G4DNAScreenedRutherfordElasticModel.cc

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// $Id: G4DNAScreenedRutherfordElasticModel.cc 97520 2016-06-03 14:23:17Z gcosmo $
//

#include "G4DNAScreenedRutherfordElasticModel.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "G4DNAMolecularMaterial.hh"
#include "G4Exp.hh"
#include "G4Log.hh"

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using namespace std;
//#define SR_VERBOSE

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G4DNAScreenedRutherfordElasticModel::
G4DNAScreenedRutherfordElasticModel(const G4ParticleDefinition*,
                                    const G4String& nam) :
    G4VEmModel(nam), isInitialised(false)
{
  fpWaterDensity = 0;

  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

#ifdef SR_VERBOSE
  if (verboseLevel > 0)
  {
    G4cout << "Screened Rutherford Elastic model is constructed "
           << G4endl
           << "Energy range: "
           << lowEnergyLimit / eV << " eV - "
           << highEnergyLimit / MeV << " MeV"
           << G4endl;
  }
#endif
  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*/)
{
#ifdef SR_VERBOSE
  if (verboseLevel > 3)
  {
    G4cout << "Calling G4DNAScreenedRutherfordElasticModel::Initialise()"
           << G4endl;
  }
#endif
  
  if(particle->GetParticleName() != "e-")
  {
    G4Exception ("*** WARNING: the G4DNAScreenedRutherfordElasticModel is not "
                 "intented to be used with another particle than the electron",
                 "",FatalException,"") ;
  }
  
  // Energy limits
  if (LowEnergyLimit() < 9*eV)
  {
    G4Exception("*** WARNING: the G4DNAScreenedRutherfordElasticModel class is "
                "not validated below 9 eV",
                "",JustWarning,"") ;
  }

  if (HighEnergyLimit() > 1*MeV)
  {
    G4Exception("*** WARNING: the G4DNAScreenedRutherfordElasticModel class is "
                "not validated above 1 MeV",
                "",JustWarning,"") ;
  }

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

  if (isInitialised) { return; } // return here, prevent reinit consts + pointer
  
  // Initialize water density pointer
  fpWaterDensity = G4DNAMolecularMaterial::Instance()->
                  GetNumMolPerVolTableFor(G4Material::GetMaterial("G4_WATER"));
  
  fParticleChangeForGamma = GetParticleChangeForGamma();
  isInitialised = true;
  
  // Constants for final state by Brenner & Zaider
  // note: if called after if(isInitialised) no need for clear and resetting
  // the values at every call

  betaCoeff=
  {
    7.51525,
    -0.41912,
    7.2017E-3,
    -4.646E-5,
    1.02897E-7};

  deltaCoeff=
  {
    2.9612,
    -0.26376,
    4.307E-3,
    -2.6895E-5,
    5.83505E-8};

  gamma035_10Coeff =
  {
    -1.7013,
    -1.48284,
    0.6331,
    -0.10911,
    8.358E-3,
    -2.388E-4};

  gamma10_100Coeff =
  {
    -3.32517,
    0.10996,
    -4.5255E-3,
    5.8372E-5,
    -2.4659E-7};

  gamma100_200Coeff =
  {
    2.4775E-2,
    -2.96264E-5,
    -1.20655E-7};
}

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G4double G4DNAScreenedRutherfordElasticModel::
CrossSectionPerVolume(const G4Material* material,
#ifdef SR_VERBOSE
                      const G4ParticleDefinition* particleDefinition,
#else
                      const G4ParticleDefinition*,
#endif
                      G4double ekin,
                      G4double,
                      G4double)
{
#ifdef SR_VERBOSE
  if (verboseLevel > 3)
  {
    G4cout << "Calling CrossSectionPerVolume() of "
            "G4DNAScreenedRutherfordElasticModel"
           << G4endl;
  }
#endif
  
  // Calculate total cross section for model

  G4double sigma=0.;
  G4double waterDensity = (*fpWaterDensity)[material->GetIndex()];

  if(waterDensity!= 0.0)
  {
    if(ekin < HighEnergyLimit() && ekin >= LowEnergyLimit())
    {
      G4double z = 10.;
      G4double n = ScreeningFactor(ekin,z);
      G4double crossSection = RutherfordCrossSection(ekin, z);
      sigma = pi * crossSection / (n * (n + 1.));
    }

#ifdef SR_VERBOSE
    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 << "=== G4DNAScreenedRutherfordElasticModel - XS INFO END"
             << G4endl;
    }
#endif
  }

  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;
}

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

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 * G4Log(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)
{
#ifdef SR_VERBOSE
  if (verboseLevel > 3)
  {
    G4cout << "Calling SampleSecondaries() of "
              "G4DNAScreenedRutherfordElasticModel"
           << G4endl;
  }
#endif
  
  G4double electronEnergy0 = aDynamicElectron->GetKineticEnergy();
  G4double cosTheta = 0.;

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

    if (electronEnergy0>=intermediateEnergyLimit)
    {
#ifdef SR_VERBOSE
      if (verboseLevel > 3)
      {G4cout << "---> Using Screened Rutherford model" << G4endl;}
#endif
      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 = G4Exp(CalculatePolynomial(k, betaCoeff));
  G4double delta = G4Exp(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 = G4Exp(CalculatePolynomial(k, gamma10_100Coeff));
    }
    else
    {
      gamma = G4Exp(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)
  {
   
   // 
   // modified by Shogo OKADA @ KEK, JP, 2016.2.27(Sat.)
   // 
   // An integral of differential cross-section formula shown above this member function
   // (integral variable: cos(theta), integral interval: [-1, x]) is as follows:
   // 
   //          1.0 + x                beta * (1 + x)
   // I = --------------------- + ----------------------   (1)
   //      (a - x) * (a + 1.0)      (b + x) * (b - 1.0)
   //
   // where a = 1.0 + 2.0 * gamma(K), b = 1.0 + 2.0 * delta(K)
   // 
   // Then, a cumulative probability (cp) is as follows:
   // 
   //  cp       1.0 + x                beta * (1 + x)      
   // ---- = --------------------- + ----------------------  (2)
   //  S      (a - x) * (a + 1.0)      (b + x) * (b - 1.0) 
   //
   // where 1/S is the integral of differnetical cross-section (1) on interval [-1, 1]
   // 
   //   1           2.0                     2.0 * beta
   //  --- = ----------------------- + -----------------------   (3)
   //   S     (a - 1.0) * (a + 1.0)     (b + 1.0) * (b - 1.0)
   //
   // x is calculated from the quadratic equation derived from (2) and (3):
   //
   // A * x^2 + B * x + C = 0
   //
   // where A, B, anc C are coefficients of the equation:
   //  A = S * {(b - 1.0) - beta * (a + 1.0)} + cp * (a + 1.0) * (b - 1.0),
   //  B = S * {(b - 1.0) * (b + 1.0) + beta * (a - 1.0) * (a + 1.0)} - cp * (a + 1.0) * (b - 1.0) * (a - b)
   //  C = S * {b * (b - 1.0) + beta * a * (a + 1.0)} - cp * (a + 1.0) * (b - 1.0) * ab
   //
   
   // sampling cumulative probability
   G4double cp = G4UniformRand();
  
   G4double a = 1.0 + 2.0 * gamma;
   G4double b = 1.0 + 2.0 * delta;
   G4double a1 = a - 1.0;
   G4double a2 = a + 1.0;
   G4double b1 = b - 1.0;
   G4double b2 = b + 1.0;
   G4double c1 = a - b;
   G4double c2 = a * b;

   G4double S = 2.0 / (a1 * a2) + 2.0 * beta / (b1 * b2); S = 1.0 / S;
 
   // coefficients for the quadratic equation
   G4double A = S * (b1 - beta * a2) + cp * a2 * b1;
   G4double B = S * (b1 * b2 + beta * a1 * a2) - cp * a2 * b1 * c1;
   G4double C = S * (b * b1 + beta * a * a2) - cp * a2 * b1 * c2;
  
   // calculate cos(theta)
   return (-1.0 * B + std::sqrt(B * B - 4.0 * A * C)) / (2.0 * A);
   
   /*
   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)
  {
  
   //
   // modified by Shogo OKADA @ KEK, JP, 2016.2.27(Sat.)
   //
   // The cumulative probability (cp) is calculated by integrating 
   // the differential cross-section fomula with cos(theta):
   // 
   //         n(K) * (1.0 + cos(theta))
   //  cp = ---------------------------------
   //         1.0 + 2.0 * n(K) - cos(theta)
   //
   // Then, cos(theta) is as follows:
   //
   //               cp * (1.0 + 2.0 * n(K)) - n(K)
   // cos(theta) = --------------------------------
   //                       n(k) + cp
   // 
   // where, K is kinetic energy, n(K) is screeing factor, and cp is cumulative probability 
   // 
  
   G4double n = ScreeningFactor(k, z);
   G4double cp = G4UniformRand();
   G4double numerator = cp * (1.0 + 2.0 * n) - n;
   G4double denominator = n + cp;
   return numerator / denominator;
      
   /*
   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.;
}