G4DNAScreenedRutherfordElasticModel.cc

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// $Id: G4DNAScreenedRutherfordElasticModel.cc 92074 2015-08-17 07:03:46Z gcosmo $
//

#include "G4DNAScreenedRutherfordElasticModel.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "G4DNAMolecularMaterial.hh"

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using namespace std;

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G4DNAScreenedRutherfordElasticModel::G4DNAScreenedRutherfordElasticModel(const G4ParticleDefinition*,
                                                                         const G4String& nam) :
    G4VEmModel(nam), isInitialised(false)
{
  //  nistwater = G4NistManager::Instance()->FindOrBuildMaterial("G4_WATER");
  fpWaterDensity = 0;

  killBelowEnergy = 9 * eV;
  lowEnergyLimit = 0 * eV;
  intermediateEnergyLimit = 200 * eV; // Switch between two final state models
  highEnergyLimit = 1. * MeV;
  SetLowEnergyLimit(lowEnergyLimit);
  SetHighEnergyLimit(highEnergyLimit);

  verboseLevel = 0;
  // Verbosity scale:
  // 0 = nothing
  // 1 = warning for energy non-conservation
  // 2 = details of energy budget
  // 3 = calculation of cross sections, file openings, sampling of atoms
  // 4 = entering in methods

  if (verboseLevel > 0)
  {
    G4cout << "Screened Rutherford Elastic model is constructed " << G4endl<< "Energy range: "
    << lowEnergyLimit / eV << " eV - "
    << highEnergyLimit / MeV << " MeV"
    << G4endl;
  }
  fParticleChangeForGamma = 0;

  // Selection of computation method
  // We do not recommend "true" usage with the current cumul. proba. settings
  fasterCode = false; 
}

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G4DNAScreenedRutherfordElasticModel::~G4DNAScreenedRutherfordElasticModel()
{
}

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void G4DNAScreenedRutherfordElasticModel::Initialise(const G4ParticleDefinition* /*particle*/,
                                                     const G4DataVector& /*cuts*/)
{

  if (verboseLevel > 3)
  G4cout << "Calling G4DNAScreenedRutherfordElasticModel::Initialise()"
  << G4endl;

  // Energy limits

  if (LowEnergyLimit() < lowEnergyLimit)
  {
    G4cout << "G4DNAScreenedRutherfordElasticModel: low energy limit increased from " <<
    LowEnergyLimit()/eV << " eV to " << lowEnergyLimit/eV << " eV" << G4endl;
    SetLowEnergyLimit(lowEnergyLimit);
  }

  if (HighEnergyLimit() > highEnergyLimit)
  {
    G4cout << "G4DNAScreenedRutherfordElasticModel: high energy limit decreased from " <<
    HighEnergyLimit()/MeV << " MeV to " << highEnergyLimit/MeV << " MeV" << G4endl;
    SetHighEnergyLimit(highEnergyLimit);
  }

  // Constants for final state by Brenner & Zaider
  // March 25th, 2014 - Vaclav Stepan, Sebastien Incerti
  // Added clear for MT

  betaCoeff.clear();
  betaCoeff.push_back(7.51525);
  betaCoeff.push_back(-0.41912);
  betaCoeff.push_back(7.2017E-3);
  betaCoeff.push_back(-4.646E-5);
  betaCoeff.push_back(1.02897E-7);

  deltaCoeff.clear();
  deltaCoeff.push_back(2.9612);
  deltaCoeff.push_back(-0.26376);
  deltaCoeff.push_back(4.307E-3);
  deltaCoeff.push_back(-2.6895E-5);
  deltaCoeff.push_back(5.83505E-8);

  gamma035_10Coeff.clear();
  gamma035_10Coeff.push_back(-1.7013);
  gamma035_10Coeff.push_back(-1.48284);
  gamma035_10Coeff.push_back(0.6331);
  gamma035_10Coeff.push_back(-0.10911);
  gamma035_10Coeff.push_back(8.358E-3);
  gamma035_10Coeff.push_back(-2.388E-4);

  gamma10_100Coeff.clear();
  gamma10_100Coeff.push_back(-3.32517);
  gamma10_100Coeff.push_back(0.10996);
  gamma10_100Coeff.push_back(-4.5255E-3);
  gamma10_100Coeff.push_back(5.8372E-5);
  gamma10_100Coeff.push_back(-2.4659E-7);

  gamma100_200Coeff.clear();
  gamma100_200Coeff.push_back(2.4775E-2);
  gamma100_200Coeff.push_back(-2.96264E-5);
  gamma100_200Coeff.push_back(-1.20655E-7);

  //

  if( verboseLevel>0 )
  {
    G4cout << "Screened Rutherford elastic model is initialized " << G4endl
    << "Energy range: "
    << LowEnergyLimit() / eV << " eV - "
    << HighEnergyLimit() / MeV << " MeV"
    << G4endl;
  }

  // Initialize water density pointer
  fpWaterDensity = G4DNAMolecularMaterial::Instance()->GetNumMolPerVolTableFor(G4Material::GetMaterial("G4_WATER"));

  if (isInitialised)
  { return;}
  fParticleChangeForGamma = GetParticleChangeForGamma();
  isInitialised = true;

}

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G4double G4DNAScreenedRutherfordElasticModel::CrossSectionPerVolume(const G4Material* material,
                                                                    const G4ParticleDefinition* particleDefinition,
                                                                    G4double ekin,
                                                                    G4double,
                                                                    G4double)
{
  if (verboseLevel > 3)
  G4cout << "Calling CrossSectionPerVolume() of G4DNAScreenedRutherfordElasticModel"
  << G4endl;

  // Calculate total cross section for model

  G4double sigma=0;

  G4double waterDensity = (*fpWaterDensity)[material->GetIndex()];

  if(waterDensity!= 0.0)
  //  if (material == nistwater || material->GetBaseMaterial() == nistwater)
  {

    if (ekin < highEnergyLimit)
    {

      if (ekin < killBelowEnergy) return DBL_MAX;

      G4double z = 10.;
      G4double n = ScreeningFactor(ekin,z);
      G4double crossSection = RutherfordCrossSection(ekin, z);
      sigma = pi * crossSection / (n * (n + 1.));
    }

    if (verboseLevel > 2)
    {
      G4cout << "__________________________________" << G4endl;
      G4cout << "=== G4DNAScreenedRutherfordElasticModel - XS INFO START" << G4endl;
      G4cout << "=== Kinetic energy(eV)=" << ekin/eV << " particle : " << particleDefinition->GetParticleName() << G4endl;
      G4cout << "=== Cross section per water molecule (cm^2)=" << sigma/cm/cm << G4endl;
      G4cout << "=== Cross section per water molecule (cm^-1)=" << sigma*waterDensity/(1./cm) << G4endl;
      // G4cout << " - Cross section per water molecule (cm^-1)=" << sigma*material->GetAtomicNumDensityVector()[1]/(1./cm) << G4endl;
      G4cout << "=== G4DNAScreenedRutherfordElasticModel - XS INFO END" << G4endl;
    }

  }

  return sigma*waterDensity;
}

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G4double G4DNAScreenedRutherfordElasticModel::RutherfordCrossSection(G4double k,
                                                                     G4double z)
{
  //
  //                               e^4         /      K + m_e c^2      \^2
  // sigma_Ruth(K) = Z (Z+1) -------------------- | --------------------- |
  //                          (4 pi epsilon_0)^2  \  K * (K + 2 m_e c^2)  /
  //
  // Where K is the electron non-relativistic kinetic energy
  //
  // NIM 155, pp. 145-156, 1978

  G4double length = (e_squared * (k + electron_mass_c2))
      / (4 * pi * epsilon0 * k * (k + 2 * electron_mass_c2));
  G4double cross = z * (z + 1) * length * length;

  return cross;
}

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G4double G4DNAScreenedRutherfordElasticModel::ScreeningFactor(G4double k,
                                                              G4double z)
{
  //
  //         alpha_1 + beta_1 ln(K/eV)   constK Z^(2/3)
  // n(T) = -------------------------- -----------------
  //              K/(m_e c^2)            2 + K/(m_e c^2)
  //
  // Where K is the electron non-relativistic kinetic energy
  //
  // n(T) > 0 for T < ~ 400 MeV
  //
  // NIM 155, pp. 145-156, 1978
  // Formulae (2) and (5)

  const G4double alpha_1(1.64);
  const G4double beta_1(-0.0825);
  const G4double constK(1.7E-5);

  G4double numerator = (alpha_1 + beta_1 * std::log(k / eV)) * constK
                       * std::pow(z, 2. / 3.);

  k /= electron_mass_c2;

  G4double denominator = k * (2 + k);

  G4double value = 0.;
  if (denominator > 0.) value = numerator / denominator;

  return value;
}

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void G4DNAScreenedRutherfordElasticModel::SampleSecondaries(std::vector<
                                                                G4DynamicParticle*>* /*fvect*/,
                                                            const G4MaterialCutsCouple* /*couple*/,
                                                            const G4DynamicParticle* aDynamicElectron,
                                                            G4double,
                                                            G4double)
{

  if (verboseLevel > 3)
  {
    G4cout << "Calling SampleSecondaries() of G4DNAScreenedRutherfordElasticModel"
           << G4endl;
  }

  G4double electronEnergy0 = aDynamicElectron->GetKineticEnergy();

  if (electronEnergy0 < killBelowEnergy)
  {
    fParticleChangeForGamma->SetProposedKineticEnergy(0.);
    fParticleChangeForGamma->ProposeTrackStatus(fStopAndKill);
    fParticleChangeForGamma->ProposeLocalEnergyDeposit(electronEnergy0);
    return;
  }

  G4double cosTheta = 0.;

  if (electronEnergy0>= killBelowEnergy && electronEnergy0 < highEnergyLimit)
  {
    if (electronEnergy0<intermediateEnergyLimit)
    {
      if (verboseLevel > 3) G4cout << "---> Using Brenner & Zaider model" << G4endl;
      cosTheta = BrennerZaiderRandomizeCosTheta(electronEnergy0);
    }

    if (electronEnergy0>=intermediateEnergyLimit)
    {
      if (verboseLevel > 3) G4cout << "---> Using Screened Rutherford model" << G4endl;
      G4double z = 10.;
      cosTheta = ScreenedRutherfordRandomizeCosTheta(electronEnergy0,z);
    }

    G4double phi = 2. * pi * G4UniformRand();

    G4ThreeVector zVers = aDynamicElectron->GetMomentumDirection();
    G4ThreeVector xVers = zVers.orthogonal();
    G4ThreeVector yVers = zVers.cross(xVers);

    G4double xDir = std::sqrt(1. - cosTheta*cosTheta);
    G4double yDir = xDir;
    xDir *= std::cos(phi);
    yDir *= std::sin(phi);

    G4ThreeVector zPrimeVers((xDir*xVers + yDir*yVers + cosTheta*zVers));

    fParticleChangeForGamma->ProposeMomentumDirection(zPrimeVers.unit());

    fParticleChangeForGamma->SetProposedKineticEnergy(electronEnergy0);
  }

}

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G4double G4DNAScreenedRutherfordElasticModel::BrennerZaiderRandomizeCosTheta(G4double k)
{
  //  d sigma_el                         1                                 beta(K)
  // ------------ (K) ~ --------------------------------- + ---------------------------------
  //   d Omega           (1 + 2 gamma(K) - cos(theta))^2     (1 + 2 delta(K) + cos(theta))^2
  //
  // Maximum is < 1/(4 gamma(K)^2) + beta(K)/((2+2delta(K))^2)
  //
  // Phys. Med. Biol. 29 N.4 (1983) 443-447

  // gamma(K), beta(K) and delta(K) are polynomials with coefficients for energy measured in eV

  k /= eV;

  G4double beta = std::exp(CalculatePolynomial(k, betaCoeff));
  G4double delta = std::exp(CalculatePolynomial(k, deltaCoeff));
  G4double gamma;

  if (k > 100.)
  {
    gamma = CalculatePolynomial(k, gamma100_200Coeff);
    // Only in this case it is not the exponent of the polynomial
  }
  else
  {
    if (k > 10)
    {
      gamma = std::exp(CalculatePolynomial(k, gamma10_100Coeff));
    }
    else
    {
      gamma = std::exp(CalculatePolynomial(k, gamma035_10Coeff));
    }
  }

  // ***** Original method
  
  if (!fasterCode)
  {

   G4double oneOverMax = 1.
      / (1. / (4. * gamma * gamma) + beta
          / ((2. + 2. * delta) * (2. + 2. * delta)));

   G4double cosTheta = 0.;
   G4double leftDenominator = 0.;
   G4double rightDenominator = 0.;
   G4double fCosTheta = 0.;

   do
   {
     cosTheta = 2. * G4UniformRand()- 1.;

     leftDenominator = (1. + 2.*gamma - cosTheta);
     rightDenominator = (1. + 2.*delta + cosTheta);
     if ( (leftDenominator * rightDenominator) != 0. )
     {
       fCosTheta = oneOverMax * (1./(leftDenominator*leftDenominator) + beta/(rightDenominator*rightDenominator));
     }
   }
   while (fCosTheta < G4UniformRand());

   return cosTheta;
  }

  // ***** Alternative method using cumulative probability
  
  if (fasterCode)
  {

   G4double cosTheta = -1;
   G4double cumul = 0;
   G4double value = 0;
   G4double leftDenominator = 0.;
   G4double rightDenominator = 0.;

   // Number of integration steps in the -1,1 range
   G4int iMax=200;

   G4double random = G4UniformRand();

   // Cumulate differential cross section
   for (G4int i=0; i<iMax; i++)
   {
    cosTheta = -1 + i*2./(iMax-1);
    leftDenominator = (1. + 2.*gamma - cosTheta);
    rightDenominator = (1. + 2.*delta + cosTheta);
    if ( (leftDenominator * rightDenominator) != 0. )
    {
      cumul = cumul + (1./(leftDenominator*leftDenominator) + beta/(rightDenominator*rightDenominator));
    }
   }

   // Select cosTheta
   for (G4int i=0; i<iMax; i++)
   {
     cosTheta = -1 + i*2./(iMax-1);
     leftDenominator = (1. + 2.*gamma - cosTheta);
     rightDenominator = (1. + 2.*delta + cosTheta);
     if (cumul !=0 && (leftDenominator * rightDenominator) != 0.)
      value = value + (1./(leftDenominator*leftDenominator) + beta/(rightDenominator*rightDenominator)) / cumul;
     if (random < value) break;
   }

   return cosTheta;
  }
 
  return 0.;
}

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

G4double G4DNAScreenedRutherfordElasticModel::CalculatePolynomial(G4double k,
                                                                  std::vector<
                                                                      G4double>& vec)
{
  // Sum_{i=0}^{size-1} vector_i k^i
  //
  // Phys. Med. Biol. 29 N.4 (1983) 443-447

  G4double result = 0.;
  size_t size = vec.size();

  while (size > 0)
  {
    size--;

    result *= k;
    result += vec[size];
  }

  return result;
}

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

G4double G4DNAScreenedRutherfordElasticModel::ScreenedRutherfordRandomizeCosTheta(G4double k,
                                                                                  G4double z)
{

  //  d sigma_el                sigma_Ruth(K)
  // ------------ (K) ~ -----------------------------
  //   d Omega           (1 + 2 n(K) - cos(theta))^2
  //
  // We extract cos(theta) distributed as (1 + 2 n(K) - cos(theta))^-2
  //
  // Maximum is for theta=0: 1/(4 n(K)^2) (When n(K) is positive, that is always satisfied within the validity of the process)
  //
  // Phys. Med. Biol. 45 (2000) 3171-3194

  // ***** Original method

  if (!fasterCode)
  {

   G4double n = ScreeningFactor(k, z);

   G4double oneOverMax = (4. * n * n);

   G4double cosTheta = 0.;
   G4double fCosTheta;

   do
   {
     cosTheta = 2. * G4UniformRand()- 1.;
     fCosTheta = (1 + 2.*n - cosTheta);
     if (fCosTheta !=0.) fCosTheta = oneOverMax / (fCosTheta*fCosTheta);
   }
   while (fCosTheta < G4UniformRand());

   return cosTheta;
  }

  // ***** Alternative method using cumulative probability
  if (fasterCode)
  {

   G4double cosTheta = -1;
   G4double cumul = 0;
   G4double value = 0;
   G4double n = ScreeningFactor(k, z);
   G4double fCosTheta;

   // Number of integration steps in the -1,1 range
   G4int iMax=200;

   G4double random = G4UniformRand();

   // Cumulate differential cross section
   for (G4int i=0; i<iMax; i++)
   {
     cosTheta = -1 + i*2./(iMax-1);
     fCosTheta = (1 + 2.*n - cosTheta);
     if (fCosTheta !=0.) cumul = cumul + 1./(fCosTheta*fCosTheta);
   }

   // Select cosTheta
   for (G4int i=0; i<iMax; i++)
   {
     cosTheta = -1 + i*2./(iMax-1);
     fCosTheta = (1 + 2.*n - cosTheta);
     if (cumul !=0.) value = value + (1./(fCosTheta*fCosTheta)) / cumul;
     if (random < value) break;
   }
   return cosTheta;
  }

  return 0.;
}