G4NeutrinoNucleusModel.cc

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// $Id: G4NeutrinoNucleusModel.cc 91806 2015-08-06 12:20:45Z gcosmo $
//
// Geant4 Header : G4NeutrinoNucleusModel
//
// Author : V.Grichine 12.2.19
//  
 
#include "G4NeutrinoNucleusModel.hh"
 
#include "G4SystemOfUnits.hh"
#include "G4ParticleTable.hh"
#include "G4ParticleDefinition.hh"
#include "G4IonTable.hh"
#include "Randomize.hh"
#include "G4RandomDirection.hh"
 
//#include "G4Integrator.hh"
#include "G4DataVector.hh"
#include "G4PhysicsTable.hh"
 
#include "G4CascadeInterface.hh"
// #include "G4BinaryCascade.hh"
#include "G4TheoFSGenerator.hh"
#include "G4GeneratorPrecompoundInterface.hh"
#include "G4ExcitationHandler.hh"
#include "G4PreCompoundModel.hh"
#include "G4LundStringFragmentation.hh"
#include "G4ExcitedStringDecay.hh"
#include "G4FTFModel.hh"
// #include "G4BinaryCascade.hh"
#include "G4HadFinalState.hh"
#include "G4HadSecondary.hh"
#include "G4HadronicInteractionRegistry.hh"
// #include "G4INCLXXInterface.hh"
#include "G4KineticTrack.hh"
#include "G4DecayKineticTracks.hh"
#include "G4KineticTrackVector.hh"
#include "G4Fragment.hh"
#include "G4ReactionProductVector.hh"
 
// #include "G4QGSModel.hh"
// #include "G4QGSMFragmentation.hh"
// #include "G4QGSParticipants.hh"
 
 
#include "G4MuonMinus.hh"
#include "G4MuonPlus.hh"
#include "G4Nucleus.hh"
#include "G4LorentzVector.hh"
 
using namespace std;
using namespace CLHEP;
 
const G4int G4NeutrinoNucleusModel::fResNumber = 6;
 
const G4double G4NeutrinoNucleusModel::fResMass[6] = // [fResNumber] = 
  {2190., 1920., 1700., 1600., 1440., 1232. };
 
const G4int G4NeutrinoNucleusModel::fClustNumber = 4;
 
const G4double G4NeutrinoNucleusModel::fMesMass[4] = {1260., 980., 770., 139.57};
const G4int    G4NeutrinoNucleusModel::fMesPDG[4]  = {20213, 9000211, 213, 211};
 
// const G4double G4NeutrinoNucleusModel::fBarMass[4] = {1905., 1600., 1232., 939.57};
// const G4int    G4NeutrinoNucleusModel::fBarPDG[4]  = {2226, 32224, 2224, 2212};
 
const G4double G4NeutrinoNucleusModel::fBarMass[4] = {1700., 1600., 1232., 939.57};
const G4int    G4NeutrinoNucleusModel::fBarPDG[4]  = {12224, 32224, 2224, 2212};
 
const G4double  G4NeutrinoNucleusModel::fNuMuEnergyLogVector[50] = {
115.603, 133.424, 153.991, 177.729, 205.126, 236.746, 273.24, 315.361, 363.973, 420.08, 484.836, 559.573, 645.832, 
745.387, 860.289, 992.903, 1145.96, 1322.61, 1526.49, 1761.8, 2033.38, 2346.83, 2708.59, 3126.12, 3608.02, 4164.19, 
4806.1, 5546.97, 6402.04, 7388.91, 8527.92, 9842.5, 11359.7, 13110.8, 15131.9, 17464.5, 20156.6, 23263.8, 26849.9, 
30988.8, 35765.7, 41279, 47642.2, 54986.3, 63462.4, 73245.2, 84536, 97567.2, 112607, 129966 };
 
 
G4double G4NeutrinoNucleusModel::fNuMuXarrayKR[50][51] = {{1.0}};
G4double G4NeutrinoNucleusModel::fNuMuXdistrKR[50][50] = {{1.0}};
G4double G4NeutrinoNucleusModel::fNuMuQarrayKR[50][51][51] = {{{1.0}}};
G4double G4NeutrinoNucleusModel::fNuMuQdistrKR[50][51][50] = {{{1.0}}};
 
///////////////////////////////////////////
 
G4NeutrinoNucleusModel::G4NeutrinoNucleusModel(const G4String& name) 
  : G4HadronicInteraction(name)
{
  SetMinEnergy( 0.0*GeV );
  SetMaxEnergy( 100.*TeV );
  SetMinEnergy(1.e-6*eV); 
 
  fNbin = 50;
  fEindex = fXindex = fQindex = 0;
  fOnePionIndex = 58;
  fIndex = 50;
  fCascade = fString = fProton = f2p2h = fBreak = false;
 
  fNuEnergy  = fQ2  = fQtransfer = fXsample = fDp = fTr = 0.;
  fCosTheta = fCosThetaPi = 1.;
  fEmuPi = fW2 = fW2pi = 0.;
 
  fMu = 105.6583745*MeV;
  fMpi = 139.57018*MeV;
  fM1 = 939.5654133*MeV;  // for nu_mu -> mu-,  and n -> p
  fM2 = 938.2720813*MeV;
 
  fEmu = fMu;
  fEx = fM1;
  fMr = 1232.*MeV;
  fMt = fM2; // threshold for N*-diffraction
 
  fMinNuEnergy = GetMinNuMuEnergy();
  
  fLVh = G4LorentzVector(0.,0.,0.,0.);
  fLVl = G4LorentzVector(0.,0.,0.,0.);
  fLVt = G4LorentzVector(0.,0.,0.,0.);
  fLVcpi = G4LorentzVector(0.,0.,0.,0.);
 
  theMuonMinus = G4MuonMinus::MuonMinus();
  theMuonPlus = G4MuonPlus::MuonPlus();
 
  // PDG2016: sin^2 theta Weinberg
 
  fSin2tW = 0.23129; // 0.2312;
 
  fCutEnergy = 0.; // default value
 
 
  /* 
  // G4VPreCompoundModel* ptr;
  // reuse existing pre-compound model as in binary cascade
  
   fPrecoInterface = new  G4GeneratorPrecompoundInterface ;  
 
    if( !fPreCompound )
    {
      G4HadronicInteraction* p =
        G4HadronicInteractionRegistry::Instance()->FindModel("PRECO");
      G4VPreCompoundModel* fPreCompound = static_cast<G4VPreCompoundModel*>(p);
      
      if(!fPreCompound)
      {
    fPreCompound = new G4PreCompoundModel();
      }
      fPrecoInterface->SetDeExcitation(fPreCompound);
    }
    fDeExcitation = GetDeExcitation()->GetExcitationHandler();
  */ 
    
  fDeExcitation   = new G4ExcitationHandler();
  fPreCompound    = new G4PreCompoundModel(fDeExcitation);
  fPrecoInterface = new  G4GeneratorPrecompoundInterface ;  
  fPrecoInterface->SetDeExcitation(fPreCompound);
  
  fPDGencoding = 0; // unphysical as default
  fRecoil = nullptr;
     
}
 
 
G4NeutrinoNucleusModel::~G4NeutrinoNucleusModel()
{
 if(fPrecoInterface) delete fPrecoInterface;
}
 
 
void G4NeutrinoNucleusModel::ModelDescription(std::ostream& outFile) const
{
 
    outFile << "G4NeutrinoNucleusModel is a neutrino-nucleus general\n"
            << "model which uses the standard model \n"
            << "transfer parameterization.  The model is fully relativistic\n";
 
}
 
/////////////////////////////////////////////////////////
 
G4bool G4NeutrinoNucleusModel::IsApplicable(const G4HadProjectile & aPart, 
                           G4Nucleus & targetNucleus)
{
  G4bool result  = false;
  G4String pName = aPart.GetDefinition()->GetParticleName();
  G4double energy = aPart.GetTotalEnergy();
  
  if(  pName == "nu_mu" // || pName == "anti_nu_mu"   ) 
        &&
        energy > fMinNuEnergy                                )
  {
    result = true;
  }
  G4int Z = targetNucleus.GetZ_asInt();
        Z *= 1;
 
  return result;
}
 
//////////////////////////////////////
 
G4double G4NeutrinoNucleusModel::SampleXkr(G4double energy)
{
  G4int i(0), nBin(50);
  G4double xx(0.), prob = G4UniformRand();
 
  for( i = 0; i < nBin; ++i ) 
  {
    if( energy <= fNuMuEnergyLogVector[i] ) break;
  }
  if( i <= 0)          // E-edge
  {
    fEindex = 0;
    xx = GetXkr( 0, prob);  
  }
  else if ( i >= nBin) 
  {
    fEindex = nBin-1;  
    xx = GetXkr( nBin-1, prob); 
  }
  else
  {
    fEindex = i;
    G4double x1 = GetXkr(i-1,prob);
    G4double x2 = GetXkr(i,prob);
 
    G4double e1 = G4Log(fNuMuEnergyLogVector[i-1]);
    G4double e2 = G4Log(fNuMuEnergyLogVector[i]);
    G4double e  = G4Log(energy);
 
    if( e2 <= e1) xx = x1 + G4UniformRand()*(x2-x1);
    else          xx = x1 + (e-e1)*(x2-x1)/(e2-e1);  // lin in energy log-scale
  }
  return xx;
}
 
//////////////////////////////////////////////
//
// sample X according to prob (xmin,1) at a given energy index iEnergy
 
G4double G4NeutrinoNucleusModel::GetXkr(G4int iEnergy, G4double prob)
{
  G4int i(0), nBin=50; 
  G4double xx(0.);
 
  for( i = 0; i < nBin; ++i ) 
  {
    if( prob <= fNuMuXdistrKR[iEnergy][i] ) 
      break;
  }
  if(i <= 0 )  // X-edge
  {
    fXindex = 0;
    xx = fNuMuXarrayKR[iEnergy][0];
  }
  if ( i >= nBin ) 
  {
    fXindex = nBin;
    xx = fNuMuXarrayKR[iEnergy][nBin];
  }  
  else
  {
    fXindex = i;
    G4double x1 = fNuMuXarrayKR[iEnergy][i];
    G4double x2 = fNuMuXarrayKR[iEnergy][i+1];
 
    G4double p1 = 0.;
 
    if( i > 0 ) p1 = fNuMuXdistrKR[iEnergy][i-1];
 
    G4double p2 = fNuMuXdistrKR[iEnergy][i];  
 
    if( p2 <= p1 ) xx = x1 + G4UniformRand()*(x2-x1);
    else           xx = x1 + (prob-p1)*(x2-x1)/(p2-p1);
  }
  return xx;
}
 
//////////////////////////////////////
//
// Sample fQtransfer at a given Enu and fX
 
G4double G4NeutrinoNucleusModel::SampleQkr( G4double energy, G4double xx)
{
  G4int nBin(50), iE=fEindex, jX=fXindex;
  G4double qq(0.), qq1(0.), qq2(0.);
  G4double prob = G4UniformRand();
 
  // first E
 
  if( iE <= 0 )          
  {
    qq1 = GetQkr( 0, jX, prob);  
  }
  else if ( iE >= nBin-1) 
  {
    qq1 = GetQkr( nBin-1, jX, prob); 
  }
  else
  {
    G4double q1 = GetQkr(iE-1,jX, prob);
    G4double q2 = GetQkr(iE,jX, prob);
 
    G4double e1 = G4Log(fNuMuEnergyLogVector[iE-1]);
    G4double e2 = G4Log(fNuMuEnergyLogVector[iE]);
    G4double e  = G4Log(energy);
 
    if( e2 <= e1) qq1 = q1 + G4UniformRand()*(q2-q1);
    else          qq1 = q1 + (e-e1)*(q2-q1)/(e2-e1);  // lin in energy log-scale
  }
 
  // then X
 
  if( jX <= 0 )          
  {
    qq2 = GetQkr( iE, 0, prob);  
  }
  else if ( jX >= nBin) 
  {
    qq2 = GetQkr( iE, nBin, prob); 
  }
  else
  {
    G4double q1 = GetQkr(iE,jX-1, prob);
    G4double q2 = GetQkr(iE,jX, prob);
 
    G4double e1 = G4Log(fNuMuXarrayKR[iE][jX-1]);
    G4double e2 = G4Log(fNuMuXarrayKR[iE][jX]);
    G4double e  = G4Log(xx);
 
    if( e2 <= e1) qq2 = q1 + G4UniformRand()*(q2-q1);
    else          qq2 = q1 + (e-e1)*(q2-q1)/(e2-e1);  // lin in energy log-scale
  }
  qq = 0.5*(qq1+qq2);
 
  return qq;
}
 
//////////////////////////////////////////////
//
// sample Q according to prob (qmin,qmax) at a given energy index iE and X index jX
 
G4double G4NeutrinoNucleusModel::GetQkr( G4int iE, G4int jX, G4double prob )
{
  G4int i(0), nBin=50; 
  G4double qq(0.);
 
  for( i = 0; i < nBin; ++i ) 
  {
    if( prob <= fNuMuQdistrKR[iE][jX][i] ) 
      break;
  }
  if(i <= 0 )  // Q-edge
  {
    fQindex = 0;
    qq = fNuMuQarrayKR[iE][jX][0];
  }
  if ( i >= nBin ) 
  {
    fQindex = nBin;
    qq = fNuMuQarrayKR[iE][jX][nBin];
  }  
  else
  {
    fQindex = i;
    G4double q1 = fNuMuQarrayKR[iE][jX][i];
    G4double q2 = fNuMuQarrayKR[iE][jX][i+1];
 
    G4double p1 = 0.;
 
    if( i > 0 ) p1 = fNuMuQdistrKR[iE][jX][i-1];
 
    G4double p2 = fNuMuQdistrKR[iE][jX][i];  
 
    if( p2 <= p1 ) qq = q1 + G4UniformRand()*(q2-q1);
    else           qq = q1 + (prob-p1)*(q2-q1)/(p2-p1);
  }
  return qq;
}
 
 
///////////////////////////////////////////////////////////
//
// Final meson to theParticleChange
 
void G4NeutrinoNucleusModel::FinalMeson( G4LorentzVector & lvM, G4int, G4int pdgM) // qM
{
  G4int pdg = pdgM;
  // if      ( qM ==  0 ) pdg = pdgM - 100;
  // else if ( qM == -1 ) pdg = -pdgM;
 
  if( pdg == 211 || pdg == -211 || pdg == 111) // pions
  {
    G4ParticleDefinition* pd2 = G4ParticleTable::GetParticleTable()->FindParticle(pdg); 
    G4DynamicParticle*    dp2 = new G4DynamicParticle( pd2, lvM);
    theParticleChange.AddSecondary( dp2 );
  }
  else // meson resonances
  {
    G4ParticleDefinition* rePart = G4ParticleTable::GetParticleTable()->
      FindParticle(pdg); 
    G4KineticTrack ddkt( rePart, 0., G4ThreeVector(0.,0.,0.), lvM);
    G4KineticTrackVector* ddktv = ddkt.Decay();
 
    G4DecayKineticTracks decay( ddktv );
 
    for( unsigned int i = 0; i < ddktv->size(); i++ ) // add products to partchange
    {
      G4DynamicParticle * aNew = 
      new G4DynamicParticle( ddktv->operator[](i)->GetDefinition(),
                             ddktv->operator[](i)->Get4Momentum());
 
      // G4cout<<"       "<<i<<", "<<aNew->GetDefinition()->GetParticleName()<<", "<<aNew->Get4Momentum()<<G4endl;
 
      theParticleChange.AddSecondary( aNew );
      delete ddktv->operator[](i);
    }
    delete ddktv;
  }
}
 
////////////////////////////////////////////////////////
//
// Final barion to theParticleChange, and recoil nucleus treatment
 
void G4NeutrinoNucleusModel::FinalBarion( G4LorentzVector & lvB, G4int, G4int pdgB) // qB
{
  G4int A(0), Z(0), pdg = pdgB;
  // G4bool FiNucleon(false);
  
  // if      ( qB ==  1 ) pdg = pdgB - 10;
  // else if ( qB ==  0 ) pdg = pdgB - 110;
  // else if ( qB == -1 ) pdg = pdgB - 1110;
 
  if( pdg == 2212 || pdg == 2112)
  {
    fMr = G4ParticleTable::GetParticleTable()->FindParticle(pdg)->GetPDGMass();
    // FiNucleon = true;
  }
  else fMr = lvB.m();
  
  G4ThreeVector bst = fLVt.boostVector();
  lvB.boost(-bst); // in fLVt rest system
  
  G4double eX = lvB.e();
  G4double det(0.), det2(0.), rM(0.), mX = lvB.m();
  G4ThreeVector dX = (lvB.vect()).unit();
  G4double pX = sqrt(eX*eX-mX*mX);
 
  if( fRecoil )
  {
    Z  = fRecoil->GetZ_asInt();
    A  = fRecoil->GetA_asInt();
    rM = fRecoil->AtomicMass(A,Z); //->AtomicMass(); // 
    rM = fLVt.m();
  }
  else // A=0 nu+p
  {
    A = 0;
    Z = 1;
    rM = electron_mass_c2;
  }
  // G4cout<<A<<", ";
 
  G4double sumE = eX + rM;   
  G4double B = sumE*sumE + rM*rM - fMr*fMr - pX*pX;
  G4double a = 4.*(sumE*sumE - pX*pX);
  G4double b = -4.*B*pX;
  G4double c = 4.*sumE*sumE*rM*rM - B*B;
  det2       = b*b-4.*a*c;
  if( det2 <= 0. ) det = 0.;
  else             det = sqrt(det2);
  G4double dP = 0.5*(-b - det )/a;
 
  fDp = dP;
 
  pX -= dP;
 
  if(pX < 0.) pX = 0.;
 
  // if( A == 0 ) G4cout<<pX/MeV<<", ";
 
  eX = sqrt( pX*pX + fMr*fMr );
  G4LorentzVector lvN( pX*dX, eX );
  lvN.boost(bst); // back to lab
 
  if( pdg == 2212 || pdg == 2112) // nucleons mX >= fMr, dP >= 0
  {
    G4ParticleDefinition* pd2 = G4ParticleTable::GetParticleTable()->FindParticle(pdg); 
    G4DynamicParticle*    dp2 = new G4DynamicParticle( pd2, lvN);
    theParticleChange.AddSecondary( dp2 );
 
  }
  else // delta resonances
  {
    G4ParticleDefinition* rePart = G4ParticleTable::GetParticleTable()->FindParticle(pdg); 
    G4KineticTrack ddkt( rePart, 0., G4ThreeVector( 0., 0., 0.), lvN);
    G4KineticTrackVector* ddktv = ddkt.Decay();
 
    G4DecayKineticTracks decay( ddktv );
 
    for( unsigned int i = 0; i < ddktv->size(); i++ ) // add products to partchange
    {
      G4DynamicParticle * aNew = 
      new G4DynamicParticle( ddktv->operator[](i)->GetDefinition(),
                             ddktv->operator[](i)->Get4Momentum()  );
 
      // G4cout<<"       "<<i<<", "<<aNew->GetDefinition()->GetParticleName()<<", "<<aNew->Get4Momentum()<<G4endl;
 
      theParticleChange.AddSecondary( aNew );
      delete ddktv->operator[](i);
    }
    delete ddktv;
  }
  // recoil nucleus
 
  G4double eRecoil = sqrt( rM*rM + dP*dP );
  fTr = eRecoil - rM;
  G4ThreeVector vRecoil(dP*dX);
  // dP += G4UniformRand()*10.*MeV;
  G4LorentzVector rec4v(vRecoil, 0.);
  rec4v.boost(bst); // back to lab
  fLVt += rec4v;
  const G4LorentzVector lvTarg = fLVt; // (vRecoil, eRecoil);
 
 
  if( fRecoil ) // proton*?
  {
    G4double grM = G4NucleiProperties::GetNuclearMass(A,Z);
    G4double exE = fLVt.m() - grM;
    if( exE < 5.*MeV ) exE = 5.*MeV + G4UniformRand()*10.*MeV;
    
    const G4LorentzVector in4v( G4ThreeVector( 0., 0., 0.), grM );   
    G4Fragment fragment( A, Z, in4v); // lvTarg );
    fragment.SetNumberOfHoles(1);
    fragment.SetExcEnergyAndMomentum( exE, lvTarg );
    
    RecoilDeexcitation(fragment);
  }
  else // momentum?
  {
    theParticleChange.SetLocalEnergyDeposit( fTr ); // eRecoil );
  }
}
 
 
///////////////////////////////////////////////////////
//
// Get final particles from excited recoil nucleus and write them to theParticleChange, delete the particle vector
 
void G4NeutrinoNucleusModel::RecoilDeexcitation( G4Fragment& fragment)
{
  G4ReactionProductVector* products = fPreCompound->DeExcite(fragment);
 
  if( products != nullptr )
  {
    for( auto iter = products->cbegin(); iter != products->cend(); ++iter )
      // for( auto & prod : products ) // prod = (*iter) is the pointer to final hadronic particle
    {
      theParticleChange.AddSecondary(new G4DynamicParticle( (*iter)->GetDefinition(),
                                                            (*iter)->GetTotalEnergy(),
                                                            (*iter)->GetMomentum() ) );
      // delete prod;
    }
    // delete products;
    products->clear();
  }
  return;
}
 
 
///////////////////////////////////////////
//
// Fragmentation of lvX directly to pion and recoil nucleus (A,Z): fLVh + fLVt -> pi + A*
 
void G4NeutrinoNucleusModel::CoherentPion( G4LorentzVector & lvP, G4int pdgP, G4Nucleus & targetNucleus)
{
  G4int A(0), Z(0), pdg = pdgP;
  fLVcpi = G4LorentzVector(0.,0.,0.,0.);
 
  G4double  rM(0.), mN(938.), det(0.), det2(0.); 
  G4double mI(0.);
  mN = G4ParticleTable::GetParticleTable()->FindParticle(2212)->GetPDGMass(); // *0.85; // *0.9; // 
 
  // mN = 1.*139.57 + G4UniformRand()*(938. - 1.*139.57);
 
  G4ThreeVector vN = lvP.boostVector(), bst(0.,0.,0.);
  //  G4double gN = lvP.e()/lvP.m();
  // G4LorentzVector  lvNu(vN*gN*mN, mN*gN);
  G4LorentzVector  lvNu(0.,0.,0., mN);  // lvNu(bst, mN);
  lvP.boost(-vN);   // 9-3-20
  lvP = lvP - lvNu; // 9-3-20  already 1pi
  lvP.boost(vN);    // 9-3-20
  lvNu.boost(vN);    // 9-3-20
 
  // G4cout<<vN-lvP.boostVector()<<", ";
 
  Z  = targetNucleus.GetZ_asInt();
  A  = targetNucleus.GetA_asInt();
  rM = targetNucleus.AtomicMass(A,Z); //->AtomicMass(); // 
 
  // G4cout<<rM<<", ";
  // G4cout<<A<<", ";
  
  if( A == 1 ) 
  {
    bst = vN; // lvNu.boostVector(); // 9-3-20
    // mI = 0.; // 9-3-20
    rM = mN;
  }
  else
  {
    G4Nucleus targ(A-1,Z);
    mI = targ.AtomicMass(A-1,Z);
    G4LorentzVector lvTar(0.,0.,0.,mI); 
    lvNu = lvNu + lvTar;
    bst = lvNu.boostVector();  
    // bst = fLVt.boostVector();  // to recoil rest frame
    // G4cout<<fLVt<<"     "<<bst<<G4endl;
  }
  lvP.boost(-bst); // 9-3-20
  fMr = G4ParticleTable::GetParticleTable()->FindParticle(pdg)->GetPDGMass();
  G4double eX = lvP.e();
  G4double mX = lvP.m();
  // G4cout<<mX-fMr<<", ";
  G4ThreeVector dX = (lvP.vect()).unit();
  // G4cout<<dX<<", ";
  G4double pX = sqrt(eX*eX-mX*mX);
  // G4cout<<pX<<", ";
  G4double sumE = eX + rM;   
  G4double B = sumE*sumE + rM*rM - fMr*fMr - pX*pX;
  G4double a = 4.*(sumE*sumE - pX*pX);
  G4double b = -4.*B*pX;
  G4double c = 4.*sumE*sumE*rM*rM - B*B;
  det2 = b*b-4.*a*c;
  if(det2 > 0.) det = sqrt(det2);
  G4double dP = 0.5*(-b - det )/a;
 
  // dP = FinalMomentum( mI, rM, fMr, lvP);
  dP = FinalMomentum( rM, rM, fMr, lvP); // 9-3-20
 
  // G4cout<<dP<<", ";
  pX -= dP;
  if( pX < 0. ) pX = 0.;
  
  eX = sqrt( dP*dP + fMr*fMr );
  G4LorentzVector lvN( dP*dX, eX );
 
  if( A >= 1 ) lvN.boost(bst); // 9-3-20 back to lab
 
  fLVcpi = lvN;
 
  G4ParticleDefinition* pd2 = G4ParticleTable::GetParticleTable()->FindParticle(pdg); 
  G4DynamicParticle*    dp2 = new G4DynamicParticle( pd2, lvN);
  theParticleChange.AddSecondary( dp2 ); // coherent pion
 
  // recoil nucleus
 
  G4double eRecoil = sqrt( rM*rM + pX*pX );
  G4ThreeVector vRecoil(pX*dX);
  G4LorentzVector lvTarg1( vRecoil, eRecoil);
  lvTarg1.boost(bst);
  
  const G4LorentzVector lvTarg = lvTarg1;
 
  if( A > 1 ) // recoil target nucleus*
  {
    G4double grM = G4NucleiProperties::GetNuclearMass(A,Z);
    G4double exE = fLVt.m() - grM;
    
    if( exE < 5.*MeV ) exE = 5.*MeV + G4UniformRand()*10.*MeV; // vmg???
    
    const G4LorentzVector in4v( G4ThreeVector( 0., 0., 0.), grM );   
    G4Fragment fragment( A, Z, in4v); // lvTarg );
    fragment.SetNumberOfHoles(1);
    fragment.SetExcEnergyAndMomentum( exE, lvTarg );
    
    RecoilDeexcitation(fragment);
  }
  else // recoil target proton 
  {
    G4double eTkin = eRecoil - rM;
    G4double eTh   = 0.01*MeV; // 10.*MeV;
    
    if( eTkin > eTh )
    {
      G4DynamicParticle * aSec = new G4DynamicParticle( G4Proton::Proton(), lvTarg);
      theParticleChange.AddSecondary(aSec);
    }
    else theParticleChange.SetLocalEnergyDeposit( eTkin );
  }
  return;
}
 
 
////////////////////////////////////////////////////////////
//
// Excited barion decay to meson and barion, 
// mass distributions and charge exchange are free parameters 
 
void G4NeutrinoNucleusModel::ClusterDecay( G4LorentzVector & lvX, G4int qX)
{
  G4bool   finB = false;
  G4int    pdgB(0), i(0), qM(0), qB(0); //   pdgM(0),
  G4double mM(0.), mB(0.), eM(0.), eB(0.), pM(0.), pB(0.);
  G4double mm1(0.), mm22(0.), M1(0.), M2(0.), mX(0.);
 
  mX = lvX.m();
 
  G4double mN  = G4ParticleTable::GetParticleTable()->FindParticle(2112)->GetPDGMass();
  G4double mPi = G4ParticleTable::GetParticleTable()->FindParticle(211)->GetPDGMass();
 
  //  G4double deltaM =  1.*MeV; // 30.*MeV; //  10.*MeV; //  100.*MeV; // 20.*MeV; // 
  G4double deltaMr[4] =  { 0.*MeV, 0.*MeV, 100.*MeV, 0.*MeV}; 
 
  G4ThreeVector   dir(0.,0.,0.);
  G4ThreeVector   bst(0.,0.,0.);
  G4LorentzVector lvM(0.,0.,0.,0.);
  G4LorentzVector lvB(0.,0.,0.,0.);
 
  for( i = 0; i < fClustNumber; ++i) // check resonance
  {
    if( mX >= fBarMass[i] )
    {
        pdgB = fBarPDG[i];
        // mB = G4ParticleTable::GetParticleTable()->FindParticle(pdgB)->GetPDGMass();
        break;
    }
  }
  if( i == fClustNumber || i == fClustNumber-1 ) // low mass, p || n
  {
    if     ( qX == 2 || qX ==  0) { pdgB = 2212; qB = 1;} // p for 2, 0
    
    else if( qX == 1 || qX == -1) { pdgB = 2112; qB = 0;} // n for 1, -1
 
    return FinalBarion( lvX, qB, pdgB);     
  }
  else if( mX < fBarMass[i] + deltaMr[i]  || mX < mN + mPi ) 
  {
    finB = true; // final barion -> out
 
    if     ( qX == 1  && pdgB != 2212)  pdgB = pdgB - 10;
    else if( qX == 0  && pdgB != 2212)  pdgB = pdgB - 110;
    else if( qX == 0  && pdgB == 2212)  pdgB = pdgB - 100;
 
    if( finB ) return FinalBarion( lvX, qX, pdgB ); // out
  }
  // no barion resonance, try 1->2 decay in COM frame
 
  // try meson mass
 
  mm1 = mPi + 1.*MeV;     // pi+
  mm22 = mX - mN; // mX-n
 
  if( mm22 <= mm1 ) // out with p or n
  {
    if( qX == 2 || qX == 0)       { pdgB = 2212; qB = 1;} // p
    else if( qX == 1 || qX == -1) { pdgB = 2112; qB = 0;} // n
 
    return FinalBarion(lvX, qB, pdgB);
  }
  else // try decay -> meson(cluster) + barion(cluster)
  {
    // G4double sigmaM = 50.*MeV; // 100.*MeV; // 200.*MeV; // 400.*MeV; // 800.*MeV; //
    G4double rand   = G4UniformRand();
 
    // mM = mm1*mm22/( mm1 + rand*(mm22 - mm1) );
    // mM = mm1*mm22/sqrt( mm1*mm1 + rand*(mm22*mm22 - mm1*mm1) );
    // mM = -sigmaM*log( (1.- rand)*exp(-mm22/sigmaM) + rand*exp(-mm1/sigmaM) );
    mM = mm1 + rand*(mm22-mm1);
 
 
    for( i = 0; i < fClustNumber; ++i)
    {
      if( mM >= fMesMass[i] )
      {
        // pdgM = fMesPDG[i];
        // mM = G4ParticleTable::GetParticleTable()->FindParticle(pdgM)->GetPDGMass();
        break;
      }
    }
    M1 = G4ParticleTable::GetParticleTable()->FindParticle(2112)->GetPDGMass()+2.*MeV; // n
    M2 = mX - mM;
 
    if( M2 <= M1 ) // 
    {
      if     ( qX == 2 || qX ==  0) { pdgB = 2212; qB = 1;} // p
      else if( qX == 1 || qX == -1) { pdgB = 2112; qB = 0;} // n
 
      return FinalBarion(lvX, qB, pdgB);     
    }
    mB = M1 + G4UniformRand()*(M2-M1);
    // mB = -sigmaM*log( (1.- rand)*exp(-M2/sigmaM) + rand*exp(-M1/sigmaM) );
 
    bst = lvX.boostVector();
 
    // dir = G4RandomDirection(); // ???
    // dir = G4ThreeVector(0.,0.,1.);
    dir = bst.orthogonal().unit(); // ??
    // G4double cost =  exp(-G4UniformRand());
    // G4double sint = sqrt((1.-cost)*(1.+cost));
    // G4double phi = twopi*G4UniformRand();
    // dir = G4ThreeVector(sint*cos(phi), sint*sin(phi), cost);
 
    eM  = 0.5*(mX*mX + mM*mM - mB*mB)/mX;
    pM  = sqrt(eM*eM - mM*mM);
    lvM = G4LorentzVector( pM*dir, eM);
    lvM.boost(bst);
 
    eB  = 0.5*(mX*mX + mB*mB - mM*mM)/mX;
    pB  = sqrt(eB*eB - mB*mB);
    lvB = G4LorentzVector(-pB*dir, eB);
    lvB.boost(bst);
 
    // G4cout<<mM<<"/"<<mB<<", ";
 
    // charge exchange
 
    if     ( qX ==  2 ) { qM =  1; qB = 1;}
    else if( qX ==  1 ) { qM =  0; qB = 1;}
    else if( qX ==  0 ) { qM =  0; qB = 0;}
    else if( qX == -1 ) { qM = -1; qB = 0;}
 
    // if     ( qM ==  0 ) pdgM =  pdgM - 100;
    // else if( qM == -1 ) pdgM = -pdgM;
 
    MesonDecay( lvM, qM); // pdgM ); //
 
    // else              
    ClusterDecay( lvB, qB ); // continue
  }
}
 
 
////////////////////////////////////////////////////////////
//
// Excited barion decay to meson and barion, 
// mass distributions and charge exchange are free parameters 
 
void G4NeutrinoNucleusModel::MesonDecay( G4LorentzVector & lvX, G4int qX)
{
  G4bool   finB = false;
  G4int    pdgM(0), pdgB(0), i(0), qM(0), qB(0);
  G4double mM(0.), mB(0.), eM(0.), eB(0.), pM(0.), pB(0.);
  G4double mm1(0.), mm22(0.), M1(0.), M2(0.), mX(0.), Tkin(0.);
 
  mX = lvX.m();
  Tkin = lvX.e() - mX;
 
  // if( mX < 1120*MeV && mX > 1020*MeV ) // phi(1020)->K+K-
  if( mX < 1080*MeV && mX > 990*MeV && Tkin < 600*MeV ) // phi(1020)->K+K-
  {
    return  FinalMeson( lvX, qB, 333);
  }
  G4double mPi = G4ParticleTable::GetParticleTable()->FindParticle(211)->GetPDGMass();
 
  G4double deltaMr[4] =  { 0.*MeV, 0.*MeV, 100.*MeV, 0.*MeV}; 
 
  G4ThreeVector   dir(0.,0.,0.);
  G4ThreeVector   bst(0.,0.,0.);
  G4LorentzVector lvM(0.,0.,0.,0.);
  G4LorentzVector lvB(0.,0.,0.,0.);
 
  for( i = 0; i < fClustNumber; ++i) // check resonance
  {
    if( mX >= fMesMass[i] )
    {
        pdgB = fMesPDG[i];
        // mB = G4ParticleTable::GetParticleTable()->FindParticle(pdgB)->GetPDGMass();
        break;
    }
  }
  if( i == fClustNumber ) // || i == fClustNumber-1 ) // low mass, p || n
  {
    if     ( qX ==  1) { pdgB = 211;  qB =  1;} // pi+   
    else if( qX == 0 ) { pdgB = 111;  qB =  0;} // pi0  
    else if( qX == -1) { pdgB = -211; qB = -1;} // pi-
 
    return FinalMeson( lvX, qB, pdgB);     
  }
  else if( mX < fMesMass[i] + deltaMr[i] ) // || mX < mPi + mPi ) //
  {
    finB = true; // final barion -> out
    pdgB = fMesPDG[i];
    
    // if     ( qX == 1  && pdgB != 2212)  pdgB = pdgB - 10;
    
    if( qX == 0 )        pdgB = pdgB - 100;
    else if( qX == -1 )  pdgB = -pdgB;
 
    if( finB ) return FinalMeson( lvX, qX, pdgB ); // out
  }
  // no resonance, try 1->2 decay in COM frame
 
  // try meson
 
  mm1 = mPi + 1.*MeV;     // pi+
  mm22 = mX - mPi - 1.*MeV; // mX-n
 
  if( mm22 <= mm1 ) // out
  {
    if     ( qX ==  1) { pdgB = 211; qB = 1;} // pi+   
    else if( qX == 0 ) { pdgB = 111; qB = 0;} // pi0  
    else if( qX == -1) { pdgB = -211; qB = -1;} // pi-
 
    return FinalMeson(lvX, qB, pdgB);
  }
  else // try decay -> pion + meson(cluster)
  {
    // G4double sigmaM = 50.*MeV; // 100.*MeV; // 200.*MeV; // 400.*MeV; // 800.*MeV; //
    G4double rand   = G4UniformRand();
 
    if     ( qX ==  1 ) { qM =  1; qB = 0;}
    else if( qX ==  0 ) { qM =  -1; qB = 1;} // { qM =  0; qB = 0;} //
    else if( qX == -1 ) { qM = -1; qB = 0;}
    /*   
    mM = mPi;
    if(qM == 0) mM = G4ParticleTable::GetParticleTable()->FindParticle(111)->GetPDGMass(); //pi0
    pdgM = fMesPDG[fClustNumber-1];
    */
    // mm1*mm22/( mm1 + rand*(mm22 - mm1) );
    // mM = mm1*mm22/sqrt( mm1*mm1 + rand*(mm22*mm22 - mm1*mm1) );
    // mM = -sigmaM*log( (1.- rand)*exp(-mm22/sigmaM) + rand*exp(-mm1/sigmaM) );
    mM = mm1 + rand*(mm22-mm1);
    // mM = mm1 + 0.9*(mm22-mm1);
 
    
    for( i = 0; i < fClustNumber; ++i)
    {
      if( mM >= fMesMass[i] )
      {
        pdgM = fMesPDG[i];
        // mM = G4ParticleTable::GetParticleTable()->FindParticle(pdgM)->GetPDGMass();
        break;
      }
    }
    if( i == fClustNumber || i == fClustNumber-1 ) // low mass, p || n
    {
      if     ( qX ==  1) { pdgB = 211; qB = 1;} // pi+   
      else if( qX == 0 ) { pdgB = 111; qB = 0;} // pi0  
      else if( qX == -1) { pdgB = -211; qB = -1;} // pi-
 
      return FinalMeson( lvX, qB, pdgB);     
    }
    else if( mX < fMesMass[i] + deltaMr[i] ) // || mX < mPi + mPi ) //
    {
      finB = true; // final barion -> out
      pdgB = fMesPDG[i];
    
    // if     ( qX == 1  && pdgB != 2212)  pdgB = pdgB - 10;
    
      if( qX == 0 )        pdgB = pdgB - 100;
      else if( qX == -1 )  pdgB = -pdgB;
 
      if( finB ) return FinalMeson( lvX, qX, pdgB ); // out
    }
    
    M1 = G4ParticleTable::GetParticleTable()->FindParticle(211)->GetPDGMass()+2.*MeV; // n
    M2 = mX - mM;
 
    if( M2 <= M1 ) // 
    {
      if     ( qX ==  1) { pdgB = 211; qB = 1;} // pi+   
      else if( qX == 0 ) { pdgB = 111; qB = 0;} // pi0  
      else if( qX == -1) { pdgB = -211; qB = -1;} // pi-
 
      return FinalMeson(lvX, qB, pdgB);     
    }
    mB = M1 + G4UniformRand()*(M2-M1);
    // mB = -sigmaM*log( (1.- rand)*exp(-M2/sigmaM) + rand*exp(-M1/sigmaM) );
    // mB = M1 + 0.9*(M2-M1);
 
    bst = lvX.boostVector();
 
    // dir = G4RandomDirection();
    dir = bst.orthogonal().unit();
 
    eM  = 0.5*(mX*mX + mM*mM - mB*mB)/mX;
    pM  = sqrt(eM*eM - mM*mM);
    lvM = G4LorentzVector( pM*dir, eM);
    lvM.boost(bst);
 
    eB  = 0.5*(mX*mX + mB*mB - mM*mM)/mX;
    pB  = sqrt(eB*eB - mB*mB);
    lvB = G4LorentzVector(-pB*dir, eB);
    lvB.boost(bst);
 
    // G4cout<<mM<<"/"<<mB<<", ";
 
    // charge exchange
 
    // if     ( qX ==  2 ) { qM =  1; qB = 1;}
 
    if     ( qM ==  0 ) pdgM =  pdgM - 100;
    else if( qM == -1 ) pdgM = -pdgM;
 
    MesonDecay( lvM, qM ); //
 
    MesonDecay( lvB, qB ); // continue
  }
}
 
///////////////////////////////////////////////////////////////////////
//
// return final momentum x in the reaction lvX + mI -> mF + mP with momenta p-x, x
 
G4double G4NeutrinoNucleusModel::FinalMomentum(G4double mI, G4double mF, G4double mP, G4LorentzVector lvX)
{
  G4double result(0.), delta(0.);
  //  G4double mI2 = mI*mI;
  G4double mF2 = mF*mF;
  G4double mP2 = mP*mP;
  G4double eX = lvX.e();
  // G4double mX = lvX.m();
  G4double pX = lvX.vect().mag();
  G4double pX2 = pX*pX;
  G4double sI = eX + mI;
  G4double sI2 = sI*sI;
  G4double B = sI2 - mF2 -pX2 + mP2;
  G4double B2 = B*B;
  G4double a = 4.*(sI2-pX2);
  G4double b = -4.*B*pX;
  G4double c = 4.*sI2*mP2 - B2;
  G4double delta2 = b*b -4.*a*c;
 
  if( delta2 >= 0. ) delta = sqrt(delta2);
 
  result = 0.5*(-b-delta)/a;
  // result = 0.5*(-b+delta)/a;
 
  return result; 
}
 
/////////////////////////////////////////////////////////////////
//
//
 
G4double G4NeutrinoNucleusModel::FermiMomentum( G4Nucleus & targetNucleus)
{
  G4int Z  = targetNucleus.GetZ_asInt();
  G4int A  = targetNucleus.GetA_asInt();
 
  G4double kF(250.*MeV);
  G4double kp = 365.*MeV;
  G4double kn = 231.*MeV;
  G4double t1 = 0.479;
  G4double t2 = 0.526;
  G4double ZpA  = G4double(Z)/G4double(A);
  G4double NpA = 1. - ZpA;
 
  if      ( Z == 1  && A == 1   ) { kF = 0.;       } // hydrogen ???
  else if ( Z == 1  && A == 2   ) { kF = 87.*MeV;  }
  else if ( Z == 2  && A == 3   ) { kF = 134.*MeV; }
  else if ( Z == 6  && A == 12  ) { kF = 221.*MeV; }
  else if ( Z == 14 && A == 28  ) { kF = 239.*MeV; }
  else if ( Z == 26 && A == 56  ) { kF = 257.*MeV; }
  else if ( Z == 82 && A == 208 ) { kF = 265.*MeV; }
  else 
  {
    kF = kp*ZpA*( 1 - pow( G4double(A), -t1 ) ) + kn*NpA*( 1 - pow( G4double(A), -t2 ) );
  }
  return kF;  
}
 
/////////////////////////////////////////////////////////////////
//
// sample nucleon momentum of Fermi motion for 1p1h and 2p2h modes
 
G4double G4NeutrinoNucleusModel::NucleonMomentum( G4Nucleus & targetNucleus)
{
  G4int A     = targetNucleus.GetA_asInt();
  G4double kF = FermiMomentum( targetNucleus);
  G4double mom(0.), kCut = 0.5*GeV; // kCut = 1.*GeV; // kCut = 2.*GeV; // kCut = 4.*GeV; //
  //  G4double cof = 2./GeV;
  // G4double ksi = kF*kF*cof*cof/pi/pi;
  G4double th  = 1.; // 1. - 6.*ksi; //
 
  if( G4UniformRand() < th || A < 3 )  // 1p1h
  {
    mom = kF*pow( G4UniformRand(), 1./3.); 
  }
  else // 2p2h
  {
    mom  = kF*kCut;
    mom /= kCut - G4UniformRand()*(kCut - kF);
    f2p2h = true;
  }
  return mom;
}
 
 
//////////////////////////////////////////////////////
//
// Excitation energy according Bodek
 
G4double G4NeutrinoNucleusModel::GetEx( G4int A, G4bool fP )
{
  G4double eX(10.*MeV), a1(0.), a2(0.), e1(0.), e2(0.), aa = G4double(A);
  G4int i(0);
  const G4int maxBin = 12;
  
  G4double refA[maxBin] = { 2., 6., 12., 16., 27., 28., 40., 50., 56., 58., 197., 208. };
 
  G4double pEx[maxBin] = { 0., 12.2, 10.1, 10.9, 21.6, 12.4, 17.8, 17., 19., 16.8, 19.5, 14.7 };  
 
  G4double nEx[maxBin] = { 0., 12.2, 10., 10.2, 21.6, 12.4, 21.8, 17., 19., 16.8, 19.5, 16.9 };
 
  G4DataVector dE(12,0.);
 
  if(fP) for( i = 0; i < maxBin; ++i ) dE[i] = pEx[i];
  else                                 dE[i] = nEx[i];
 
  for( i = 0; i < maxBin; ++i )
  {
    if( aa <= refA[i] ) break;
  }
  if( i >= maxBin ) eX = dE[maxBin-1];
  else if( i <= 0 ) eX = dE[0];
  else
  {
    a1 = refA[i-1];
    a2 = refA[i];
    e1 = dE[i-1];
    e2 = dE[i];
    if (a1 == a2 || e1 == e2 ) eX = dE[i];
    else eX = e1 + (e2-e1)*(aa-a1)/(a2-a1);
  }
  return eX;
}
 
 
 
///////////////////////////////////////////////////////
//
// Two G-function sampling for the nucleon momentum  
 
G4double G4NeutrinoNucleusModel::GgSampleNM(G4Nucleus & nucl)
{
  f2p2h = false;
  G4double /* distr(0.), tail(0.), */ shift(1.), xx(1.), mom(0.), th(0.1);
  G4double kF = FermiMomentum( nucl);
  G4double momMax = 2.*kF; //  1.*GeV; //  1.*GeV; // 
  G4double aa = 5.5;
  G4double ll = 6.0; //  6.5; //
 
  G4int A = nucl.GetA_asInt();
 
  if( A <= 12) th = 0.1;
  else
  {
    // th = 0.1/(1.+log(G4double(A)/12.));
    th = 1.2/( G4double(A) + 1.35*log(G4double(A)/12.) );
  }
  shift = 0.99; // 0.95; //
  xx = mom/shift/kF;
 
  G4double rr = G4UniformRand();
 
  if( rr > th )
  {
    aa = 5.5;
    
    if( A <= 12 ) ll = 6.0;
    else
    {
      ll = 6.0 + 1.35*log(G4double(A)/12.);
    }
    xx = RandGamma::shoot(aa,ll);
    shift = 0.99;
    mom = xx*shift*kF;
  }
  else
  {
    f2p2h = true;
    aa = 6.5;
    ll = 6.5;
    xx = RandGamma::shoot(aa,ll);
    shift = 2.5;
    mom = xx*shift*kF;
  }
  if( mom > momMax ) mom = G4UniformRand()*momMax;
  if( mom > 2.*kF  ) f2p2h = true;
 
  // mom = 0.;
 
  return mom;
}
 
 
///////////////////////////////////// experimental arrays and get functions ////////////////////////////////////////
//
// Return index of nu/anu energy array corresponding to the neutrino energy
 
G4int G4NeutrinoNucleusModel::GetEnergyIndex(G4double energy)
{
  G4int i, eIndex = 0;
 
  for( i = 0; i < fIndex; i++)
  {
    if( energy <= fNuMuEnergy[i]*GeV ) 
    {
      eIndex = i;
      break;
    }
  }
  if( i >= fIndex ) eIndex = fIndex;
  // G4cout<<"eIndex = "<<eIndex<<G4endl;
  return eIndex;
}
 
/////////////////////////////////////////////////////
//
// nu_mu QE/Tot ratio for index-1, index linear over energy
 
G4double G4NeutrinoNucleusModel::GetNuMuQeTotRat(G4int index, G4double energy)
{
  G4double ratio(0.);
  // GetMinNuMuEnergy()
  if( index <= 0 || energy < fNuMuEnergy[0] ) ratio = 0.;
  else if (index >= fIndex) ratio = fNuMuQeTotRat[fIndex-1]*fOnePionEnergy[fIndex-1]*GeV/energy;
  else
  {
    G4double x1 = fNuMuEnergy[index-1]*GeV;
    G4double x2 = fNuMuEnergy[index]*GeV;
    G4double y1 = fNuMuQeTotRat[index-1];
    G4double y2 = fNuMuQeTotRat[index];
 
    if(x1 >= x2) return fNuMuQeTotRat[index];
    else
    {
      G4double angle = (y2-y1)/(x2-x1);
      ratio = y1 + (energy-x1)*angle;
    }
  }
  return ratio;
}
 
////////////////////////////////////////////////////////
 
const G4double G4NeutrinoNucleusModel::fNuMuEnergy[50] = 
{
  0.112103, 0.117359, 0.123119, 0.129443, 0.136404, 
  0.144084, 0.152576, 0.161991, 0.172458, 0.184126, 
  0.197171, 0.211801, 0.228261, 0.24684, 0.267887, 
  0.291816, 0.319125, 0.350417, 0.386422, 0.428032, 
  0.47634, 0.532692, 0.598756, 0.676612, 0.768868, 
  0.878812, 1.01062, 1.16963, 1.36271, 1.59876, 
  1.88943, 2.25002, 2.70086, 3.26916, 3.99166, 
  4.91843, 6.11836, 7.6872, 9.75942, 12.5259, 
  16.2605, 21.3615, 28.4141, 38.2903, 52.3062, 
  72.4763, 101.93, 145.6, 211.39, 312.172 
};
 
////////////////////////////////////////////////////////
 
const G4double G4NeutrinoNucleusModel::fNuMuQeTotRat[50] = 
{
  // 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 
  // 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 
  // 1., 1., 1., 0.982311, 
  0.98, 0.98, 0.98, 0.98, 0.98, 0.98, 0.98, 0.98, 0.98, 0.98,
  0.98, 0.98, 0.98, 0.98, 0.98, 0.98, 0.98, 0.98, 0.98, 0.98,
  0.97, 0.96, 0.95, 0.93,
  0.917794, 0.850239, 0.780412, 0.709339, 0.638134, 0.568165, 
  0.500236, 0.435528, 0.375015, 0.319157, 0.268463, 0.2232, 0.183284, 
  0.148627, 0.119008, 0.0940699, 0.0733255, 0.0563819, 0.0427312, 0.0319274, 
  0.0235026, 0.0170486, 0.0122149, 0.00857825, 0.00594018, 0.00405037 
};
 
/////////////////////////////////////////////////////
//
// Return index of one pion array corresponding to the neutrino energy
 
G4int G4NeutrinoNucleusModel::GetOnePionIndex(G4double energy)
{
  G4int i, eIndex = 0;
 
  for( i = 0; i < fOnePionIndex; i++)
  {
    if( energy <= fOnePionEnergy[i]*GeV ) 
    {
      eIndex = i;
      break;
    }
  }
  if( i >= fOnePionIndex ) eIndex = fOnePionIndex;
  // G4cout<<"eIndex = "<<eIndex<<G4endl;
  return eIndex;
}
 
/////////////////////////////////////////////////////
//
// nu_mu 1pi/Tot ratio for index-1, index linear over energy
 
G4double G4NeutrinoNucleusModel::GetNuMuOnePionProb(G4int index, G4double energy)
{
  G4double ratio(0.);
 
  if(       index <= 0 || energy < fOnePionEnergy[0] ) ratio = 0.;
  else if ( index >= fOnePionIndex )      ratio = fOnePionProb[fOnePionIndex-1]*fOnePionEnergy[fOnePionIndex-1]*GeV/energy;
  else
  {
    G4double x1 = fOnePionEnergy[index-1]*GeV;
    G4double x2 = fOnePionEnergy[index]*GeV;
    G4double y1 = fOnePionProb[index-1];
    G4double y2 = fOnePionProb[index];
 
    if( x1 >= x2) return fOnePionProb[index];
    else
    {
      G4double angle = (y2-y1)/(x2-x1);
      ratio = y1 + (energy-x1)*angle;
    }
  }
  return ratio;
}
 
////////////////////////////////////////////////////////////////////////////////////////////////////
 
const G4double G4NeutrinoNucleusModel::fOnePionEnergy[58] = 
{
 
  0.275314, 0.293652, 0.31729, 0.33409, 0.351746, 0.365629, 0.380041, 0.400165, 0.437941, 0.479237, 
  0.504391, 0.537803, 0.588487, 0.627532, 0.686839, 0.791905, 0.878332, 0.987405, 1.08162, 1.16971, 
  1.2982, 1.40393, 1.49854, 1.64168, 1.7524, 1.87058, 2.02273, 2.15894, 2.3654, 2.55792, 2.73017, 
  3.03005, 3.40733, 3.88128, 4.53725, 5.16786, 5.73439, 6.53106, 7.43879, 8.36214, 9.39965, 10.296, 
  11.5735, 13.1801, 15.2052, 17.5414, 19.7178, 22.7462, 25.9026, 29.4955, 33.5867, 39.2516, 46.4716, 
  53.6065, 63.4668, 73.2147, 85.5593, 99.9854 
};
 
 
////////////////////////////////////////////////////////////////////////////////////////////////////
 
const G4double G4NeutrinoNucleusModel::fOnePionProb[58] = 
{
  0.0019357, 0.0189361, 0.0378722, 0.0502758, 0.0662559, 0.0754581, 0.0865008, 0.0987275, 0.124112, 
  0.153787, 0.18308, 0.213996, 0.245358, 0.274425, 0.301536, 0.326612, 0.338208, 0.337806, 0.335948, 
  0.328092, 0.313557, 0.304965, 0.292169, 0.28481, 0.269474, 0.254138, 0.247499, 0.236249, 0.221654, 
  0.205492, 0.198781, 0.182216, 0.162251, 0.142878, 0.128631, 0.116001, 0.108435, 0.0974843, 0.082092, 
  0.0755204, 0.0703121, 0.0607066, 0.0554278, 0.0480401, 0.0427023, 0.0377123, 0.0323248, 0.0298584, 
  0.0244296, 0.0218526, 0.019121, 0.016477, 0.0137309, 0.0137963, 0.0110371, 0.00834028, 0.00686127, 0.00538226
};
 
 
//
//
///////////////////////////