G4DiffuseElastic.cc

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// $Id: G4DiffuseElastic.cc 70682 2013-06-04 07:57:01Z gcosmo $
//
//
// Physics model class G4DiffuseElastic 
//
//
// G4 Model: optical diffuse elastic scattering with 4-momentum balance
//                         
// 24-May-07 V. Grichine
//

#include "G4DiffuseElastic.hh"
#include "G4ParticleTable.hh"
#include "G4ParticleDefinition.hh"
#include "G4IonTable.hh"
#include "G4NucleiProperties.hh"

#include "Randomize.hh"
#include "G4Integrator.hh"
#include "globals.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"

#include "G4Proton.hh"
#include "G4Neutron.hh"
#include "G4Deuteron.hh"
#include "G4Alpha.hh"
#include "G4PionPlus.hh"
#include "G4PionMinus.hh"

#include "G4Element.hh"
#include "G4ElementTable.hh"
#include "G4PhysicsTable.hh"
#include "G4PhysicsLogVector.hh"
#include "G4PhysicsFreeVector.hh"

/////////////////////////////////////////////////////////////////////////
//
// Test Constructor. Just to check xsc


G4DiffuseElastic::G4DiffuseElastic() 
  : G4HadronElastic("DiffuseElastic"), fParticle(0)
{
  SetMinEnergy( 0.01*GeV );
  SetMaxEnergy( 1.*TeV );
  verboseLevel = 0;
  lowEnergyRecoilLimit = 100.*keV;  
  lowEnergyLimitQ  = 0.0*GeV;  
  lowEnergyLimitHE = 0.0*GeV;  
  lowestEnergyLimit= 0.0*keV;  
  plabLowLimit     = 20.0*MeV;

  theProton   = G4Proton::Proton();
  theNeutron  = G4Neutron::Neutron();
  theDeuteron = G4Deuteron::Deuteron();
  theAlpha    = G4Alpha::Alpha();
  thePionPlus = G4PionPlus::PionPlus();
  thePionMinus= G4PionMinus::PionMinus();

  fEnergyBin = 200;
  fAngleBin  = 200;

  fEnergyVector =  new G4PhysicsLogVector( theMinEnergy, theMaxEnergy, fEnergyBin );
  fAngleTable = 0;

  fParticle = 0;
  fWaveVector = 0.;
  fAtomicWeight = 0.;
  fAtomicNumber = 0.;
  fNuclearRadius = 0.;
  fBeta = 0.;
  fZommerfeld = 0.;
  fAm = 0.;
  fAddCoulomb = false;
}

//////////////////////////////////////////////////////////////////////////////
//
// Destructor

G4DiffuseElastic::~G4DiffuseElastic()
{
  if(fEnergyVector) delete fEnergyVector;

  if( fAngleTable )
  {
      fAngleTable->clearAndDestroy();
      delete fAngleTable ;
  }
}

//////////////////////////////////////////////////////////////////////////////
//
// Initialisation for given particle using element table of application

void G4DiffuseElastic::Initialise() 
{

  // fEnergyVector = new G4PhysicsLogVector( theMinEnergy, theMaxEnergy, fEnergyBin );

  const G4ElementTable* theElementTable = G4Element::GetElementTable();

  size_t jEl, numOfEl = G4Element::GetNumberOfElements();

  for(jEl = 0 ; jEl < numOfEl; ++jEl) // application element loop
  {
    fAtomicNumber = (*theElementTable)[jEl]->GetZ();     // atomic number
    fAtomicWeight = (*theElementTable)[jEl]->GetN();     // number of nucleons
    fNuclearRadius = CalculateNuclearRad(fAtomicWeight);

    if(verboseLevel > 0) 
    {   
      G4cout<<"G4DiffuseElastic::Initialise() the element: "
        <<(*theElementTable)[jEl]->GetName()<<G4endl;
    }
    fElementNumberVector.push_back(fAtomicNumber);
    fElementNameVector.push_back((*theElementTable)[jEl]->GetName());

    BuildAngleTable();
    fAngleBank.push_back(fAngleTable);
  }  
  return;
}

////////////////////////////////////////////////////////////////////////////
//
// return differential elastic cross section d(sigma)/d(omega) 

G4double 
G4DiffuseElastic::GetDiffuseElasticXsc( const G4ParticleDefinition* particle, 
                                        G4double theta, 
                            G4double momentum, 
                                        G4double A         )
{
  fParticle      = particle;
  fWaveVector    = momentum/hbarc;
  fAtomicWeight  = A;
  fAddCoulomb    = false;
  fNuclearRadius = CalculateNuclearRad(A);

  G4double sigma = fNuclearRadius*fNuclearRadius*GetDiffElasticProb(theta);

  return sigma;
}

////////////////////////////////////////////////////////////////////////////
//
// return invariant differential elastic cross section d(sigma)/d(tMand) 

G4double 
G4DiffuseElastic::GetInvElasticXsc( const G4ParticleDefinition* particle, 
                                        G4double tMand, 
                            G4double plab, 
                                        G4double A, G4double Z         )
{
  G4double m1 = particle->GetPDGMass();
  G4LorentzVector lv1(0.,0.,plab,std::sqrt(plab*plab+m1*m1));

  G4int iZ = static_cast<G4int>(Z+0.5);
  G4int iA = static_cast<G4int>(A+0.5);
  G4ParticleDefinition * theDef = 0;

  if      (iZ == 1 && iA == 1) theDef = theProton;
  else if (iZ == 1 && iA == 2) theDef = theDeuteron;
  else if (iZ == 1 && iA == 3) theDef = G4Triton::Triton();
  else if (iZ == 2 && iA == 3) theDef = G4He3::He3();
  else if (iZ == 2 && iA == 4) theDef = theAlpha;
  else theDef = G4ParticleTable::GetParticleTable()->GetIonTable()->GetIon(iZ,iA,0);
 
  G4double tmass = theDef->GetPDGMass();

  G4LorentzVector lv(0.0,0.0,0.0,tmass);   
  lv += lv1;

  G4ThreeVector bst = lv.boostVector();
  lv1.boost(-bst);

  G4ThreeVector p1 = lv1.vect();
  G4double ptot    = p1.mag();
  G4double ptot2 = ptot*ptot;
  G4double cost = 1 - 0.5*std::fabs(tMand)/ptot2;

  if( cost >= 1.0 )      cost = 1.0;  
  else if( cost <= -1.0) cost = -1.0;
  
  G4double thetaCMS = std::acos(cost);

  G4double sigma = GetDiffuseElasticXsc( particle, thetaCMS, ptot, A);

  sigma *= pi/ptot2;

  return sigma;
}

////////////////////////////////////////////////////////////////////////////
//
// return differential elastic cross section d(sigma)/d(omega) with Coulomb
// correction

G4double 
G4DiffuseElastic::GetDiffuseElasticSumXsc( const G4ParticleDefinition* particle, 
                                        G4double theta, 
                            G4double momentum, 
                                        G4double A, G4double Z         )
{
  fParticle      = particle;
  fWaveVector    = momentum/hbarc;
  fAtomicWeight  = A;
  fAtomicNumber  = Z;
  fNuclearRadius = CalculateNuclearRad(A);
  fAddCoulomb    = false;

  G4double z     = particle->GetPDGCharge();

  G4double kRt   = fWaveVector*fNuclearRadius*theta;
  G4double kRtC  = 1.9;

  if( z && (kRt > kRtC) )
  {
    fAddCoulomb = true;
    fBeta       = CalculateParticleBeta( particle, momentum);
    fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
    fAm         = CalculateAm( momentum, fZommerfeld, fAtomicNumber);
  }
  G4double sigma = fNuclearRadius*fNuclearRadius*GetDiffElasticSumProb(theta);

  return sigma;
}

////////////////////////////////////////////////////////////////////////////
//
// return invariant differential elastic cross section d(sigma)/d(tMand) with Coulomb
// correction

G4double 
G4DiffuseElastic::GetInvElasticSumXsc( const G4ParticleDefinition* particle, 
                                        G4double tMand, 
                            G4double plab, 
                                        G4double A, G4double Z         )
{
  G4double m1 = particle->GetPDGMass();

  G4LorentzVector lv1(0.,0.,plab,std::sqrt(plab*plab+m1*m1));

  G4int iZ = static_cast<G4int>(Z+0.5);
  G4int iA = static_cast<G4int>(A+0.5);

  G4ParticleDefinition* theDef = 0;

  if      (iZ == 1 && iA == 1) theDef = theProton;
  else if (iZ == 1 && iA == 2) theDef = theDeuteron;
  else if (iZ == 1 && iA == 3) theDef = G4Triton::Triton();
  else if (iZ == 2 && iA == 3) theDef = G4He3::He3();
  else if (iZ == 2 && iA == 4) theDef = theAlpha;
  else theDef = G4ParticleTable::GetParticleTable()->GetIonTable()->GetIon(iZ,iA,0);
 
  G4double tmass = theDef->GetPDGMass();

  G4LorentzVector lv(0.0,0.0,0.0,tmass);   
  lv += lv1;

  G4ThreeVector bst = lv.boostVector();
  lv1.boost(-bst);

  G4ThreeVector p1 = lv1.vect();
  G4double ptot    = p1.mag();
  G4double ptot2   = ptot*ptot;
  G4double cost    = 1 - 0.5*std::fabs(tMand)/ptot2;

  if( cost >= 1.0 )      cost = 1.0;  
  else if( cost <= -1.0) cost = -1.0;
  
  G4double thetaCMS = std::acos(cost);

  G4double sigma = GetDiffuseElasticSumXsc( particle, thetaCMS, ptot, A, Z );

  sigma *= pi/ptot2;

  return sigma;
}

////////////////////////////////////////////////////////////////////////////
//
// return invariant differential elastic cross section d(sigma)/d(tMand) with Coulomb
// correction

G4double 
G4DiffuseElastic::GetInvCoulombElasticXsc( const G4ParticleDefinition* particle, 
                                        G4double tMand, 
                            G4double plab, 
                                        G4double A, G4double Z         )
{
  G4double m1 = particle->GetPDGMass();
  G4LorentzVector lv1(0.,0.,plab,std::sqrt(plab*plab+m1*m1));

  G4int iZ = static_cast<G4int>(Z+0.5);
  G4int iA = static_cast<G4int>(A+0.5);
  G4ParticleDefinition * theDef = 0;

  if      (iZ == 1 && iA == 1) theDef = theProton;
  else if (iZ == 1 && iA == 2) theDef = theDeuteron;
  else if (iZ == 1 && iA == 3) theDef = G4Triton::Triton();
  else if (iZ == 2 && iA == 3) theDef = G4He3::He3();
  else if (iZ == 2 && iA == 4) theDef = theAlpha;
  else theDef = G4ParticleTable::GetParticleTable()->GetIonTable()->GetIon(iZ,iA,0);
 
  G4double tmass = theDef->GetPDGMass();

  G4LorentzVector lv(0.0,0.0,0.0,tmass);   
  lv += lv1;

  G4ThreeVector bst = lv.boostVector();
  lv1.boost(-bst);

  G4ThreeVector p1 = lv1.vect();
  G4double ptot    = p1.mag();
  G4double ptot2 = ptot*ptot;
  G4double cost = 1 - 0.5*std::fabs(tMand)/ptot2;

  if( cost >= 1.0 )      cost = 1.0;  
  else if( cost <= -1.0) cost = -1.0;
  
  G4double thetaCMS = std::acos(cost);

  G4double sigma = GetCoulombElasticXsc( particle, thetaCMS, ptot, Z );

  sigma *= pi/ptot2;

  return sigma;
}

////////////////////////////////////////////////////////////////////////////
//
// return differential elastic probability d(probability)/d(omega) 

G4double 
G4DiffuseElastic::GetDiffElasticProb( // G4ParticleDefinition* particle, 
                                        G4double theta 
                    //  G4double momentum, 
                    // G4double A         
                                     )
{
  G4double sigma, bzero, bzero2, bonebyarg, bonebyarg2, damp, damp2;
  G4double delta, diffuse, gamma;
  G4double e1, e2, bone, bone2;

  // G4double wavek = momentum/hbarc;  // wave vector
  // G4double r0    = 1.08*fermi;
  // G4double rad   = r0*std::pow(A, 1./3.);

  G4double kr    = fWaveVector*fNuclearRadius; // wavek*rad;
  G4double kr2   = kr*kr;
  G4double krt   = kr*theta;

  bzero      = BesselJzero(krt);
  bzero2     = bzero*bzero;    
  bone       = BesselJone(krt);
  bone2      = bone*bone;
  bonebyarg  = BesselOneByArg(krt);
  bonebyarg2 = bonebyarg*bonebyarg;  

  if (fParticle == theProton)
  {
    diffuse = 0.63*fermi;
    gamma   = 0.3*fermi;
    delta   = 0.1*fermi*fermi;
    e1      = 0.3*fermi;
    e2      = 0.35*fermi;
  }
  else // as proton, if were not defined 
  {
    diffuse = 0.63*fermi;
    gamma   = 0.3*fermi;
    delta   = 0.1*fermi*fermi;
    e1      = 0.3*fermi;
    e2      = 0.35*fermi;
  }
  G4double lambda = 15.; // 15 ok

  //  G4double kgamma    = fWaveVector*gamma;   // wavek*delta;

  G4double kgamma    = lambda*(1.-std::exp(-fWaveVector*gamma/lambda));   // wavek*delta;
  G4double kgamma2   = kgamma*kgamma;

  // G4double dk2t  = delta*fWaveVector*fWaveVector*theta; // delta*wavek*wavek*theta;
  // G4double dk2t2 = dk2t*dk2t;
  // G4double pikdt = pi*fWaveVector*diffuse*theta;// pi*wavek*diffuse*theta;

  G4double pikdt    = lambda*(1.-std::exp(-pi*fWaveVector*diffuse*theta/lambda));   // wavek*delta;

  damp           = DampFactor(pikdt);
  damp2          = damp*damp;

  G4double mode2k2 = (e1*e1+e2*e2)*fWaveVector*fWaveVector;  
  G4double e2dk3t  = -2.*e2*delta*fWaveVector*fWaveVector*fWaveVector*theta;


  sigma  = kgamma2;
  // sigma  += dk2t2;
  sigma *= bzero2;
  sigma += mode2k2*bone2 + e2dk3t*bzero*bone;
  sigma += kr2*bonebyarg2;
  sigma *= damp2;          // *rad*rad;

  return sigma;
}

////////////////////////////////////////////////////////////////////////////
//
// return differential elastic probability d(probability)/d(omega) with 
// Coulomb correction

G4double 
G4DiffuseElastic::GetDiffElasticSumProb( // G4ParticleDefinition* particle, 
                                        G4double theta 
                    //  G4double momentum, 
                    // G4double A         
                                     )
{
  G4double sigma, bzero, bzero2, bonebyarg, bonebyarg2, damp, damp2;
  G4double delta, diffuse, gamma;
  G4double e1, e2, bone, bone2;

  // G4double wavek = momentum/hbarc;  // wave vector
  // G4double r0    = 1.08*fermi;
  // G4double rad   = r0*std::pow(A, 1./3.);

  G4double kr    = fWaveVector*fNuclearRadius; // wavek*rad;
  G4double kr2   = kr*kr;
  G4double krt   = kr*theta;

  bzero      = BesselJzero(krt);
  bzero2     = bzero*bzero;    
  bone       = BesselJone(krt);
  bone2      = bone*bone;
  bonebyarg  = BesselOneByArg(krt);
  bonebyarg2 = bonebyarg*bonebyarg;  

  if (fParticle == theProton)
  {
    diffuse = 0.63*fermi;
    // diffuse = 0.6*fermi;
    gamma   = 0.3*fermi;
    delta   = 0.1*fermi*fermi;
    e1      = 0.3*fermi;
    e2      = 0.35*fermi;
  }
  else // as proton, if were not defined 
  {
    diffuse = 0.63*fermi;
    gamma   = 0.3*fermi;
    delta   = 0.1*fermi*fermi;
    e1      = 0.3*fermi;
    e2      = 0.35*fermi;
  }
  G4double lambda = 15.; // 15 ok
  // G4double kgamma    = fWaveVector*gamma;   // wavek*delta;
  G4double kgamma    = lambda*(1.-std::exp(-fWaveVector*gamma/lambda));   // wavek*delta;

  // G4cout<<"kgamma = "<<kgamma<<G4endl;

  if(fAddCoulomb)  // add Coulomb correction
  {
    G4double sinHalfTheta  = std::sin(0.5*theta);
    G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;

    kgamma += 0.5*fZommerfeld/kr/(sinHalfTheta2+fAm); // correction at J0()
  // kgamma += 0.65*fZommerfeld/kr/(sinHalfTheta2+fAm); // correction at J0()
  }

  G4double kgamma2   = kgamma*kgamma;

  // G4double dk2t  = delta*fWaveVector*fWaveVector*theta; // delta*wavek*wavek*theta;
  //   G4cout<<"dk2t = "<<dk2t<<G4endl;
  // G4double dk2t2 = dk2t*dk2t;
  // G4double pikdt = pi*fWaveVector*diffuse*theta;// pi*wavek*diffuse*theta;

  G4double pikdt    = lambda*(1.-std::exp(-pi*fWaveVector*diffuse*theta/lambda));   // wavek*delta;

  // G4cout<<"pikdt = "<<pikdt<<G4endl;

  damp           = DampFactor(pikdt);
  damp2          = damp*damp;

  G4double mode2k2 = (e1*e1+e2*e2)*fWaveVector*fWaveVector;  
  G4double e2dk3t  = -2.*e2*delta*fWaveVector*fWaveVector*fWaveVector*theta;

  sigma  = kgamma2;
  // sigma += dk2t2;
  sigma *= bzero2;
  sigma += mode2k2*bone2; 
  sigma += e2dk3t*bzero*bone;

  // sigma += kr2*(1 + 8.*fZommerfeld*fZommerfeld/kr2)*bonebyarg2;  // correction at J1()/()
  sigma += kr2*bonebyarg2;  // correction at J1()/()

  sigma *= damp2;          // *rad*rad;

  return sigma;
}


////////////////////////////////////////////////////////////////////////////
//
// return differential elastic probability d(probability)/d(t) with 
// Coulomb correction

G4double 
G4DiffuseElastic::GetDiffElasticSumProbA( G4double alpha )
{
  G4double theta; 

  theta = std::sqrt(alpha);

  // theta = std::acos( 1 - alpha/2. );

  G4double sigma, bzero, bzero2, bonebyarg, bonebyarg2, damp, damp2;
  G4double delta, diffuse, gamma;
  G4double e1, e2, bone, bone2;

  // G4double wavek = momentum/hbarc;  // wave vector
  // G4double r0    = 1.08*fermi;
  // G4double rad   = r0*std::pow(A, 1./3.);

  G4double kr    = fWaveVector*fNuclearRadius; // wavek*rad;
  G4double kr2   = kr*kr;
  G4double krt   = kr*theta;

  bzero      = BesselJzero(krt);
  bzero2     = bzero*bzero;    
  bone       = BesselJone(krt);
  bone2      = bone*bone;
  bonebyarg  = BesselOneByArg(krt);
  bonebyarg2 = bonebyarg*bonebyarg;  

  if (fParticle == theProton)
  {
    diffuse = 0.63*fermi;
    // diffuse = 0.6*fermi;
    gamma   = 0.3*fermi;
    delta   = 0.1*fermi*fermi;
    e1      = 0.3*fermi;
    e2      = 0.35*fermi;
  }
  else // as proton, if were not defined 
  {
    diffuse = 0.63*fermi;
    gamma   = 0.3*fermi;
    delta   = 0.1*fermi*fermi;
    e1      = 0.3*fermi;
    e2      = 0.35*fermi;
  }
  G4double lambda = 15.; // 15 ok
  // G4double kgamma    = fWaveVector*gamma;   // wavek*delta;
  G4double kgamma    = lambda*(1.-std::exp(-fWaveVector*gamma/lambda));   // wavek*delta;

  // G4cout<<"kgamma = "<<kgamma<<G4endl;

  if(fAddCoulomb)  // add Coulomb correction
  {
    G4double sinHalfTheta  = theta*0.5; // std::sin(0.5*theta);
    G4double sinHalfTheta2 = sinHalfTheta*sinHalfTheta;

    kgamma += 0.5*fZommerfeld/kr/(sinHalfTheta2+fAm); // correction at J0()
  // kgamma += 0.65*fZommerfeld/kr/(sinHalfTheta2+fAm); // correction at J0()
  }

  G4double kgamma2   = kgamma*kgamma;

  // G4double dk2t  = delta*fWaveVector*fWaveVector*theta; // delta*wavek*wavek*theta;
  //   G4cout<<"dk2t = "<<dk2t<<G4endl;
  // G4double dk2t2 = dk2t*dk2t;
  // G4double pikdt = pi*fWaveVector*diffuse*theta;// pi*wavek*diffuse*theta;

  G4double pikdt    = lambda*(1.-std::exp(-pi*fWaveVector*diffuse*theta/lambda));   // wavek*delta;

  // G4cout<<"pikdt = "<<pikdt<<G4endl;

  damp           = DampFactor(pikdt);
  damp2          = damp*damp;

  G4double mode2k2 = (e1*e1+e2*e2)*fWaveVector*fWaveVector;  
  G4double e2dk3t  = -2.*e2*delta*fWaveVector*fWaveVector*fWaveVector*theta;

  sigma  = kgamma2;
  // sigma += dk2t2;
  sigma *= bzero2;
  sigma += mode2k2*bone2; 
  sigma += e2dk3t*bzero*bone;

  // sigma += kr2*(1 + 8.*fZommerfeld*fZommerfeld/kr2)*bonebyarg2;  // correction at J1()/()
  sigma += kr2*bonebyarg2;  // correction at J1()/()

  sigma *= damp2;          // *rad*rad;

  return sigma;
}


////////////////////////////////////////////////////////////////////////////
//
// return differential elastic probability 2*pi*sin(theta)*d(probability)/d(omega) 

G4double 
G4DiffuseElastic::GetIntegrandFunction( G4double alpha )
{
  G4double result;

  result  = GetDiffElasticSumProbA(alpha);

  // result *= 2*pi*std::sin(theta);

  return result;
}

////////////////////////////////////////////////////////////////////////////
//
// return integral elastic cross section d(sigma)/d(omega) integrated 0 - theta 

G4double 
G4DiffuseElastic::IntegralElasticProb(  const G4ParticleDefinition* particle, 
                                        G4double theta, 
                            G4double momentum, 
                                        G4double A         )
{
  G4double result;
  fParticle      = particle;
  fWaveVector    = momentum/hbarc;
  fAtomicWeight  = A;

  fNuclearRadius = CalculateNuclearRad(A);


  G4Integrator<G4DiffuseElastic,G4double(G4DiffuseElastic::*)(G4double)> integral;

  // result = integral.Legendre10(this,&G4DiffuseElastic::GetIntegrandFunction, 0., theta ); 
  result = integral.Legendre96(this,&G4DiffuseElastic::GetIntegrandFunction, 0., theta ); 

  return result;
}

////////////////////////////////////////////////////////////////////////////
//
// Return inv momentum transfer -t > 0

G4double G4DiffuseElastic::SampleT( const G4ParticleDefinition* aParticle, G4double p, G4double A)
{
  G4double theta = SampleThetaCMS( aParticle,  p, A); // sample theta in cms
  G4double t     = 2*p*p*( 1 - std::cos(theta) ); // -t !!!
  return t;
}

////////////////////////////////////////////////////////////////////////////
//
// Return scattering angle sampled in cms


G4double 
G4DiffuseElastic::SampleThetaCMS(const G4ParticleDefinition* particle, 
                                       G4double momentum, G4double A)
{
  G4int i, iMax = 100;  
  G4double norm, result, theta1, theta2, thetaMax, sum = 0.;

  fParticle      = particle;
  fWaveVector    = momentum/hbarc;
  fAtomicWeight  = A;

  fNuclearRadius = CalculateNuclearRad(A);
  
  thetaMax = 10.174/fWaveVector/fNuclearRadius;

  if (thetaMax > pi) thetaMax = pi;

  G4Integrator<G4DiffuseElastic,G4double(G4DiffuseElastic::*)(G4double)> integral;

  // result = integral.Legendre10(this,&G4DiffuseElastic::GetIntegrandFunction, 0., theta ); 
  norm = integral.Legendre96(this,&G4DiffuseElastic::GetIntegrandFunction, 0., thetaMax );

  norm *= G4UniformRand();

  for(i = 1; i <= iMax; i++)
  {
    theta1 = (i-1)*thetaMax/iMax; 
    theta2 = i*thetaMax/iMax;
    sum   += integral.Legendre10(this,&G4DiffuseElastic::GetIntegrandFunction, theta1, theta2);

    if ( sum >= norm ) 
    {
      result = 0.5*(theta1 + theta2);
      break;
    }
  }
  if (i > iMax ) result = 0.5*(theta1 + theta2);

  G4double sigma = pi*thetaMax/iMax;

  result += G4RandGauss::shoot(0.,sigma);

  if(result < 0.) result = 0.;
  if(result > thetaMax) result = thetaMax;

  return result;
}

/////////////////////////////////////////////////////////////////////////////
/////////////////////  Table preparation and reading ////////////////////////
////////////////////////////////////////////////////////////////////////////
//
// Return inv momentum transfer -t > 0 from initialisation table

G4double G4DiffuseElastic::SampleInvariantT( const G4ParticleDefinition* aParticle, G4double p, 
                                               G4int Z, G4int A)
{
  fParticle = aParticle;
  G4double m1 = fParticle->GetPDGMass();
  G4double totElab = std::sqrt(m1*m1+p*p);
  G4double mass2 = G4NucleiProperties::GetNuclearMass(A, Z);
  G4LorentzVector lv1(p,0.0,0.0,totElab);
  G4LorentzVector  lv(0.0,0.0,0.0,mass2);   
  lv += lv1;

  G4ThreeVector bst = lv.boostVector();
  lv1.boost(-bst);

  G4ThreeVector p1 = lv1.vect();
  G4double momentumCMS = p1.mag();

  G4double t = SampleTableT( aParticle,  momentumCMS, G4double(Z), G4double(A) ); // sample theta2 in cms
  return t;
}

////////////////////////////////////////////////////////////////////////////
//
// Return inv momentum transfer -t > 0 from initialisation table

G4double G4DiffuseElastic::SampleTableT( const G4ParticleDefinition* aParticle, G4double p, 
                                               G4double Z, G4double A)
{
  G4double alpha = SampleTableThetaCMS( aParticle,  p, Z, A); // sample theta2 in cms
  // G4double t     = 2*p*p*( 1 - std::cos(std::sqrt(alpha)) );             // -t !!!
  G4double t     = p*p*alpha;             // -t !!!
  return t;
}

////////////////////////////////////////////////////////////////////////////
//
// Return scattering angle2 sampled in cms according to precalculated table.


G4double 
G4DiffuseElastic::SampleTableThetaCMS(const G4ParticleDefinition* particle, 
                                       G4double momentum, G4double Z, G4double A)
{
  size_t iElement;
  G4int iMomentum, iAngle;  
  G4double randAngle, position, theta1, theta2, E1, E2, W1, W2, W;  
  G4double m1 = particle->GetPDGMass();

  for(iElement = 0; iElement < fElementNumberVector.size(); iElement++)
  {
    if( std::fabs(Z - fElementNumberVector[iElement]) < 0.5) break;
  }
  if ( iElement == fElementNumberVector.size() ) 
  {
    InitialiseOnFly(Z,A); // table preparation, if needed

    // iElement--;

    // G4cout << "G4DiffuseElastic: Element with atomic number " << Z
    // << " is not found, return zero angle" << G4endl;
    // return 0.; // no table for this element
  }
  // G4cout<<"iElement = "<<iElement<<G4endl;

  fAngleTable = fAngleBank[iElement];

  G4double kinE = std::sqrt(momentum*momentum + m1*m1) - m1;

  for( iMomentum = 0; iMomentum < fEnergyBin; iMomentum++)
  {
    if( kinE < fEnergyVector->GetLowEdgeEnergy(iMomentum) ) break;
  }
  if ( iMomentum >= fEnergyBin ) iMomentum = fEnergyBin-1;   // kinE is more then theMaxEnergy
  if ( iMomentum < 0 )           iMomentum = 0; // against negative index, kinE < theMinEnergy

  // G4cout<<"iMomentum = "<<iMomentum<<G4endl;

  if (iMomentum == fEnergyBin -1 || iMomentum == 0 )   // the table edges
  {
    position = (*(*fAngleTable)(iMomentum))(fAngleBin-2)*G4UniformRand();

    // G4cout<<"position = "<<position<<G4endl;

    for(iAngle = 0; iAngle < fAngleBin-1; iAngle++)
    {
      if( position < (*(*fAngleTable)(iMomentum))(iAngle) ) break;
    }
    if (iAngle >= fAngleBin-1) iAngle = fAngleBin-2;

    // G4cout<<"iAngle = "<<iAngle<<G4endl;

    randAngle = GetScatteringAngle(iMomentum, iAngle, position);

    // G4cout<<"randAngle = "<<randAngle<<G4endl;
  }
  else  // kinE inside between energy table edges
  {
    // position = (*(*fAngleTable)(iMomentum))(fAngleBin-2)*G4UniformRand();
    position = (*(*fAngleTable)(iMomentum))(0)*G4UniformRand();

    // G4cout<<"position = "<<position<<G4endl;

    for(iAngle = 0; iAngle < fAngleBin-1; iAngle++)
    {
      // if( position < (*(*fAngleTable)(iMomentum))(iAngle) ) break;
      if( position > (*(*fAngleTable)(iMomentum))(iAngle) ) break;
    }
    if (iAngle >= fAngleBin-1) iAngle = fAngleBin-2;

    // G4cout<<"iAngle = "<<iAngle<<G4endl;

    theta2  = GetScatteringAngle(iMomentum, iAngle, position);

    // G4cout<<"theta2 = "<<theta2<<G4endl;
    E2 = fEnergyVector->GetLowEdgeEnergy(iMomentum);

    // G4cout<<"E2 = "<<E2<<G4endl;
    
    iMomentum--;
    
    // position = (*(*fAngleTable)(iMomentum))(fAngleBin-2)*G4UniformRand();

    // G4cout<<"position = "<<position<<G4endl;

    for(iAngle = 0; iAngle < fAngleBin-1; iAngle++)
    {
      // if( position < (*(*fAngleTable)(iMomentum))(iAngle) ) break;
      if( position > (*(*fAngleTable)(iMomentum))(iAngle) ) break;
    }
    if (iAngle >= fAngleBin-1) iAngle = fAngleBin-2;
    
    theta1  = GetScatteringAngle(iMomentum, iAngle, position);

    // G4cout<<"theta1 = "<<theta1<<G4endl;

    E1 = fEnergyVector->GetLowEdgeEnergy(iMomentum);

    // G4cout<<"E1 = "<<E1<<G4endl;

    W  = 1.0/(E2 - E1);
    W1 = (E2 - kinE)*W;
    W2 = (kinE - E1)*W;

    randAngle = W1*theta1 + W2*theta2;
    
    // randAngle = theta2;
    // G4cout<<"randAngle = "<<randAngle<<G4endl;
  }
  // G4double angle = randAngle;
  // if (randAngle > 0.) randAngle /= 2*pi*std::sin(angle);

  return randAngle;
}

//////////////////////////////////////////////////////////////////////////////
//
// Initialisation for given particle on fly using new element number

void G4DiffuseElastic::InitialiseOnFly(G4double Z, G4double A) 
{
  fAtomicNumber  = Z;     // atomic number
  fAtomicWeight  = A;     // number of nucleons

  fNuclearRadius = CalculateNuclearRad(fAtomicWeight);
  
  if( verboseLevel > 0 )    
  {
    G4cout<<"G4DiffuseElastic::Initialise() the element with Z = "
      <<Z<<"; and A = "<<A<<G4endl;
  }
  fElementNumberVector.push_back(fAtomicNumber);

  BuildAngleTable();

  fAngleBank.push_back(fAngleTable);

  return;
}

///////////////////////////////////////////////////////////////////////////////
//
// Build for given particle and element table of momentum, angle probability.
// For the moment in lab system. 

void G4DiffuseElastic::BuildAngleTable() 
{
  G4int i, j;
  G4double partMom, kinE, a = 0., z = fParticle->GetPDGCharge(), m1 = fParticle->GetPDGMass();
  G4double alpha1, alpha2, alphaMax, alphaCoulomb, delta = 0., sum = 0.;

  G4Integrator<G4DiffuseElastic,G4double(G4DiffuseElastic::*)(G4double)> integral;
  
  fAngleTable = new G4PhysicsTable(fEnergyBin);

  for( i = 0; i < fEnergyBin; i++)
  {
    kinE        = fEnergyVector->GetLowEdgeEnergy(i);
    partMom     = std::sqrt( kinE*(kinE + 2*m1) );

    fWaveVector = partMom/hbarc;

    G4double kR     = fWaveVector*fNuclearRadius;
    G4double kR2    = kR*kR;
    G4double kRmax  = 18.6; // 10.6; 10.6, 18, 10.174; ~ 3 maxima of J1 or 15., 25.
    G4double kRcoul = 1.9; // 1.2; 1.4, 2.5; // on the first slope of J1
    // G4double kRlim  = 1.2;
    // G4double kRlim2 = kRlim*kRlim/kR2;

    alphaMax = kRmax*kRmax/kR2;

    if (alphaMax > 4.) alphaMax = 4.;  // vmg05-02-09: was pi2 

    alphaCoulomb = kRcoul*kRcoul/kR2;

    if( z )
    {
      a           = partMom/m1;         // beta*gamma for m1
      fBeta       = a/std::sqrt(1+a*a);
      fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
      fAm         = CalculateAm( partMom, fZommerfeld, fAtomicNumber);
    }
    G4PhysicsFreeVector* angleVector = new G4PhysicsFreeVector(fAngleBin-1);

    // G4PhysicsLogVector*  angleBins = new G4PhysicsLogVector( 0.001*alphaMax, alphaMax, fAngleBin );

    G4double delth = alphaMax/fAngleBin;
        
    sum = 0.;

    // fAddCoulomb = false;
    fAddCoulomb = true;

    // for(j = 1; j < fAngleBin; j++)
    for(j = fAngleBin-1; j >= 1; j--)
    {
      // alpha1 = angleBins->GetLowEdgeEnergy(j-1);
      // alpha2 = angleBins->GetLowEdgeEnergy(j);

      // alpha1 = alphaMax*(j-1)/fAngleBin;
      // alpha2 = alphaMax*( j )/fAngleBin;

      alpha1 = delth*(j-1);
      // if(alpha1 < kRlim2) alpha1 = kRlim2;
      alpha2 = alpha1 + delth;

      // if( ( alpha2 > alphaCoulomb ) && z ) fAddCoulomb = true;
      if( ( alpha1 < alphaCoulomb ) && z ) fAddCoulomb = false;

      delta = integral.Legendre10(this, &G4DiffuseElastic::GetIntegrandFunction, alpha1, alpha2);
      // delta = integral.Legendre96(this, &G4DiffuseElastic::GetIntegrandFunction, alpha1, alpha2);

      sum += delta;
      
      angleVector->PutValue( j-1 , alpha1, sum ); // alpha2
      // G4cout<<"j-1 = "<<j-1<<"; alpha2 = "<<alpha2<<"; sum = "<<sum<<G4endl;
    }
    fAngleTable->insertAt(i,angleVector);

    // delete[] angleVector; 
    // delete[] angleBins; 
  }
  return;
}

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

G4double 
G4DiffuseElastic:: GetScatteringAngle( G4int iMomentum, G4int iAngle, G4double position )
{
 G4double x1, x2, y1, y2, randAngle;

  if( iAngle == 0 )
  {
    randAngle = (*fAngleTable)(iMomentum)->GetLowEdgeEnergy(iAngle);
    // iAngle++;
  }
  else
  {
    if ( iAngle >= G4int((*fAngleTable)(iMomentum)->GetVectorLength()) )
    {
      iAngle = (*fAngleTable)(iMomentum)->GetVectorLength() - 1;
    }
    y1 = (*(*fAngleTable)(iMomentum))(iAngle-1);
    y2 = (*(*fAngleTable)(iMomentum))(iAngle);

    x1 = (*fAngleTable)(iMomentum)->GetLowEdgeEnergy(iAngle-1);
    x2 = (*fAngleTable)(iMomentum)->GetLowEdgeEnergy(iAngle);

    if ( x1 == x2 )   randAngle = x2;
    else
    {
      if ( y1 == y2 ) randAngle = x1 + ( x2 - x1 )*G4UniformRand();
      else
      {
        randAngle = x1 + ( position - y1 )*( x2 - x1 )/( y2 - y1 );
      }
    }
  }
  return randAngle;
}



////////////////////////////////////////////////////////////////////////////
//
// Return scattering angle sampled in lab system (target at rest)



G4double 
G4DiffuseElastic::SampleThetaLab( const G4HadProjectile* aParticle, 
                                        G4double tmass, G4double A)
{
  const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
  G4double m1 = theParticle->GetPDGMass();
  G4double plab = aParticle->GetTotalMomentum();
  G4LorentzVector lv1 = aParticle->Get4Momentum();
  G4LorentzVector lv(0.0,0.0,0.0,tmass);   
  lv += lv1;

  G4ThreeVector bst = lv.boostVector();
  lv1.boost(-bst);

  G4ThreeVector p1 = lv1.vect();
  G4double ptot    = p1.mag();
  G4double tmax    = 4.0*ptot*ptot;
  G4double t       = 0.0;


  //
  // Sample t
  //
  
  t = SampleT( theParticle, ptot, A);

  // NaN finder
  if(!(t < 0.0 || t >= 0.0)) 
  {
    if (verboseLevel > 0) 
    {
      G4cout << "G4DiffuseElastic:WARNING: A = " << A 
         << " mom(GeV)= " << plab/GeV 
             << " S-wave will be sampled" 
         << G4endl; 
    }
    t = G4UniformRand()*tmax; 
  }
  if(verboseLevel>1)
  {
    G4cout <<" t= " << t << " tmax= " << tmax 
       << " ptot= " << ptot << G4endl;
  }
  // Sampling of angles in CM system

  G4double phi  = G4UniformRand()*twopi;
  G4double cost = 1. - 2.0*t/tmax;
  G4double sint;

  if( cost >= 1.0 ) 
  {
    cost = 1.0;
    sint = 0.0;
  }
  else if( cost <= -1.0) 
  {
    cost = -1.0;
    sint =  0.0;
  }
  else  
  {
    sint = std::sqrt((1.0-cost)*(1.0+cost));
  }    
  if (verboseLevel>1) 
  {
    G4cout << "cos(t)=" << cost << " std::sin(t)=" << sint << G4endl;
  }
  G4ThreeVector v1(sint*std::cos(phi),sint*std::sin(phi),cost);
  v1 *= ptot;
  G4LorentzVector nlv1(v1.x(),v1.y(),v1.z(),std::sqrt(ptot*ptot + m1*m1));

  nlv1.boost(bst); 

  G4ThreeVector np1 = nlv1.vect();

    // G4double theta = std::acos( np1.z()/np1.mag() );  // degree;

  G4double theta = np1.theta();

  return theta;
}

////////////////////////////////////////////////////////////////////////////
//
// Return scattering angle in lab system (target at rest) knowing theta in CMS



G4double 
G4DiffuseElastic::ThetaCMStoThetaLab( const G4DynamicParticle* aParticle, 
                                        G4double tmass, G4double thetaCMS)
{
  const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
  G4double m1 = theParticle->GetPDGMass();
  // G4double plab = aParticle->GetTotalMomentum();
  G4LorentzVector lv1 = aParticle->Get4Momentum();
  G4LorentzVector lv(0.0,0.0,0.0,tmass);   

  lv += lv1;

  G4ThreeVector bst = lv.boostVector();

  lv1.boost(-bst);

  G4ThreeVector p1 = lv1.vect();
  G4double ptot    = p1.mag();

  G4double phi  = G4UniformRand()*twopi;
  G4double cost = std::cos(thetaCMS);
  G4double sint;

  if( cost >= 1.0 ) 
  {
    cost = 1.0;
    sint = 0.0;
  }
  else if( cost <= -1.0) 
  {
    cost = -1.0;
    sint =  0.0;
  }
  else  
  {
    sint = std::sqrt((1.0-cost)*(1.0+cost));
  }    
  if (verboseLevel>1) 
  {
    G4cout << "cos(tcms)=" << cost << " std::sin(tcms)=" << sint << G4endl;
  }
  G4ThreeVector v1(sint*std::cos(phi),sint*std::sin(phi),cost);
  v1 *= ptot;
  G4LorentzVector nlv1(v1.x(),v1.y(),v1.z(),std::sqrt(ptot*ptot + m1*m1));

  nlv1.boost(bst); 

  G4ThreeVector np1 = nlv1.vect();


  G4double thetaLab = np1.theta();

  return thetaLab;
}
////////////////////////////////////////////////////////////////////////////
//
// Return scattering angle in CMS system (target at rest) knowing theta in Lab



G4double 
G4DiffuseElastic::ThetaLabToThetaCMS( const G4DynamicParticle* aParticle, 
                                        G4double tmass, G4double thetaLab)
{
  const G4ParticleDefinition* theParticle = aParticle->GetDefinition();
  G4double m1 = theParticle->GetPDGMass();
  G4double plab = aParticle->GetTotalMomentum();
  G4LorentzVector lv1 = aParticle->Get4Momentum();
  G4LorentzVector lv(0.0,0.0,0.0,tmass);   

  lv += lv1;

  G4ThreeVector bst = lv.boostVector();

  // lv1.boost(-bst);

  // G4ThreeVector p1 = lv1.vect();
  // G4double ptot    = p1.mag();

  G4double phi  = G4UniformRand()*twopi;
  G4double cost = std::cos(thetaLab);
  G4double sint;

  if( cost >= 1.0 ) 
  {
    cost = 1.0;
    sint = 0.0;
  }
  else if( cost <= -1.0) 
  {
    cost = -1.0;
    sint =  0.0;
  }
  else  
  {
    sint = std::sqrt((1.0-cost)*(1.0+cost));
  }    
  if (verboseLevel>1) 
  {
    G4cout << "cos(tlab)=" << cost << " std::sin(tlab)=" << sint << G4endl;
  }
  G4ThreeVector v1(sint*std::cos(phi),sint*std::sin(phi),cost);
  v1 *= plab;
  G4LorentzVector nlv1(v1.x(),v1.y(),v1.z(),std::sqrt(plab*plab + m1*m1));

  nlv1.boost(-bst); 

  G4ThreeVector np1 = nlv1.vect();


  G4double thetaCMS = np1.theta();

  return thetaCMS;
}

///////////////////////////////////////////////////////////////////////////////
//
// Test for given particle and element table of momentum, angle probability.
// For the moment in lab system. 

void G4DiffuseElastic::TestAngleTable(const G4ParticleDefinition* theParticle, G4double partMom,
                                            G4double Z, G4double A) 
{
  fAtomicNumber  = Z;     // atomic number
  fAtomicWeight  = A;     // number of nucleons
  fNuclearRadius = CalculateNuclearRad(fAtomicWeight);
  
     
  
  G4cout<<"G4DiffuseElastic::TestAngleTable() init the element with Z = "
      <<Z<<"; and A = "<<A<<G4endl;
 
  fElementNumberVector.push_back(fAtomicNumber);

 


  G4int i=0, j;
  G4double a = 0., z = theParticle->GetPDGCharge(),  m1 = fParticle->GetPDGMass();
  G4double alpha1=0., alpha2=0., alphaMax=0., alphaCoulomb=0.;
  G4double deltaL10 = 0., deltaL96 = 0., deltaAG = 0.;
  G4double sumL10 = 0.,sumL96 = 0.,sumAG = 0.;
  G4double epsilon = 0.001;

  G4Integrator<G4DiffuseElastic,G4double(G4DiffuseElastic::*)(G4double)> integral;
  
  fAngleTable = new G4PhysicsTable(fEnergyBin);

  fWaveVector = partMom/hbarc;

  G4double kR     = fWaveVector*fNuclearRadius;
  G4double kR2    = kR*kR;
  G4double kRmax  = 10.6; // 10.6, 18, 10.174; ~ 3 maxima of J1 or 15., 25.
  G4double kRcoul = 1.2; // 1.4, 2.5; // on the first slope of J1

  alphaMax = kRmax*kRmax/kR2;

  if (alphaMax > 4.) alphaMax = 4.;  // vmg05-02-09: was pi2 

  alphaCoulomb = kRcoul*kRcoul/kR2;

  if( z )
  {
      a           = partMom/m1; // beta*gamma for m1
      fBeta       = a/std::sqrt(1+a*a);
      fZommerfeld = CalculateZommerfeld( fBeta, z, fAtomicNumber);
      fAm         = CalculateAm( partMom, fZommerfeld, fAtomicNumber);
  }
  G4PhysicsFreeVector* angleVector = new G4PhysicsFreeVector(fAngleBin-1);

  // G4PhysicsLogVector*  angleBins = new G4PhysicsLogVector( 0.001*alphaMax, alphaMax, fAngleBin );
    
  
  fAddCoulomb = false;

  for(j = 1; j < fAngleBin; j++)
  {
      // alpha1 = angleBins->GetLowEdgeEnergy(j-1);
      // alpha2 = angleBins->GetLowEdgeEnergy(j);

    alpha1 = alphaMax*(j-1)/fAngleBin;
    alpha2 = alphaMax*( j )/fAngleBin;

    if( ( alpha2 > alphaCoulomb ) && z ) fAddCoulomb = true;

    deltaL10 = integral.Legendre10(this, &G4DiffuseElastic::GetIntegrandFunction, alpha1, alpha2);
    deltaL96 = integral.Legendre96(this, &G4DiffuseElastic::GetIntegrandFunction, alpha1, alpha2);
    deltaAG  = integral.AdaptiveGauss(this, &G4DiffuseElastic::GetIntegrandFunction, 
                                       alpha1, alpha2,epsilon);

      // G4cout<<alpha1<<"\t"<<std::sqrt(alpha1)/degree<<"\t"
      //     <<deltaL10<<"\t"<<deltaL96<<"\t"<<deltaAG<<G4endl;

    sumL10 += deltaL10;
    sumL96 += deltaL96;
    sumAG  += deltaAG;

    G4cout<<alpha1<<"\t"<<std::sqrt(alpha1)/degree<<"\t"
            <<sumL10<<"\t"<<sumL96<<"\t"<<sumAG<<G4endl;
      
    angleVector->PutValue( j-1 , alpha1, sumL10 ); // alpha2
  }
  fAngleTable->insertAt(i,angleVector);
  fAngleBank.push_back(fAngleTable);

  /*
  // Integral over all angle range - Bad accuracy !!!

  sumL10 = integral.Legendre10(this, &G4DiffuseElastic::GetIntegrandFunction, 0., alpha2);
  sumL96 = integral.Legendre96(this, &G4DiffuseElastic::GetIntegrandFunction, 0., alpha2);
  sumAG  = integral.AdaptiveGauss(this, &G4DiffuseElastic::GetIntegrandFunction, 
                                       0., alpha2,epsilon);
  G4cout<<G4endl;
  G4cout<<alpha2<<"\t"<<std::sqrt(alpha2)/degree<<"\t"
            <<sumL10<<"\t"<<sumL96<<"\t"<<sumAG<<G4endl;
  */
  return;
}

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