polzz != 0.) dice *= (1. + std::fabs(polzz*ISPzz/unpXS));
  if(polzz != 0.) {
    dice *= (1. + (polzz*ISPzz/unpXS));
    if (dice<0.) dice=0.;
  }
    // prepare final state coefficients
  if (flag==2) {
    //
    // circular polarisation
    //
    G4double circ1 = 0., circ2 = 0., circ3 = 0.;
    helpVar1 = 8.*sqr(1. - eps)*sqr(eps)*(gam - 1.)*sqr(gam + 1.)/std::sqrt(gam*gam - 1.);
    helpVar2 =  sqr(gam + 1.)*sqr(eps)*(-2.*eps + 3.) - (gam*gam + 3.*gam + 2.)*eps;
    circ1 = helpVar2 + gam;
    circ1 /= helpVar1;
    circ2 = helpVar2 + 1.;
    circ2 /= helpVar1;
    helpVar1 = std::sqrt(std::fabs(eps*(1. - eps)*2.*(gam + 1.) - 1.));
    helpVar1 /= std::sqrt(gam*gam - 1.);
    calcVector = G4ThreeVector(1., -2.*gam, 0.);
    circ3 = 0.125*(calcVector * sumEpsVector)/(gam + 1.);
    circ3 *= helpVar1;

    phi2.setZ( circ2*pol1.z() + circ1*pol0.z() + circ3*(pol1.x() + pol0.x()));
    phi3.setZ(-circ1*pol1.z() - circ2*pol0.z() - circ3*(pol1.x() + pol0.x()));
    //
    // common to both linear polarisation
    //
    calcVector = G4ThreeVector(-1., 2.*gam, 0.);
    G4double linearZero = 0.125*(calcVector * sumEpsVector)/sqr(gam + 1.);
    //   
    //        Linear Polarisation #1 
    //
    helpVar1 = std::sqrt(std::fabs(2.*(gam + 1.)*(1. - eps)*eps - 1.))/((gam + 1.)*eps*(1. - eps));
    helpVar2 = helpVar1*helpVar1;
    //
    // photon 1
    //
    G4double diagContrib = 0.125*helpVar2*(polxx + polyy - polzz);
    G4double nonDiagContrib = 0.125*helpVar1*(-polxz/(1. - eps) + polzx/eps);

    phi2.setX(linearZero + diagContrib + nonDiagContrib);
    //
    // photon 2
    //
    nonDiagContrib = 0.125*helpVar1*(polxz/eps - polzx/(1. - eps));


    phi3.setX(linearZero + diagContrib + nonDiagContrib);
   //   
   //        Linear Polarisation #2
   //
    helpVar1 = std::sqrt(gam*gam - 1.)*(2.*(gam + 1.)*eps*(1. - eps) - 1.);
    helpVar1 /= 8.*sqr(1. - eps)*sqr(eps)*sqr(gam + 1.)*(gam - 1.);
    helpVar2 = std::sqrt((gam*gam - 1.)*std::fabs(2.*(gam + 1.)*eps*(1. - eps) - 1.));
    helpVar2 /= 8.*sqr(1. - eps)*sqr(eps)*sqr(gam + 1.)*(gam - 1.);

    G4double contrib21 = (-polxy + polyx)*helpVar1;
    G4double contrib32 = -(eps*(gam + 1.) - 1.)*polyz + (eps*(gam + 1.) - gam)*polzy;

             contrib32 *=helpVar2;
    phi2.setY(contrib21 + contrib32);

             contrib32 = -(eps*(gam + 1.) - gam)*polyz + (eps*(gam + 1.) - 1.)*polzy;
             contrib32 *=helpVar2;
    phi3.setY(contrib21 + contrib32);

  }
  phi0 *= diffXSFactor;
  phi2 *= diffXSFactor;
  phi3 *= diffXSFactor;
}


//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4PolarizedAnnihilationCrossSection::XSection(const G4StokesVector & pol2,
                                                       const G4StokesVector & pol3)
{
  G4double xs=phi0+pol2*phi2+pol3*phi3;
  return xs;
}
//
// calculate total cross section
//
G4double G4PolarizedAnnihilationCrossSection::TotalXSection(
  G4double ,G4double ,G4double gam,
  const G4StokesVector & pol0,const G4StokesVector & pol1)
{
  totalXSFactor =pi*re2/(gam + 1.);  // atomic number ignored  
  DefineCoefficients(pol0,pol1);

  G4double xs = 0.;


  G4double gam2 = gam*gam;
  G4double sqrtgam1 = std::sqrt(gam2 - 1.);
  G4double logMEM  = std::log(gam+sqrtgam1);
  G4double unpME = (gam*(gam + 4.) + 1.)*logMEM;
  unpME += -(gam + 3.)*sqrtgam1;
  unpME /= 4.*(gam2 - 1.);
//   G4double longPart = - 2.*(gam*(gam + 4.) + 1.)*logMEM; 
//   longPart += (gam*(gam + 4.) + 7.)*sqrtgam1;
//   longPart /= 4.*sqr(gam - 1.)*(gam + 1.);
  G4double longPart = (3+gam*(gam*(gam + 1.) + 7.))*logMEM; 
  longPart += - (5.+ gam*(3*gam + 4.))*sqrtgam1;
  longPart /= 4.*sqr(gam - 1.)*(gam + 1.);
  G4double tranPart = -(5*gam + 1.)*logMEM;
  tranPart += (gam + 5.)*sqrtgam1;
  tranPart /= 4.*sqr(gam - 1.)*(gam + 1.);
                                   
  xs += unpME;
  xs += polzz*longPart;
  xs += (polxx + polyy)*tranPart;

  return xs*totalXSFactor;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4StokesVector G4PolarizedAnnihilationCrossSection::GetPol2()
{
  // Note, mean polarization can not contain correlation
  // effects.
  return  1./phi0 * phi2;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4StokesVector G4PolarizedAnnihilationCrossSection::GetPol3()
{
  // Note, mean polarization can not contain correlation
  // effects.
  return  1./phi0 * phi3;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
void G4PolarizedAnnihilationCrossSection::DefineCoefficients(const G4StokesVector & pol0,
                                                             const G4StokesVector & pol1)
{
  polxx=pol0.x()*pol1.x();
  polyy=pol0.y()*pol1.y();
  polzz=pol0.z()*pol1.z();  

  polxz=pol0.x()*pol1.z();
  polzx=pol0.z()*pol1.x();

  polyz=pol0.y()*pol1.z();
  polzy=pol0.z()*pol1.y();

  polxy=pol0.x()*pol1.y();
  polyx=pol0.y()*pol1.x();
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4PolarizedAnnihilationCrossSection::GetXmin(G4double y)
{
  return 0.5*(1.-std::sqrt((y-1.)/(y+1.)));
}
G4double G4PolarizedAnnihilationCrossSection::GetXmax(G4double y)
{
  return 0.5*(1.+std::sqrt((y-1.)/(y+1.)));
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4double G4PolarizedAnnihilationCrossSection::DiceEpsilon()
{
  return dice;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4double G4PolarizedAnnihilationCrossSection::getVar(G4int choice)
{
  if (choice == -1) return polXS/unpXS;
  if (choice == 0) return unpXS;
  if (choice == 1) return ISPxx;
  if (choice == 2) return ISPyy;
  if (choice == 3) return ISPzz;
  if (choice == 4) return ISPnd;
  return 0;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......