G4CompetitiveFission.cc

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// $Id: G4CompetitiveFission.cc 98739 2016-08-09 12:56:55Z gcosmo $
//
// Hadronic Process: Nuclear De-excitations
// by V. Lara (Oct 1998)
//
// J. M. Quesada (March 2009). Bugs fixed:
//          - Full relativistic calculation (Lorentz boosts)
//          - Fission pairing energy is included in fragment excitation energies
// Now Energy and momentum are conserved in fission 

#include "G4CompetitiveFission.hh"
#include "G4PairingCorrection.hh"
#include "G4ParticleMomentum.hh"
#include "G4Pow.hh"
#include "G4Exp.hh"
#include "G4PhysicalConstants.hh"

G4CompetitiveFission::G4CompetitiveFission() : G4VEvaporationChannel("fission")
{
  theFissionBarrierPtr = new G4FissionBarrier;
  MyOwnFissionBarrier = true;

  theFissionProbabilityPtr = new G4FissionProbability;
  MyOwnFissionProbability = true;
  
  theLevelDensityPtr = new G4FissionLevelDensityParameter;
  MyOwnLevelDensity = true;

  MaximalKineticEnergy = -1000.0;
  FissionBarrier = 0.0;
  FissionProbability = 0.0;
  LevelDensityParameter = 0.0;
  pairingCorrection = G4PairingCorrection::GetInstance();
}

G4CompetitiveFission::~G4CompetitiveFission()
{
  if (MyOwnFissionBarrier) delete theFissionBarrierPtr;
  if (MyOwnFissionProbability) delete theFissionProbabilityPtr;
  if (MyOwnLevelDensity) delete theLevelDensityPtr;
}

G4double G4CompetitiveFission::GetEmissionProbability(G4Fragment* fragment)
{
  G4int anA = fragment->GetA_asInt();
  G4int aZ  = fragment->GetZ_asInt();
  G4double ExEnergy = fragment->GetExcitationEnergy() - 
    pairingCorrection->GetFissionPairingCorrection(anA,aZ);
  
  // Saddle point excitation energy ---> A = 65
  // Fission is excluded for A < 65
  if (anA >= 65 && ExEnergy > 0.0) {
    FissionBarrier = theFissionBarrierPtr->FissionBarrier(anA,aZ,ExEnergy);
    MaximalKineticEnergy = ExEnergy - FissionBarrier;
    LevelDensityParameter = 
      theLevelDensityPtr->LevelDensityParameter(anA,aZ,ExEnergy);
    FissionProbability = 
      theFissionProbabilityPtr->EmissionProbability(*fragment,
                            MaximalKineticEnergy);
    }
  else {
    MaximalKineticEnergy = -1000.0;
    LevelDensityParameter = 0.0;
    FissionProbability = 0.0;
  }
  return FissionProbability;
}

G4Fragment* G4CompetitiveFission::EmittedFragment(G4Fragment* theNucleus)
{
  G4Fragment * Fragment1 = 0; 
  // Nucleus data
  // Atomic number of nucleus
  G4int A = theNucleus->GetA_asInt();
  // Charge of nucleus
  G4int Z = theNucleus->GetZ_asInt();
  //   Excitation energy (in MeV)
  G4double U = theNucleus->GetExcitationEnergy();
  G4double pcorr = pairingCorrection->GetFissionPairingCorrection(A,Z);
  if (U <= pcorr) { return Fragment1; }

  // Atomic Mass of Nucleus (in MeV)
  G4double M = theNucleus->GetGroundStateMass();

  // Nucleus Momentum
  G4LorentzVector theNucleusMomentum = theNucleus->GetMomentum();

  // Calculate fission parameters
  theParam.DefineParameters(A, Z, U-pcorr, FissionBarrier);
  
  // First fragment
  G4int A1 = 0;
  G4int Z1 = 0;
  G4double M1 = 0.0;

  // Second fragment
  G4int A2 = 0;
  G4int Z2 = 0;
  G4double M2 = 0.0;

  G4double FragmentsExcitationEnergy = 0.0;
  G4double FragmentsKineticEnergy = 0.0;

  G4int Trials = 0;
  do {

    // First fragment 
    A1 = FissionAtomicNumber(A);
    Z1 = FissionCharge(A, Z, A1);
    M1 = G4NucleiProperties::GetNuclearMass(A1, Z1);

    // Second Fragment
    A2 = A - A1;
    Z2 = Z - Z1;
    if (A2 < 1 || Z2 < 0 || Z2 > A2) {
      FragmentsExcitationEnergy = -1.0;
      continue;
    }
    M2 = G4NucleiProperties::GetNuclearMass(A2, Z2);
    // Maximal Kinetic Energy (available energy for fragments)
    G4double Tmax = M + U - M1 - M2 - pcorr;

    // Check that fragment masses are less or equal than total energy
    if (Tmax < 0.0) {
      FragmentsExcitationEnergy = -1.0;
      continue;
    }

    FragmentsKineticEnergy = FissionKineticEnergy( A , Z,
                           A1, Z1,
                           A2, Z2,
                           U , Tmax);
    
    // Excitation Energy
    // FragmentsExcitationEnergy = Tmax - FragmentsKineticEnergy;
    // JMQ 04/03/09 BUG FIXED: in order to fulfill energy conservation the
    // fragments carry the fission pairing energy in form of 
    // excitation energy

    FragmentsExcitationEnergy = 
      // Tmax - FragmentsKineticEnergy;
      Tmax - FragmentsKineticEnergy + pcorr;

    // Loop checking, 05-Aug-2015, Vladimir Ivanchenko
  } while (FragmentsExcitationEnergy < 0.0
       && ++Trials < 100);
    
  if (FragmentsExcitationEnergy <= 0.0) { 
    throw G4HadronicException(__FILE__, __LINE__, 
      "G4CompetitiveFission::BreakItUp: Excitation energy for fragments < 0.0!");
  }

  // Fragment 1
  M1 += FragmentsExcitationEnergy * A1/static_cast<G4double>(A);
  // Fragment 2
  M2 += FragmentsExcitationEnergy * A2/static_cast<G4double>(A);
  // primary
  M += U;

  G4double etot1 = ((M - M2)*(M + M2) + M1*M1)/(2*M);
  G4ParticleMomentum Momentum1(IsotropicVector(std::sqrt((etot1 - M1)*(etot1+M1))));
  G4LorentzVector FourMomentum1(Momentum1, etot1);
  FourMomentum1.boost(theNucleusMomentum.boostVector());
    
  // Create Fragments
  Fragment1 = new G4Fragment( A1, Z1, FourMomentum1);
  theNucleusMomentum -= FourMomentum1;
  theNucleus->SetZandA_asInt(Z2, A2);
  theNucleus->SetMomentum(theNucleusMomentum);
  return Fragment1;
}

G4int 
G4CompetitiveFission::FissionAtomicNumber(G4int A)
  // Calculates the atomic number of a fission product
{

  // For Simplicity reading code
  G4int A1 = theParam.GetA1();
  G4int A2 = theParam.GetA2();
  G4double As = theParam.GetAs();
  G4double Sigma2 = theParam.GetSigma2();
  G4double SigmaS = theParam.GetSigmaS();
  G4double w = theParam.GetW();
  
  G4double C2A = A2 + 3.72*Sigma2;
  G4double C2S = As + 3.72*SigmaS;
  
  G4double C2 = 0.0;
  if (w > 1000.0 )    { C2 = C2S; }
  else if (w < 0.001) { C2 = C2A; }
  else                { C2 =  std::max(C2A,C2S); }

  G4double C1 = A-C2;
  if (C1 < 30.0) {
    C2 = A-30.0;
    C1 = 30.0;
  }

  G4double Am1 = (As + A1)*0.5;
  G4double Am2 = (A1 + A2)*0.5;

  // Get Mass distributions as sum of symmetric and asymmetric Gasussians
  G4double Mass1 = MassDistribution(As,A); 
  G4double Mass2 = MassDistribution(Am1,A); 
  G4double Mass3 = MassDistribution(G4double(A1),A); 
  G4double Mass4 = MassDistribution(Am2,A); 
  G4double Mass5 = MassDistribution(G4double(A2),A); 
  // get maximal value among Mass1,...,Mass5
  G4double MassMax = Mass1;
  if (Mass2 > MassMax) { MassMax = Mass2; }
  if (Mass3 > MassMax) { MassMax = Mass3; }
  if (Mass4 > MassMax) { MassMax = Mass4; }
  if (Mass5 > MassMax) { MassMax = Mass5; }

  // Sample a fragment mass number, which lies between C1 and C2
  G4double xm;
  G4double Pm;
  do {
    xm = C1+G4UniformRand()*(C2-C1);
    Pm = MassDistribution(xm,A); 
    // Loop checking, 05-Aug-2015, Vladimir Ivanchenko
  } while (MassMax*G4UniformRand() > Pm);
  G4int ires = G4lrint(xm);

  return ires;
}

G4double 
G4CompetitiveFission::MassDistribution(G4double x, G4int A)
  // This method gives mass distribution F(x) = F_{asym}(x)+w*F_{sym}(x)
  // which consist of symmetric and asymmetric sum of gaussians components.
{
  G4double y0 = (x-theParam.GetAs())/theParam.GetSigmaS();
  G4double Xsym = G4Exp(-0.5*y0*y0);

  G4double y1 = (x - theParam.GetA1())/theParam.GetSigma1();
  G4double y2 = (x - theParam.GetA2())/theParam.GetSigma2();
  G4double z1 = (x - A + theParam.GetA1())/theParam.GetSigma1();
  G4double z2 = (x - A + theParam.GetA2())/theParam.GetSigma2();
  G4double Xasym = G4Exp(-0.5*y1*y1) + G4Exp(-0.5*y2*y2) 
    + 0.5*( G4Exp(-0.5*z1*z1) + G4Exp(-0.5*z2*z2));

  G4double res;
  G4double w = theParam.GetW();
  if (w > 1000)       { res = Xsym; }
  else if (w < 0.001) { res = Xasym; }
  else                { res = w*Xsym+Xasym; }
  return res;
}

G4int G4CompetitiveFission::FissionCharge(G4int A, G4int Z, G4double Af)
  // Calculates the charge of a fission product for a given atomic number Af
{
  static const G4double sigma = 0.6;
  G4double DeltaZ = 0.0;
  if (Af >= 134.0)          { DeltaZ = -0.45; }  
  else if (Af <= (A-134.0)) { DeltaZ = 0.45; }
  else                      { DeltaZ = -0.45*(Af-A*0.5)/(134.0-A*0.5); }

  G4double Zmean = (Af/A)*Z + DeltaZ;
 
  G4double theZ;
  do {
    theZ = G4RandGauss::shoot(Zmean,sigma);
    // Loop checking, 05-Aug-2015, Vladimir Ivanchenko
  } while (theZ  < 1.0 || theZ > (Z-1.0) || theZ > Af);
  
  return G4lrint(theZ);
}

G4double 
G4CompetitiveFission::FissionKineticEnergy(G4int A, G4int Z,
                       G4int Af1, G4int /*Zf1*/,
                       G4int Af2, G4int /*Zf2*/,
                       G4double /*U*/, G4double Tmax)
  // Gives the kinetic energy of fission products
{
  // Find maximal value of A for fragments
  G4int AfMax = std::max(Af1,Af2);

  // Weights for symmetric and asymmetric components
  G4double Pas = 0.0;
  if (theParam.GetW() <= 1000) { 
    G4double x1 = (AfMax-theParam.GetA1())/theParam.GetSigma1();
    G4double x2 = (AfMax-theParam.GetA2())/theParam.GetSigma2();
    Pas = 0.5*G4Exp(-0.5*x1*x1) + G4Exp(-0.5*x2*x2);
  }

  G4double Ps = 0.0;
  if (theParam.GetW() >= 0.001) {
    G4double xs = (AfMax-theParam.GetAs())/theParam.GetSigmaS();
    Ps = theParam.GetW()*G4Exp(-0.5*xs*xs);
  }
  G4double Psy = Ps/(Pas+Ps);

  // Fission fractions Xsy and Xas formed in symmetric and asymmetric modes
  G4double PPas = theParam.GetSigma1() + 2.0 * theParam.GetSigma2();
  G4double PPsy = theParam.GetW() * theParam.GetSigmaS();
  G4double Xas = PPas / (PPas+PPsy);
  G4double Xsy = PPsy / (PPas+PPsy);

  // Average kinetic energy for symmetric and asymmetric components
  G4double Eaverage = (0.1071*(Z*Z)/G4Pow::GetInstance()->Z13(A) + 22.2)*CLHEP::MeV;

  // Compute maximal average kinetic energy of fragments and Energy Dispersion 
  G4double TaverageAfMax;
  G4double ESigma = 10*CLHEP::MeV;
  // Select randomly fission mode (symmetric or asymmetric)
  if (G4UniformRand() > Psy) { // Asymmetric Mode
    G4double A11 = theParam.GetA1()-0.7979*theParam.GetSigma1();
    G4double A12 = theParam.GetA1()+0.7979*theParam.GetSigma1();
    G4double A21 = theParam.GetA2()-0.7979*theParam.GetSigma2();
    G4double A22 = theParam.GetA2()+0.7979*theParam.GetSigma2();
    // scale factor
    G4double ScaleFactor = 0.5*theParam.GetSigma1()*
      (AsymmetricRatio(A,A11)+AsymmetricRatio(A,A12))+
      theParam.GetSigma2()*(AsymmetricRatio(A,A21)+AsymmetricRatio(A,A22));
    // Compute average kinetic energy for fragment with AfMax
    TaverageAfMax = (Eaverage + 12.5 * Xsy) * (PPas/ScaleFactor) * 
      AsymmetricRatio(A,G4double(AfMax));

  } else { // Symmetric Mode
    G4double As0 = theParam.GetAs() + 0.7979*theParam.GetSigmaS();
    // Compute average kinetic energy for fragment with AfMax
    TaverageAfMax = (Eaverage - 12.5*CLHEP::MeV*Xas)
      *SymmetricRatio(A, G4double(AfMax))/SymmetricRatio(A, As0);
    ESigma = 8.0*CLHEP::MeV;
  }

  // Select randomly, in accordance with Gaussian distribution, 
  // fragment kinetic energy
  G4double KineticEnergy;
  G4int i = 0;
  do {
    KineticEnergy = G4RandGauss::shoot(TaverageAfMax, ESigma);
    if (++i > 100) return Eaverage;
    // Loop checking, 05-Aug-2015, Vladimir Ivanchenko
  } while (KineticEnergy < Eaverage-3.72*ESigma || 
       KineticEnergy > Eaverage+3.72*ESigma ||
       KineticEnergy > Tmax);
  
  return KineticEnergy;
}