G4LivermorePolarizedGammaConversionModel.cc

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// $Id: G4LivermorePolarizedGammaConversionModel.hh,v 1.2 2010-11-23 16:42:15 flongo Exp $
// GEANT4 tag $Name: not supported by cvs2svn $
//
// Authors: G.Depaola & F.Longo
//
//
 
#include "G4LivermorePolarizedGammaConversionModel.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
 
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
 
using namespace std;
 
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
 
G4LivermorePolarizedGammaConversionModel::G4LivermorePolarizedGammaConversionModel(
   const G4ParticleDefinition*, const G4String& nam)
  :G4VEmModel(nam),fParticleChange(0),
   isInitialised(false),meanFreePathTable(0),crossSectionHandler(0)
{
  lowEnergyLimit = 2*electron_mass_c2;
  highEnergyLimit = 100 * GeV;
  SetLowEnergyLimit(lowEnergyLimit);
  SetHighEnergyLimit(highEnergyLimit);
  smallEnergy = 2.*MeV;
 
  Phi=0.;
  Psi=0.;
  
  verboseLevel= 0;
  // Verbosity scale:
  // 0 = nothing 
  // 1 = warning for energy non-conservation 
  // 2 = details of energy budget
  // 3 = calculation of cross sections, file openings, samping of atoms
  // 4 = entering in methods
 
  if(verboseLevel > 0) {
    G4cout << "Livermore Polarized GammaConversion is constructed " << G4endl
       << "Energy range: "
       << lowEnergyLimit / keV << " keV - "
       << highEnergyLimit / GeV << " GeV"
       << G4endl;
  }
 
  crossSectionHandler = new G4CrossSectionHandler();
  crossSectionHandler->Initialise(0,lowEnergyLimit,highEnergyLimit,400);
}
 
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
 
G4LivermorePolarizedGammaConversionModel::~G4LivermorePolarizedGammaConversionModel()
{  
  delete crossSectionHandler;
}
 
 
 
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
 
void G4LivermorePolarizedGammaConversionModel::Initialise(const G4ParticleDefinition* particle,
                                       const G4DataVector& cuts)
{
  if (verboseLevel > 3)
    G4cout << "Calling G4LivermorePolarizedGammaConversionModel::Initialise()" << G4endl;
 
  if (crossSectionHandler)
  {
    crossSectionHandler->Clear();
    delete crossSectionHandler;
  }
 
  // Energy limits
  /*
  // V.Ivanchenko: this was meanless check  
  if (LowEnergyLimit() < lowEnergyLimit)
    {
      G4cout << "G4LivermorePolarizedGammaConversionModel: low energy limit increased from " << 
    LowEnergyLimit()/eV << " eV to " << lowEnergyLimit << " eV" << G4endl;
      //      SetLowEnergyLimit(lowEnergyLimit);
    }
  */
  if (HighEnergyLimit() > highEnergyLimit)
    {
      G4cout << "G4LivermorePolarizedGammaConversionModel: high energy limit decreased from " << 
    HighEnergyLimit()/GeV << " GeV to " << highEnergyLimit << " GeV" << G4endl;
      // V.Ivanchenko: this is forbidden 
     // SetHighEnergyLimit(highEnergyLimit);
    }
 
  // Reading of data files - all materials are read
  
  crossSectionHandler = new G4CrossSectionHandler;
  crossSectionHandler->Clear();
  G4String crossSectionFile = "pair/pp-cs-";
  crossSectionHandler->LoadData(crossSectionFile);
 
  //
  if (verboseLevel > 2) {
    G4cout << "Loaded cross section files for Livermore Polarized GammaConversion model" 
       << G4endl;
  }
  InitialiseElementSelectors(particle,cuts);
 
  if(verboseLevel > 0) {
    G4cout << "Livermore Polarized GammaConversion model is initialized " << G4endl
       << "Energy range: "
       << LowEnergyLimit() / keV << " keV - "
       << HighEnergyLimit() / GeV << " GeV"
       << G4endl;
  }
 
  //    
  if(!isInitialised) { 
    isInitialised = true;
    fParticleChange = GetParticleChangeForGamma();
  }
}
 
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
 
G4double G4LivermorePolarizedGammaConversionModel::ComputeCrossSectionPerAtom(
                                       const G4ParticleDefinition*,
                       G4double GammaEnergy,
                       G4double Z, G4double,
                       G4double, G4double)
{
  if (verboseLevel > 3) {
    G4cout << "G4LivermorePolarizedGammaConversionModel::ComputeCrossSectionPerAtom()" 
       << G4endl;
  }
  if(Z < 0.9 || GammaEnergy <= lowEnergyLimit) { return 0.0; }
  G4double cs = crossSectionHandler->FindValue(G4int(Z), GammaEnergy);
  return cs;
}
 
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
 
void 
G4LivermorePolarizedGammaConversionModel::SampleSecondaries(std::vector<G4DynamicParticle*>* fvect,
                                const G4MaterialCutsCouple* couple,
                                const G4DynamicParticle* aDynamicGamma,
                                G4double,
                                G4double)
{
 
  // Fluorescence generated according to:
  // J. Stepanek ,"A program to determine the radiation spectra due to a single atomic
  // subshell ionisation by a particle or due to deexcitation or decay of radionuclides",
  // Comp. Phys. Comm. 1206 pp 1-1-9 (1997)
 
  if (verboseLevel > 3)
    G4cout << "Calling SampleSecondaries() of G4LivermorePolarizedGammaConversionModel" << G4endl;
 
  G4double photonEnergy = aDynamicGamma->GetKineticEnergy();
  // Within energy limit?
 
  if(photonEnergy <= lowEnergyLimit)
    {
      fParticleChange->ProposeTrackStatus(fStopAndKill);
      fParticleChange->SetProposedKineticEnergy(0.);
      return;
    }
 
 
  G4ThreeVector gammaPolarization0 = aDynamicGamma->GetPolarization();
  G4ThreeVector gammaDirection0 = aDynamicGamma->GetMomentumDirection();
 
  // Make sure that the polarization vector is perpendicular to the
  // gamma direction. If not
 
  if(!(gammaPolarization0.isOrthogonal(gammaDirection0, 1e-6))||(gammaPolarization0.mag()==0))
    { // only for testing now
      gammaPolarization0 = GetRandomPolarization(gammaDirection0);
    }
  else
    {
      if ( gammaPolarization0.howOrthogonal(gammaDirection0) != 0)
    {
      gammaPolarization0 = GetPerpendicularPolarization(gammaDirection0, gammaPolarization0);
    }
    }
 
  // End of Protection
 
 
  G4double epsilon ;
  G4double epsilon0Local = electron_mass_c2 / photonEnergy ;
 
  // Do it fast if photon energy < 2. MeV
 
  if (photonEnergy < smallEnergy )
    {
      epsilon = epsilon0Local + (0.5 - epsilon0Local) * G4UniformRand();
    }
  else
    {
 
 // Select randomly one element in the current material
 
      //     G4int Z = crossSectionHandler->SelectRandomAtom(couple,photonEnergy);
      //const G4Element* element = crossSectionHandler->SelectRandomElement(couple,photonEnergy);
 
      const G4ParticleDefinition* particle =  aDynamicGamma->GetDefinition();
      const G4Element* element = SelectRandomAtom(couple,particle,photonEnergy);
 
      /*
      if (element == 0)
        {
          G4cout << "G4LivermorePolarizedGammaConversionModel::PostStepDoIt - element = 0" << G4endl;
        }
      */
      
      G4IonisParamElm* ionisation = element->GetIonisation();
      
      /*
      if (ionisation == 0)
        {
          G4cout << "G4LivermorePolarizedGammaConversionModel::PostStepDoIt - ionisation = 0" << G4endl;
        }
      */
 
 
      // Extract Coulomb factor for this Element
 
      G4double fZ = 8. * (ionisation->GetlogZ3());
      if (photonEnergy > 50. * MeV) fZ += 8. * (element->GetfCoulomb());
 
      // Limits of the screening variable
      G4double screenFactor = 136. * epsilon0Local / (element->GetIonisation()->GetZ3()) ;
      G4double screenMax = exp ((42.24 - fZ)/8.368) - 0.952 ;
      G4double screenMin = std::min(4.*screenFactor,screenMax) ;
 
      // Limits of the energy sampling
      G4double epsilon1 = 0.5 - 0.5 * sqrt(1. - screenMin / screenMax) ;
      G4double epsilonMin = std::max(epsilon0Local,epsilon1);
      G4double epsilonRange = 0.5 - epsilonMin ;
 
      // Sample the energy rate of the created electron (or positron)
      G4double screen;
      G4double gReject ;
 
      G4double f10 = ScreenFunction1(screenMin) - fZ;
      G4double f20 = ScreenFunction2(screenMin) - fZ;
      G4double normF1 = std::max(f10 * epsilonRange * epsilonRange,0.);
      G4double normF2 = std::max(1.5 * f20,0.);
 
      do {
        if (normF1 / (normF1 + normF2) > G4UniformRand() )
          {
            epsilon = 0.5 - epsilonRange * pow(G4UniformRand(), 0.3333) ;
            screen = screenFactor / (epsilon * (1. - epsilon));
            gReject = (ScreenFunction1(screen) - fZ) / f10 ;
          }
        else
          {
            epsilon = epsilonMin + epsilonRange * G4UniformRand();
            screen = screenFactor / (epsilon * (1 - epsilon));
            gReject = (ScreenFunction2(screen) - fZ) / f20 ;
 
 
      }
      } while ( gReject < G4UniformRand() );
 
    }   //  End of epsilon sampling
  
  // Fix charges randomly
  
  G4double electronTotEnergy;
  G4double positronTotEnergy;
 
 
  if (G4int(2*G4UniformRand()))  
    {
      electronTotEnergy = (1. - epsilon) * photonEnergy;
      positronTotEnergy = epsilon * photonEnergy;
    }
  else
    {
      positronTotEnergy = (1. - epsilon) * photonEnergy;
      electronTotEnergy = epsilon * photonEnergy;
    }
 
  // 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;
  G4double a2 = 3. * a1;
 
  if (0.25 > G4UniformRand())
    {
      u = - log(G4UniformRand() * G4UniformRand()) / a1 ;
    }
  else
    {
      u = - log(G4UniformRand() * G4UniformRand()) / a2 ;
    }
*/
 
  G4double Ene = electronTotEnergy/electron_mass_c2; // Normalized energy
 
  G4double cosTheta = 0.;
  G4double sinTheta = 0.;
 
  SetTheta(&cosTheta,&sinTheta,Ene);
 
  //  G4double theta = u * electron_mass_c2 / photonEnergy ;
  //  G4double phi  = twopi * G4UniformRand() ;
 
  G4double phi,psi=0.;
 
  //corrected e+ e- angular angular distribution //preliminary!
 
  //  if(photonEnergy>50*MeV)
  // {
  phi = SetPhi(photonEnergy);
  psi = SetPsi(photonEnergy,phi);
  //  }
  //else
  // {
  //psi = G4UniformRand()*2.*pi;
  //phi = pi; // coplanar
  // }
 
  Psi = psi;
  Phi = phi;
  //G4cout << "PHI " << phi << G4endl;
  //G4cout << "PSI " << psi << G4endl;
 
  G4double phie = psi; //azimuthal angle for the electron
 
  G4double dirX = sinTheta*cos(phie);
  G4double dirY = sinTheta*sin(phie);
  G4double dirZ = cosTheta;
  G4ThreeVector electronDirection(dirX,dirY,dirZ);
  // Kinematics 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 localEnergyDeposit = 0. ;
 
  G4double electronKineEnergy = std::max(0.,electronTotEnergy - electron_mass_c2) ;
 
  SystemOfRefChange(gammaDirection0,electronDirection,
            gammaPolarization0);
 
  G4DynamicParticle* particle1 = new G4DynamicParticle (G4Electron::Electron(),
                            electronDirection,
                            electronKineEnergy);
 
  // The e+ is always created (even with kinetic energy = 0) for further annihilation
 
  Ene = positronTotEnergy/electron_mass_c2; // Normalized energy
 
  cosTheta = 0.;
  sinTheta = 0.;
 
  SetTheta(&cosTheta,&sinTheta,Ene);
  G4double phip = phie+phi; //azimuthal angle for the positron
 
  dirX = sinTheta*cos(phip);
  dirY = sinTheta*sin(phip);
  dirZ = cosTheta;
  G4ThreeVector positronDirection(dirX,dirY,dirZ);
 
  G4double positronKineEnergy = std::max(0.,positronTotEnergy - electron_mass_c2) ;
  SystemOfRefChange(gammaDirection0,positronDirection,
            gammaPolarization0);
 
  // Create G4DynamicParticle object for the particle2
  G4DynamicParticle* particle2 = new G4DynamicParticle(G4Positron::Positron(),
                                                       positronDirection, positronKineEnergy);
 
 
  fvect->push_back(particle1);
  fvect->push_back(particle2);
 
 
 
  // Kill the incident photon
 
 
 
  // Create lists of pointers to DynamicParticles (photons and electrons)
  // (Is the electron vector necessary? To be checked)
  //  std::vector<G4DynamicParticle*>* photonVector = 0;
  //std::vector<G4DynamicParticle*> electronVector;
 
  fParticleChange->ProposeMomentumDirection( 0., 0., 0. );
  fParticleChange->SetProposedKineticEnergy(0.);
  fParticleChange->ProposeTrackStatus(fStopAndKill);
 
}
 
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
 
G4double G4LivermorePolarizedGammaConversionModel::ScreenFunction1(G4double screenVariable)
{
  // Compute the value of the screening function 3*phi1 - phi2
 
  G4double value;
 
  if (screenVariable > 1.)
    value = 42.24 - 8.368 * log(screenVariable + 0.952);
  else
    value = 42.392 - screenVariable * (7.796 - 1.961 * screenVariable);
 
  return value;
}
 
 
 
G4double G4LivermorePolarizedGammaConversionModel::ScreenFunction2(G4double screenVariable)
{
  // Compute the value of the screening function 1.5*phi1 - 0.5*phi2
 
  G4double value;
 
  if (screenVariable > 1.)
    value = 42.24 - 8.368 * log(screenVariable + 0.952);
  else
    value = 41.405 - screenVariable * (5.828 - 0.8945 * screenVariable);
 
  return value;
}
 
 
void G4LivermorePolarizedGammaConversionModel::SetTheta(G4double* p_cosTheta, G4double* p_sinTheta, G4double Energy)
{
 
  // to avoid computational errors since Theta could be very small
  // Energy in Normalized Units (!)
 
  G4double Momentum = sqrt(Energy*Energy -1);
  G4double Rand = G4UniformRand();
 
  *p_cosTheta = (Energy*((2*Rand)- 1) + Momentum)/((Momentum*(2*Rand-1))+Energy);
  *p_sinTheta = (2*sqrt(Rand*(1-Rand)))/(Momentum*(2*Rand-1)+Energy);
}
 
 
 
G4double G4LivermorePolarizedGammaConversionModel::SetPhi(G4double Energy)
{
 
 
  G4double value = 0.;
  G4double Ene = Energy/MeV;
 
  G4double pl[4];
 
 
  G4double pt[2];
  G4double xi = 0;
  G4double xe = 0.;
  G4double n1=0.;
  G4double n2=0.;
 
 
  if (Ene>=50.)
    {
      const G4double ay0=5.6, by0=18.6, aa0=2.9, ba0 = 8.16E-3;
      const G4double aw = 0.0151, bw = 10.7, cw = -410.;
 
      const G4double axc = 3.1455, bxc = -1.11, cxc = 310.;
 
      pl[0] = Fln(ay0,by0,Ene);
      pl[1] = aa0 + ba0*(Ene);
      pl[2] = Poli(aw,bw,cw,Ene);
      pl[3] = Poli(axc,bxc,cxc,Ene);
 
      const G4double abf = 3.1216, bbf = 2.68;
      pt[0] = -1.4;
      pt[1] = abf + bbf/Ene;
 
 
 
      //G4cout << "PL > 50. "<< pl[0] << " " << pl[1] << " " << pl[2] << " " <<pl[3] << " " << G4endl;
 
      xi = 3.0;
      xe = Encu(pl,pt,xi);
      //G4cout << "ENCU "<< xe << G4endl;
      n1 = Fintlor(pl,pi) - Fintlor(pl,xe);
      n2 = Finttan(pt,xe) - Finttan(pt,0.);
    }
  else
    {
      const G4double ay0=0.144, by0=0.11;
      const G4double aa0=2.7, ba0 = 2.74;
      const G4double aw = 0.21, bw = 10.8, cw = -58.;
      const G4double axc = 3.17, bxc = -0.87, cxc = -6.;
 
      pl[0] = Fln(ay0, by0, Ene);
      pl[1] = Fln(aa0, ba0, Ene);
      pl[2] = Poli(aw,bw,cw,Ene);
      pl[3] = Poli(axc,bxc,cxc,Ene);
 
      //G4cout << "PL < 50."<< pl[0] << " " << pl[1] << " " << pl[2] << " " <<pl[3] << " " << G4endl;
      //G4cout << "ENCU "<< xe << G4endl;
      n1 = Fintlor(pl,pi) - Fintlor(pl,xe);
 
    }
 
 
  G4double n=0.;
  n = n1+n2;
 
  G4double c1 = 0.;
  c1 = Glor(pl, xe);
 
/*
  G4double xm = 0.;
  xm = Flor(pl,pl[3])*Glor(pl,pl[3]);
*/
 
  G4double r1,r2,r3;
  G4double xco=0.;
 
  if (Ene>=50.)
    {
      r1= G4UniformRand();
      if( r1>=n2/n)
        {
          do
        {
              r2 = G4UniformRand();
              value = Finvlor(pl,xe,r2);
              xco = Glor(pl,value)/c1;
              r3 = G4UniformRand();
            } while(r3>=xco);
        }
      else
        {
          value = Finvtan(pt,n,r1);
        }
    }
  else
    {
      do
        {
          r2 = G4UniformRand();
          value = Finvlor(pl,xe,r2);
          xco = Glor(pl,value)/c1;
          r3 = G4UniformRand();
        } while(r3>=xco);
    }
 
  //  G4cout << "PHI = " <<value <<  G4endl;
  return value;
}
G4double G4LivermorePolarizedGammaConversionModel::SetPsi(G4double Energy, G4double PhiLocal)
{
 
  G4double value = 0.;
  G4double Ene = Energy/MeV;
 
  G4double p0l[4];
  G4double ppml[4];
  G4double p0t[2];
  G4double ppmt[2];
 
  G4double xi = 0.;
  G4double xe0 = 0.;
  G4double xepm = 0.;
 
  if (Ene>=50.)
    {
      const G4double ay00 = 3.4, by00 = 9.8, aa00 = 1.34, ba00 = 5.3;
      const G4double aw0 = 0.014, bw0 = 9.7, cw0 = -2.E4;
      const G4double axc0 = 3.1423, bxc0 = -2.35, cxc0 = 0.;
      const G4double ay0p = 1.53, by0p = 3.2, aap = 0.67, bap = 8.5E-3;
      const G4double awp = 6.9E-3, bwp = 12.6, cwp = -3.8E4;
      const G4double axcp = 2.8E-3,bxcp = -3.133;
      const G4double abf0 = 3.1213, bbf0 = 2.61;
      const G4double abfpm = 3.1231, bbfpm = 2.84;
 
      p0l[0] = Fln(ay00, by00, Ene);
      p0l[1] = Fln(aa00, ba00, Ene);
      p0l[2] = Poli(aw0, bw0, cw0, Ene);
      p0l[3] = Poli(axc0, bxc0, cxc0, Ene);
 
      ppml[0] = Fln(ay0p, by0p, Ene);
      ppml[1] = aap + bap*(Ene);
      ppml[2] = Poli(awp, bwp, cwp, Ene);
      ppml[3] = Fln(axcp,bxcp,Ene);
 
      p0t[0] = -0.81;
      p0t[1] = abf0 + bbf0/Ene;
      ppmt[0] = -0.6;
      ppmt[1] = abfpm + bbfpm/Ene;
 
      //G4cout << "P0L > 50"<< p0l[0] << " " << p0l[1] << " " << p0l[2] << " " <<p0l[3] << " " << G4endl;
      //G4cout << "PPML > 50"<< ppml[0] << " " << ppml[1] << " " << ppml[2] << " " <<ppml[3] << " " << G4endl;
 
      xi = 3.0;
      xe0 = Encu(p0l, p0t, xi);
      //G4cout << "ENCU1 "<< xe0 << G4endl;
      xepm = Encu(ppml, ppmt, xi);
      //G4cout << "ENCU2 "<< xepm << G4endl;
    }
  else
    {
      const G4double ay00 = 2.82, by00 = 6.35;
      const G4double aa00 = -1.75, ba00 = 0.25;
 
      const G4double aw0 = 0.028, bw0 = 5., cw0 = -50.;
      const G4double axc0 = 3.14213, bxc0 = -2.3, cxc0 = 5.7;
      const G4double ay0p = 1.56, by0p = 3.6;
      const G4double aap = 0.86, bap = 8.3E-3;
      const G4double awp = 0.022, bwp = 7.4, cwp = -51.;
      const G4double xcp = 3.1486;
 
      p0l[0] = Fln(ay00, by00, Ene);
      p0l[1] = aa00+pow(Ene, ba00);
      p0l[2] = Poli(aw0, bw0, cw0, Ene);
      p0l[3] = Poli(axc0, bxc0, cxc0, Ene);
      ppml[0] = Fln(ay0p, by0p, Ene);
      ppml[1] = aap + bap*(Ene);
      ppml[2] = Poli(awp, bwp, cwp, Ene);
      ppml[3] = xcp;
 
    }
 
  G4double a,b=0.;
 
  if (Ene>=50.)
    {
      if (PhiLocal>xepm)
    {
          b = (ppml[0]+2*ppml[1]*ppml[2]*Flor(ppml,PhiLocal));
        }
      else
        {
          b = Ftan(ppmt,PhiLocal);
        }
      if (PhiLocal>xe0)
        {
          a = (p0l[0]+2*p0l[1]*p0l[2]*Flor(p0l,PhiLocal));
        }
      else
        {
          a = Ftan(p0t,PhiLocal);
        }
    }
  else
    {
      b = (ppml[0]+2*ppml[1]*ppml[2]*Flor(ppml,PhiLocal));
      a = (p0l[0]+2*p0l[1]*p0l[2]*Flor(p0l,PhiLocal));
    }
  G4double nr =0.;
 
  if (b>a)
    {
      nr = 1./b;
    }
  else
    {
      nr = 1./a;
    }
 
  G4double r1,r2=0.;
  G4double r3 =-1.;
  do
    {
      r1 = G4UniformRand();
      r2 = G4UniformRand();
      value = r2*pi;
      r3 = nr*(a*cos(value)*cos(value) + b*sin(value)*sin(value));
    }while(r1>r3);
 
  return value;
}
 
 
G4double G4LivermorePolarizedGammaConversionModel::Poli
(G4double a, G4double b, G4double c, G4double x)
{
  G4double value=0.;
  if(x>0.)
    {
      value =(a + b/x + c/(x*x*x));
    }
  else
    {
      //G4cout << "ERROR in Poli! " << G4endl;
    }
  return value;
}
G4double G4LivermorePolarizedGammaConversionModel::Fln
(G4double a, G4double b, G4double x)
{
  G4double value=0.;
  if(x>0.)
    {
      value =(a*log(x)-b);
    }
  else
    {
      //G4cout << "ERROR in Fln! " << G4endl;
    }
  return value;
}
 
 
G4double G4LivermorePolarizedGammaConversionModel::Encu
(G4double* p_p1, G4double* p_p2, G4double x0)
{
  G4int i=0;
  G4double fx = 1.;
  G4double x = x0;
  const G4double xmax = 3.0;
 
  for(i=0; i<100; ++i)
    {
      fx = (Flor(p_p1,x)*Glor(p_p1,x) - Ftan(p_p2, x))/
    (Fdlor(p_p1,x) - Fdtan(p_p2,x));
      x -= fx;
      if(x > xmax) { return xmax; }
      //      x -= (Flor(p_p1, x)*Glor(p_p1,x) - Ftan(p_p2, x))/
      //  (Fdlor(p_p1,x) - Fdtan(p_p2,x));
      // fx = Flor(p_p1,x)*Glor(p_p1,x) - Ftan(p_p2, x);
      // G4cout << std::fabs(fx) << " " << i << " " << x << "dentro ENCU " << G4endl;
      if(std::fabs(fx) <= x*1.0e-6) { break; }
    } 
 
  if(x < 0.0) { x = 0.0; }
  return x;
}
 
 
G4double G4LivermorePolarizedGammaConversionModel::Flor(G4double* p_p1, G4double x)
{
  G4double value =0.;
  // G4double y0 = p_p1[0];
  // G4double A = p_p1[1];
  G4double w = p_p1[2];
  G4double xc = p_p1[3];
 
  value = 1./(pi*(w*w + 4.*(x-xc)*(x-xc)));
  return value;
}
 
 
G4double G4LivermorePolarizedGammaConversionModel::Glor(G4double* p_p1, G4double x)
{
  G4double value =0.;
  G4double y0 = p_p1[0];
  G4double A = p_p1[1];
  G4double w = p_p1[2];
  G4double xc = p_p1[3];
 
  value = (y0 *pi*(w*w +  4.*(x-xc)*(x-xc)) + 2.*A*w);
  return value;
}
 
 
G4double G4LivermorePolarizedGammaConversionModel::Fdlor(G4double* p_p1, G4double x)
{
  G4double value =0.;
  //G4double y0 = p_p1[0];
  G4double A = p_p1[1];
  G4double w = p_p1[2];
  G4double xc = p_p1[3];
 
  value = (-16.*A*w*(x-xc))/
    (pi*(w*w+4.*(x-xc)*(x-xc))*(w*w+4.*(x-xc)*(x-xc)));
  return value;
}
 
 
G4double G4LivermorePolarizedGammaConversionModel::Fintlor(G4double* p_p1, G4double x)
{
  G4double value =0.;
  G4double y0 = p_p1[0];
  G4double A = p_p1[1];
  G4double w = p_p1[2];
  G4double xc = p_p1[3];
 
  value = y0*x + A*atan( 2*(x-xc)/w) / pi;
  return value;
}
 
 
G4double G4LivermorePolarizedGammaConversionModel::Finvlor(G4double* p_p1, G4double x, G4double r)
{
  G4double value = 0.;
  G4double nor = 0.;
  //G4double y0 = p_p1[0];
  //  G4double A = p_p1[1];
  G4double w = p_p1[2];
  G4double xc = p_p1[3];
 
  nor = atan(2.*(pi-xc)/w)/(2.*pi*w) - atan(2.*(x-xc)/w)/(2.*pi*w);
  value = xc - (w/2.)*tan(-2.*r*nor*pi*w+atan(2*(xc-x)/w));
 
  return value;
}
 
 
G4double G4LivermorePolarizedGammaConversionModel::Ftan(G4double* p_p1, G4double x)
{
  G4double value =0.;
  G4double a = p_p1[0];
  G4double b = p_p1[1];
 
  value = a /(x-b);
  return value;
}
 
 
G4double G4LivermorePolarizedGammaConversionModel::Fdtan(G4double* p_p1, G4double x)
{
  G4double value =0.;
  G4double a = p_p1[0];
  G4double b = p_p1[1];
 
  value = -1.*a / ((x-b)*(x-b));
  return value;
}
 
 
G4double G4LivermorePolarizedGammaConversionModel::Finttan(G4double* p_p1, G4double x)
{
  G4double value =0.;
  G4double a = p_p1[0];
  G4double b = p_p1[1];
 
 
  value = a*log(b-x);
  return value;
}
 
 
G4double G4LivermorePolarizedGammaConversionModel::Finvtan(G4double* p_p1, G4double cnor, G4double r)
{
  G4double value =0.;
  G4double a = p_p1[0];
  G4double b = p_p1[1];
 
  value = b*(1-exp(r*cnor/a));
 
  return value;
}
 
 
 
 
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
 
G4ThreeVector G4LivermorePolarizedGammaConversionModel::SetPerpendicularVector(G4ThreeVector& a)
{
  G4double dx = a.x();
  G4double dy = a.y();
  G4double dz = a.z();
  G4double x = dx < 0.0 ? -dx : dx;
  G4double y = dy < 0.0 ? -dy : dy;
  G4double z = dz < 0.0 ? -dz : dz;
  if (x < y) {
    return x < z ? G4ThreeVector(-dy,dx,0) : G4ThreeVector(0,-dz,dy);
  }else{
    return y < z ? G4ThreeVector(dz,0,-dx) : G4ThreeVector(-dy,dx,0);
  }
}
 
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
 
G4ThreeVector G4LivermorePolarizedGammaConversionModel::GetRandomPolarization(G4ThreeVector& direction0)
{
  G4ThreeVector d0 = direction0.unit();
  G4ThreeVector a1 = SetPerpendicularVector(d0); //different orthogonal
  G4ThreeVector a0 = a1.unit(); // unit vector
 
  G4double rand1 = G4UniformRand();
  
  G4double angle = twopi*rand1; // random polar angle
  G4ThreeVector b0 = d0.cross(a0); // cross product
  
  G4ThreeVector c;
  
  c.setX(std::cos(angle)*(a0.x())+std::sin(angle)*b0.x());
  c.setY(std::cos(angle)*(a0.y())+std::sin(angle)*b0.y());
  c.setZ(std::cos(angle)*(a0.z())+std::sin(angle)*b0.z());
  
  G4ThreeVector c0 = c.unit();
 
  return c0;
  
}
 
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
 
G4ThreeVector G4LivermorePolarizedGammaConversionModel::GetPerpendicularPolarization
(const G4ThreeVector& gammaDirection, const G4ThreeVector& gammaPolarization) const
{
 
  // 
  // The polarization of a photon is always perpendicular to its momentum direction.
  // Therefore this function removes those vector component of gammaPolarization, which
  // points in direction of gammaDirection
  //
  // Mathematically we search the projection of the vector a on the plane E, where n is the
  // plains normal vector.
  // The basic equation can be found in each geometry book (e.g. Bronstein):
  // p = a - (a o n)/(n o n)*n
  
  return gammaPolarization - gammaPolarization.dot(gammaDirection)/gammaDirection.dot(gammaDirection) * gammaDirection;
}
 
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
 
 
void G4LivermorePolarizedGammaConversionModel::SystemOfRefChange
    (G4ThreeVector& direction0,G4ThreeVector& direction1,
     G4ThreeVector& polarization0)
{
  // direction0 is the original photon direction ---> z
  // polarization0 is the original photon polarization ---> x
  // need to specify y axis in the real reference frame ---> y 
  G4ThreeVector Axis_Z0 = direction0.unit();
  G4ThreeVector Axis_X0 = polarization0.unit();
  G4ThreeVector Axis_Y0 = (Axis_Z0.cross(Axis_X0)).unit(); // to be confirmed;
  
  G4double direction_x = direction1.getX();
  G4double direction_y = direction1.getY();
  G4double direction_z = direction1.getZ();
  
  direction1 = (direction_x*Axis_X0 + direction_y*Axis_Y0 +  direction_z*Axis_Z0).unit();
  
}