G4EvaporationProbability.cc

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//
//J.M. Quesada (August2008). Based on:
//
// Hadronic Process: Nuclear De-excitations
// by V. Lara (Oct 1998)
//
// Modif (03 September 2008) by J. M. Quesada for external choice of inverse 
// cross section option
// JMQ (06 September 2008) Also external choices have been added for 
// superimposed Coulomb barrier (if useSICB is set true, by default is false) 
//
// JMQ (14 february 2009) bug fixed in emission width: hbarc instead of hbar_Planck in the denominator
//
#include <iostream>

#include "G4EvaporationProbability.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "G4PairingCorrection.hh"
#include "G4ParticleTable.hh"
#include "G4IonTable.hh"

using namespace std;

G4EvaporationProbability::G4EvaporationProbability(G4int anA, G4int aZ, 
                           G4double aGamma,
                           G4VCoulombBarrier * aCoulombBarrier) 
  : theA(anA),
    theZ(aZ),
    Gamma(aGamma),
    theCoulombBarrierptr(aCoulombBarrier) 
{}

G4EvaporationProbability::G4EvaporationProbability()
  : theA(0),
    theZ(0),
    Gamma(0.0),
    theCoulombBarrierptr(0) 
{}

G4EvaporationProbability::~G4EvaporationProbability() 
{}
  
G4double 
G4EvaporationProbability::EmissionProbability(const G4Fragment & fragment, 
                          G4double anEnergy)
{
  G4double probability = 0.0;

  if (anEnergy > 0.0 && fragment.GetExcitationEnergy() > 0.0) {
    probability = CalculateProbability(fragment, anEnergy);

  }
  return probability;
}

////////////////////////////////////

// Computes the integrated probability of evaporation channel
G4double 
G4EvaporationProbability::CalculateProbability(const G4Fragment & fragment, 
                           G4double MaximalKineticEnergy)
{
  G4int ResidualA = fragment.GetA_asInt() - theA;
  G4int ResidualZ = fragment.GetZ_asInt() - theZ;
  G4double U = fragment.GetExcitationEnergy();
   
  if (OPTxs==0) {

    G4double NuclearMass = fragment.ComputeGroundStateMass(theZ,theA);

    G4double delta0 = fPairCorr->GetPairingCorrection(fragment.GetA_asInt(),
                              fragment.GetZ_asInt());

    G4double SystemEntropy = 2.0*std::sqrt(
      theEvapLDPptr->LevelDensityParameter(fragment.GetA_asInt(),fragment.GetZ_asInt(),U)*
      (U-delta0));
                                  
    static const G4double RN = 1.5*fermi;

    G4double Alpha = CalcAlphaParam(fragment);
    G4double Beta = CalcBetaParam(fragment);
    
    G4double Rmax = MaximalKineticEnergy;
    G4double a = theEvapLDPptr->LevelDensityParameter(ResidualA,ResidualZ,Rmax);
    G4double GlobalFactor = Gamma * Alpha/(a*a) *
    (NuclearMass*RN*RN*fG4pow->Z23(ResidualA))/
    (twopi* hbar_Planck*hbar_Planck);
    G4double Term1 = (2.0*Beta*a-3.0)/2.0 + Rmax*a;
    G4double Term2 = (2.0*Beta*a-3.0)*std::sqrt(Rmax*a) + 2.0*a*Rmax;
    
    G4double ExpTerm1 = 0.0;
    if (SystemEntropy <= 600.0) { ExpTerm1 = std::exp(-SystemEntropy); }
    
    G4double ExpTerm2 = 2.*std::sqrt(a*Rmax) - SystemEntropy;
    if (ExpTerm2 > 700.0) { ExpTerm2 = 700.0; }
    ExpTerm2 = std::exp(ExpTerm2);
    
    G4double Width = GlobalFactor*(Term1*ExpTerm1 + Term2*ExpTerm2);
    
    return Width;
             
 } else if (OPTxs==1 || OPTxs==2 ||OPTxs==3 || OPTxs==4) {

   G4double EvaporatedMass = fragment.ComputeGroundStateMass(theZ,theA);
   G4double ResidulalMass = fragment.ComputeGroundStateMass(ResidualZ,ResidualA);
   G4double limit = std::max(0.0,fragment.GetGroundStateMass()-EvaporatedMass-ResidulalMass);
   if (useSICB) {
     limit = std::max(limit,theCoulombBarrierptr->GetCoulombBarrier(ResidualA,ResidualZ,U));
   }

   if (MaximalKineticEnergy <= limit) { return 0.0; }

   // if Coulomb barrier cutoff is superimposed for all cross sections 
   // then the limit is the Coulomb Barrier
   G4double LowerLimit= limit;

   //MaximalKineticEnergy: asimptotic value (already accounted for in G4EvaporationChannel)     

   G4double UpperLimit = MaximalKineticEnergy;

   G4double Width = IntegrateEmissionProbability(fragment,LowerLimit,UpperLimit);

   return Width;
 } else {
   std::ostringstream errOs;
   errOs << "Bad option for cross sections at evaporation"  <<G4endl;
   throw G4HadronicException(__FILE__, __LINE__, errOs.str());
 }
  
}

/////////////////////////////////////////////////////////////////////

G4double G4EvaporationProbability::
IntegrateEmissionProbability(const G4Fragment & fragment, 
                 const G4double & Low, const G4double & Up )
{
  static const G4int N = 10;
  // 10-Points Gauss-Legendre abcisas and weights
  static const G4double w[N] = {
    0.0666713443086881,
    0.149451349150581,
    0.219086362515982,
    0.269266719309996,
    0.295524224714753,
    0.295524224714753,
    0.269266719309996,
    0.219086362515982,
    0.149451349150581,
    0.0666713443086881
  };
  static const G4double x[N] = {
    -0.973906528517172,
    -0.865063366688985,
    -0.679409568299024,
    -0.433395394129247,
    -0.148874338981631,
    0.148874338981631,
    0.433395394129247,
    0.679409568299024,
    0.865063366688985,
    0.973906528517172
  };

  G4double Total = 0.0;


  for (G4int i = 0; i < N; i++) 
    {

      G4double KineticE = ((Up-Low)*x[i]+(Up+Low))/2.0;

      Total += w[i]*ProbabilityDistributionFunction(fragment, KineticE);

    }
  Total *= (Up-Low)/2.0;
  return Total;
}


/////////////////////////////////////////////////////////
//New method (OPT=1,2,3,4)

G4double 
G4EvaporationProbability::ProbabilityDistributionFunction( const G4Fragment & fragment, 
                               G4double K)
{ 
  G4int ResidualA = fragment.GetA_asInt() - theA;
  G4int ResidualZ = fragment.GetZ_asInt() - theZ;  
  G4double U = fragment.GetExcitationEnergy();
  //G4cout << "### G4EvaporationProbability::ProbabilityDistributionFunction" << G4endl;
  //G4cout << "FragZ= " << fragment.GetZ_asInt() << " FragA= " << fragment.GetA_asInt()
  //     << " Z= " << theZ << "  A= " << theA << G4endl;
  //G4cout << "PC " << fPairCorr << "   DP " << theEvapLDPptr << G4endl;

  // if(K <= theCoulombBarrierptr->GetCoulombBarrier(ResidualA,ResidualZ,U)) return 0.0;

  G4double delta1 = fPairCorr->GetPairingCorrection(ResidualA,ResidualZ);
 
  G4double delta0 = fPairCorr->GetPairingCorrection(fragment.GetA_asInt(),
                            fragment.GetZ_asInt());

  
  G4double ParticleMass = fragment.ComputeGroundStateMass(theZ,theA);
  G4double ResidualMass = fragment.ComputeGroundStateMass(ResidualZ,ResidualA);

  G4double theSeparationEnergy = ParticleMass + ResidualMass 
    - fragment.GetGroundStateMass();

  G4double a0 = theEvapLDPptr->LevelDensityParameter(fragment.GetA_asInt(),
                             fragment.GetZ_asInt(),
                             U - delta0);

  G4double a1 = theEvapLDPptr->LevelDensityParameter(ResidualA, ResidualZ,
                             U - theSeparationEnergy - delta1);
  
  
  G4double E0 = U - delta0;

  G4double E1 = U - theSeparationEnergy - delta1 - K;

  if (E1<0.) { return 0.; }

  //JMQ 14/02/09 BUG fixed: hbarc should be in the denominator instead of hbar_Planck 
  //Without 1/hbar_Panck remains as a width

  //G4double Prob=Gamma*ParticleMass/((pi*hbarc)*(pi*hbarc)*std::exp(2*std::sqrt(a0*E0)))
  //  *K*CrossSection(fragment,K)*std::exp(2*std::sqrt(a1*E1))*millibarn;

  static const G4double pcoeff = millibarn/((pi*hbarc)*(pi*hbarc)); 

  // Fixed numerical problem
  G4double Prob = pcoeff*Gamma*ParticleMass*std::exp(2*(std::sqrt(a1*E1) - std::sqrt(a0*E0)))
    *K*CrossSection(fragment,K);

  return Prob;
}