G4DNAScreenedRutherfordElasticModel.cc

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// $Id: G4DNAScreenedRutherfordElasticModel.cc 70171 2013-05-24 13:34:18Z 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;
}

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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 stae by Brenner & Zaider

    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.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.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.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.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*material->GetAtomicNumDensityVector()[1];
}

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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

    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
    /*
 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;
*/

}

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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;
}

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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

    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
    /*
 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;
*/
}