G4ScreeningMottCrossSection.cc

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//
//      G4ScreeningMottCrossSection.cc
//-------------------------------------------------------------------
//
// GEANT4 Class header file
//
// File name:    G4ScreeningMottCrossSection
//
// Author:      Cristina Consolandi
//
// Creation date: 20.10.2011  
//
// Modifications:
// 27-05-2012 Added Analytic Fitting to the Mott Cross Section by means of G4MottCoefficients class.
//
//
// Class Description:
//      Computation of electron Coulomb Scattering Cross Section.
//      Suitable for high energy electrons and light target materials. 
//
//      Reference:
//      M.J. Boschini et al.
//     "Non Ionizing Energy Loss induced by Electrons in the Space Environment"
//      Proc. of the 13th International Conference on Particle Physics and Advanced Technology 
//      (13th ICPPAT, Como 3-7/10/2011), World Scientific (Singapore).
//      Available at: http://arxiv.org/abs/1111.4042v4
//
//      1) Mott Differential Cross Section Approximation:  
//         For Target material up to Z=92 (U):
//         As described in http://arxiv.org/abs/1111.4042v4 
//         par. 2.1 , eq. (16)-(17)
//         Else (Z>92):
//         W. A. McKinley and H. Fashbach, Phys. Rev. 74, (1948) 1759.
//      2) Screening coefficient: 
//      vomn G. Moliere, Z. Naturforsh A2 (1947), 133-145; A3 (1948), 78.
//      3) Nuclear Form Factor: 
//      A.V. Butkevich et al. Nucl. Instr. and Meth. in Phys. Res. A 488 (2002), 282-294.
//
// -------------------------------------------------------------------------------------
//
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....

#include "G4ScreeningMottCrossSection.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "G4MottCoefficients.hh"
#include "Randomize.hh"
#include "G4Proton.hh"
#include "G4LossTableManager.hh"
#include "G4NucleiProperties.hh"
#include "G4Element.hh"
#include "G4UnitsTable.hh"

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

static G4double angle[DIM]={1e-07,1.02329e-07,1.04713e-07,1.07152e-07,1.09648e-07,1.12202e-07,1.14815e-07,1.1749e-07,1.20226e-07,1.23027e-07,1.25893e-07,1.28825e-07,1.31826e-07,1.34896e-07,1.38038e-07,1.41254e-07,1.44544e-07,1.47911e-07,1.51356e-07,1.54882e-07,1.58489e-07,1.62181e-07,1.65959e-07,1.69824e-07,1.7378e-07,1.77828e-07,1.8197e-07,1.86209e-07,1.90546e-07,1.94984e-07,1.99526e-07,2.04174e-07,2.0893e-07,2.13796e-07,2.18776e-07,2.23872e-07,2.29087e-07,2.34423e-07,2.39883e-07,2.45471e-07,2.51189e-07,2.5704e-07,2.63027e-07,2.69153e-07,2.75423e-07,2.81838e-07,2.88403e-07,2.95121e-07,3.01995e-07,3.0903e-07,3.16228e-07,3.23594e-07,3.31131e-07,3.38844e-07,3.46737e-07,3.54813e-07,3.63078e-07,3.71535e-07,3.80189e-07,3.89045e-07,3.98107e-07,4.0738e-07,4.16869e-07,4.2658e-07,4.36516e-07,4.46684e-07,4.57088e-07,4.67735e-07,4.7863e-07,4.89779e-07,5.01187e-07,5.12861e-07,5.24807e-07,5.37032e-07,5.49541e-07,5.62341e-07,5.7544e-07,5.88844e-07,6.0256e-07,6.16595e-07,6.30957e-07,6.45654e-07,6.60693e-07,6.76083e-07,6.91831e-07,7.07946e-07,7.24436e-07,7.4131e-07,7.58578e-07,7.76247e-07,7.94328e-07,8.12831e-07,8.31764e-07,8.51138e-07,8.70964e-07,8.91251e-07,9.12011e-07,9.33254e-07,9.54993e-07,9.77237e-07,1e-06,1.02329e-06,1.04713e-06,1.07152e-06,1.09648e-06,1.12202e-06,1.14815e-06,1.1749e-06,1.20226e-06,1.23027e-06,1.25893e-06,1.28825e-06,1.31826e-06,1.34896e-06,1.38038e-06,1.41254e-06,1.44544e-06,1.47911e-06,1.51356e-06,1.54882e-06,1.58489e-06,1.62181e-06,1.65959e-06,1.69824e-06,1.7378e-06,1.77828e-06,1.8197e-06,1.86209e-06,1.90546e-06,1.94984e-06,1.99526e-06,2.04174e-06,2.0893e-06,2.13796e-06,2.18776e-06,2.23872e-06,2.29087e-06,2.34423e-06,2.39883e-06,2.45471e-06,2.51189e-06,2.5704e-06,2.63027e-06,2.69153e-06,2.75423e-06,2.81838e-06,2.88403e-06,2.95121e-06,3.01995e-06,3.0903e-06,3.16228e-06,3.23594e-06,3.31131e-06,3.38844e-06,3.46737e-06,3.54813e-06,3.63078e-06,3.71535e-06,3.80189e-06,3.89045e-06,3.98107e-06,4.0738e-06,4.16869e-06,4.2658e-06,4.36516e-06,4.46684e-06,4.57088e-06,4.67735e-06,4.7863e-06,4.89779e-06,5.01187e-06,5.12861e-06,5.24807e-06,5.37032e-06,5.49541e-06,5.62341e-06,5.7544e-06,5.88844e-06,6.0256e-06,6.16595e-06,6.30957e-06,6.45654e-06,6.60693e-06,6.76083e-06,6.91831e-06,7.07946e-06,7.24436e-06,7.4131e-06,7.58578e-06,7.76247e-06,7.94328e-06,8.12831e-06,8.31764e-06,8.51138e-06,8.70964e-06,8.91251e-06,9.12011e-06,9.33254e-06,9.54993e-06,9.77237e-06,1e-05,1.02329e-05,1.04713e-05,1.07152e-05,1.09648e-05,1.12202e-05,1.14815e-05,1.1749e-05,1.20226e-05,1.23027e-05,1.25893e-05,1.28825e-05,1.31826e-05,1.34896e-05,1.38038e-05,1.41254e-05,1.44544e-05,1.47911e-05,1.51356e-05,1.54882e-05,1.58489e-05,1.62181e-05,1.65959e-05,1.69824e-05,1.7378e-05,1.77828e-05,1.8197e-05,1.86209e-05,1.90546e-05,1.94984e-05,1.99526e-05,2.04174e-05,2.0893e-05,2.13796e-05,2.18776e-05,2.23872e-05,2.29087e-05,2.34423e-05,2.39883e-05,2.45471e-05,2.51189e-05,2.5704e-05,2.63027e-05,2.69153e-05,2.75423e-05,2.81838e-05,2.88403e-05,2.95121e-05,3.01995e-05,3.0903e-05,3.16228e-05,3.23594e-05,3.31131e-05,3.38844e-05,3.46737e-05,3.54813e-05,3.63078e-05,3.71535e-05,3.80189e-05,3.89045e-05,3.98107e-05,4.0738e-05,4.16869e-05,4.2658e-05,4.36516e-05,4.46684e-05,4.57088e-05,4.67735e-05,4.7863e-05,4.89779e-05,5.01187e-05,5.12861e-05,5.24807e-05,5.37032e-05,5.49541e-05,5.62341e-05,5.7544e-05,5.88844e-05,6.0256e-05,6.16595e-05,6.30957e-05,6.45654e-05,6.60693e-05,6.76083e-05,6.91831e-05,7.07946e-05,7.24436e-05,7.4131e-05,7.58578e-05,7.76247e-05,7.94328e-05,8.12831e-05,8.31764e-05,8.51138e-05,8.70964e-05,8.91251e-05,9.12011e-05,9.33254e-05,9.54993e-05,9.77237e-05,0.0001,0.000102329,0.000104713,0.000107152,0.000109648,0.000112202,0.000114815,0.00011749,0.000120226,0.000123027,0.000125893,0.000128825,0.000131826,0.000134896,0.000138038,0.000141254,0.000144544,0.000147911,0.000151356,0.000154882,0.000158489,0.000162181,0.000165959,0.000169824,0.00017378,0.000177828,0.00018197,0.000186209,0.000190546,0.000194984,0.000199526,0.000204174,0.00020893,0.000213796,0.000218776,0.000223872,0.000229087,0.000234423,0.000239883,0.000245471,0.000251189,0.00025704,0.000263027,0.000269153,0.000275423,0.000281838,0.000288403,0.000295121,0.000301995,0.00030903,0.000316228,0.000323594,0.000331131,0.000338844,0.000346737,0.000354813,0.000363078,0.000371535,0.000380189,0.000389045,0.000398107,0.00040738,0.000416869,0.00042658,0.000436516,0.000446684,0.000457088,0.000467735,0.00047863,0.000489779,0.000501187,0.000512861,0.000524807,0.000537032,0.000549541,0.000562341,0.00057544,0.000588844,0.00060256,0.000616595,0.000630957,0.000645654,0.000660693,0.000676083,0.000691831,0.000707946,0.000724436,0.00074131,0.000758578,0.000776247,0.000794328,0.000812831,0.000831764,0.000851138,0.000870964,0.000891251,0.000912011,0.000933254,0.000954993,0.000977237,0.001,0.00102329,0.00104713,0.00107152,0.00109648,0.00112202,0.00114815,0.0011749,0.00120226,0.00123027,0.00125893,0.00128825,0.00131826,0.00134896,0.00138038,0.00141254,0.00144544,0.00147911,0.00151356,0.00154882,0.00158489,0.00162181,0.00165959,0.00169824,0.0017378,0.00177828,0.0018197,0.00186209,0.00190546,0.00194984,0.00199526,0.00204174,0.0020893,0.00213796,0.00218776,0.00223872,0.00229087,0.00234423,0.00239883,0.00245471,0.00251189,0.0025704,0.00263027,0.00269153,0.00275423,0.00281838,0.00288403,0.00295121,0.00301995,0.0030903,0.00316228,0.00323594,0.00331131,0.00338844,0.00346737,0.00354813,0.00363078,0.00371535,0.00380189,0.00389045,0.00398107,0.0040738,0.00416869,0.0042658,0.00436516,0.00446684,0.00457088,0.00467735,0.0047863,0.00489779,0.00501187,0.00512861,0.00524807,0.00537032,0.00549541,0.00562341,0.0057544,0.00588844,0.0060256,0.00616595,0.00630957,0.00645654,0.00660693,0.00676083,0.00691831,0.00707946,0.00724436,0.0074131,0.00758578,0.00776247,0.00794328,0.00812831,0.00831764,0.00851138,0.00870964,0.00891251,0.00912011,0.00933254,0.00954993,0.00977237,0.01,0.0102329,0.0104713,0.0107152,0.0109648,0.0112202,0.0114815,0.011749,0.0120226,0.0123027,0.0125893,0.0128825,0.0131826,0.0134896,0.0138038,0.0141254,0.0144544,0.0147911,0.0151356,0.0154882,0.0158489,0.0162181,0.0165959,0.0169824,0.017378,0.0177828,0.018197,0.0186209,0.0190546,0.0194984,0.0199526,0.0204174,0.020893,0.0213796,0.0218776,0.0223872,0.0229087,0.0234423,0.0239883,0.0245471,0.0251189,0.025704,0.0263027,0.0269153,0.0275423,0.0281838,0.0288403,0.0295121,0.0301995,0.030903,0.0316228,0.0323594,0.0331131,0.0338844,0.0346737,0.0354813,0.0363078,0.0371535,0.0380189,0.0389045,0.0398107,0.040738,0.0416869,0.042658,0.0436516,0.0446684,0.0457088,0.0467735,0.047863,0.0489779,0.0501187,0.0512861,0.0524807,0.0537032,0.0549541,0.0562341,0.057544,0.0588844,0.060256,0.0616595,0.0630957,0.0645654,0.0660693,0.0676083,0.0691831,0.0707946,0.0724436,0.074131,0.0758578,0.0776247,0.0794328,0.0812831,0.0831764,0.0851138,0.0870964,0.0891251,0.0912011,0.0933254,0.0954993,0.0977237,0.1,0.102329,0.104713,0.107152,0.109648,0.112202,0.114815,0.11749,0.120226,0.123027,0.125893,0.128825,0.131826,0.134896,0.138038,0.141254,0.144544,0.147911,0.151356,0.154882,0.158489,0.162181,0.165959,0.169824,0.17378,0.177828,0.18197,0.186209,0.190546,0.194984,0.199526,0.204174,0.20893,0.213796,0.218776,0.223872,0.229087,0.234423,0.239883,0.245471,0.251189,0.25704,0.263027,0.269153,0.275423,0.281838,0.288403,0.295121,0.301995,0.30903,0.316228,0.323594,0.331131,0.338844,0.346737,0.354813,0.363078,0.371535,0.380189,0.389045,0.398107,0.40738,0.416869,0.42658,0.436516,0.446684,0.457088,0.467735,0.47863,0.489779,0.501187,0.512861,0.524807,0.537032,0.549541,0.562341,0.57544,0.588844,0.60256,0.616595,0.630957,0.645654,0.660693,0.676083,0.691831,0.707946,0.724436,0.74131,0.758578,0.776247,0.794328,0.812831,0.831764,0.851138,0.870964,0.891251,0.912011,0.933254,0.954993,0.977237,1,1.02329,1.04713,1.07152,1.09648,1.12202,1.14815,1.1749,1.20226,1.23027,1.25893,1.28825,1.31826,1.34896,1.38038,1.41254,1.44544,1.47911,1.51356,1.54882,1.58489,1.62181,1.65959,1.69824,1.7378,1.77828,1.8197,1.86209,1.90546,1.94984,1.99526,2.04174,2.0893,2.13796,2.18776,2.23872,2.29087,2.34423,2.39883,2.45471,2.51189,2.5704,2.63027,2.69153,2.75423,2.81838,2.88403,2.95121,3.01995,3.0903};

G4double G4ScreeningMottCrossSection::dangle[] = {0.0};
G4double G4ScreeningMottCrossSection::tet[] = {0.0};

using namespace std;

G4ScreeningMottCrossSection::G4ScreeningMottCrossSection():
   cosThetaMin(1.0),
   cosThetaMax(-1.0),
   alpha(fine_structure_const),
   htc2(hbarc_squared),
   e2(electron_mass_c2*classic_electr_radius) 
{
  TotalCross=0;

  fNistManager = G4NistManager::Instance();
  fG4pow = G4Pow::GetInstance();
  particle=0;

  spin = mass = mu_rel=0;
  tkinLab = momLab2 = invbetaLab2=0;
  tkin = mom2 = invbeta2=beta=gamma=0;

  Trec=targetZ = targetMass = As =0;
  etag = ecut = 0.0;

  targetA = 0;

  cosTetMinNuc=0;
  cosTetMaxNuc=0;

  for(G4int i=0 ; i<5;  ++i){
    for(G4int j=0; j< 6; ++j){
      coeffb[i][j]=0;
    }
  }
  if(dangle[0] == 0.0) {
    for(G4int i=0; i<DIM; ++i){
      cross[i]=0;
    }
  
    for(G4int i=0; i<DIM; ++i){
      if(i != DIM-1){
        dangle[i] = (angle[i+1]-angle[i]);
        tet[i] = (angle[i+1]+angle[i])*0.5;
      } else {
        dangle[i] = dangle[i-1];
        tet[i] = angle[i]+dangle[i]*0.5;
      }
    }
  }

  mottcoeff = new G4MottCoefficients();
}

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

G4ScreeningMottCrossSection::~G4ScreeningMottCrossSection()
{
  delete mottcoeff;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....

void G4ScreeningMottCrossSection::Initialise(const G4ParticleDefinition* p,
                                          G4double CosThetaLim)
{
  SetupParticle(p);
  tkin = targetZ = mom2 = DBL_MIN;
  ecut = etag = DBL_MAX;
  particle = p;
  cosThetaMin = CosThetaLim; 

}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
void G4ScreeningMottCrossSection::SetScreeningCoefficient()
{
  G4double alpha2=alpha*alpha;
  //Bohr radius 
  G4double a0=  Bohr_radius  ;//0.529e-8*cm;
  //Thomas-Fermi screening length
  G4double aU=0.88534*a0/fG4pow->Z13(targetZ);
  G4double twoR2=aU*aU;

  G4double factor= 1.13 + 3.76*targetZ*targetZ*invbeta2*alpha2;
  As=0.25*(htc2)/(twoR2*mom2)*factor;
  //cout<<"0k .........................As  "<<As<<endl;
}

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

G4double G4ScreeningMottCrossSection::GetScreeningAngle()
{
  SetScreeningCoefficient();

  G4double screenangle=2.*asin(sqrt(As));
  //    cout<<"  screenangle  "<<  screenangle <<endl;
  if(screenangle>=pi) screenangle=pi;
        
  return screenangle;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....

void G4ScreeningMottCrossSection::SetupKinematic(G4double ekin, G4double Z )
{
  //...Target
  G4int iz = G4int(Z);
  G4double A = fNistManager->GetAtomicMassAmu(iz);
  G4int ia = G4int(A);
  G4double mass2 = G4NucleiProperties::GetNuclearMass(ia, iz);

  targetZ = Z;
  targetA = fNistManager->GetAtomicMassAmu(iz);
  targetMass= mass2;

  mottcoeff->SetMottCoeff(targetZ, coeffb);

  //cout<<"......... targetA "<< targetA <<endl;
  //cout<<"......... targetMass "<< targetMass/MeV <<endl;

  // incident particle lab
  tkinLab = ekin;
  momLab2 = tkinLab*(tkinLab + 2.0*mass);
  invbetaLab2 = 1.0 +  mass*mass/momLab2;

  G4double etot = tkinLab + mass;
  G4double ptot = sqrt(momLab2);
  G4double m12  = mass*mass;
                
  // relativistic reduced mass from publucation
  // A.P. Martynenko, R.N. Faustov, Teoret. mat. Fiz. 64 (1985) 179
        
  //incident particle & target nucleus
  G4double Ecm=sqrt(m12 + mass2*mass2 + 2.0*etot*mass2);
  mu_rel=mass*mass2/Ecm;
  G4double momCM= ptot*mass2/Ecm;
  // relative system
  mom2 = momCM*momCM;
  invbeta2 = 1.0 +  mu_rel*mu_rel/mom2;
  tkin = momCM*sqrt(invbeta2) - mu_rel;//Ekin of mu_rel
  G4double  beta2=1./invbeta2;
  beta=std::sqrt(beta2) ;
  G4double gamma2= 1./(1.-beta2);
  gamma=std::sqrt(gamma2);

  //.........................................................

  
  SetScreeningCoefficient();

  //Integration Angles definition

  cosTetMinNuc =cosThetaMin;
  cosTetMaxNuc =cosThetaMax;

  for(G4int i=0; i<DIM;  ++i ){
    cross[i]=0;
  }
}

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

G4double G4ScreeningMottCrossSection::FormFactor2ExpHof(G4double angles)
{
  G4double M=targetMass; 
  G4double E=tkinLab;
  G4double Etot=E+mass;
  G4double Tmax=2.*M*E*(E+2.*mass)/(mass*mass+M*M+2.*M*Etot);
  G4double T=Tmax*fG4pow->powN(sin(angles*0.5), 2);
  G4double q2=T*(T+2.*M);
  q2/=htc2;//1/cm2
  G4double RN=1.27e-13*G4Exp(G4Log(targetA)*0.27)*cm;
  G4double xN= (RN*RN*q2);
  G4double den=(1.+xN/12.);
  G4double FN=1./(den*den);
  G4double form2=(FN*FN);

  return form2;

  //cout<<"..................... form2 "<< form2<<endl;
}

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

G4double G4ScreeningMottCrossSection::McFcorrection(G4double angles )
{
  G4double  beta2=1./invbeta2;
  G4double sintmezzi=std::sin(angles/2.);
  G4double sin2tmezzi = sintmezzi*sintmezzi;
  G4double R=1.-beta2*sin2tmezzi + targetZ*alpha*beta*pi*sintmezzi*(1.-sintmezzi);
  return R;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
G4double G4ScreeningMottCrossSection::RatioMottRutherford(G4double angles)
{
  G4double R=0;
  G4double fcost=std::sqrt((1. -cos(angles)));
  G4double a[5];
  const G4double shift=0.7181228;
  G4double beta0= beta -shift;

  for(G4int j=0 ;j<=4;j++){
    a[j]=0;
  }

  for(G4int j=0 ;j<=4;j++){
    for(G4int k=0;k<=5;k++ ){  
      a[j]+=coeffb[j][k]*fG4pow->powN(beta0,k);
    }
  }

  for(G4int j=0; j<=4; ++j){
    R+=a[j]*fG4pow->powN(fcost,j);
  }
  return R;
}

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

G4double G4ScreeningMottCrossSection::NuclearCrossSection()
{
  if(cosTetMaxNuc >= cosTetMinNuc) return 0.0;

  TotalCross=0;

  for(G4int i=0; i<DIM; ++i){
    G4double R=0;
    G4double F2=FormFactor2ExpHof(tet[i]);
                        
    if (coeffb[0][0]!=0){
      //cout<<" Mott....targetZ "<< targetZ<<endl;      
      R=RatioMottRutherford(tet[i]);
    } else if (coeffb[0][0]==0){
      // cout<<" McF.... targetZ "<< targetZ<<endl;
      R=McFcorrection(tet[i]);
    }

    //cout<<"----------------- R "<<R<<" F2 "<<F2<<endl;
    //                cout<<"angle "<<tet[i] << " F2 "<<F2<<endl;

    G4double e4=e2*e2;
    G4double den=2.*As+2.*fG4pow->powN(sin(tet[i]*0.5),2);
    G4double func=1./(den*den);

    G4double fatt= targetZ/(mu_rel*gamma*beta*beta);
    G4double sigma=e4*fatt*fatt*func;
    cross[i]=F2*R*sigma;
    G4double pi2sintet=twopi*sin(tet[i]);

    TotalCross+=pi2sintet*cross[i]*dangle[i];
  }//end integral

  //cout<< "ok ......... TotalCross "<<TotalCross<<endl;
  return TotalCross;
}

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

G4double G4ScreeningMottCrossSection::AngleDistribution(G4double anglein)
{
  G4double total=TotalCross ;
  G4double fatt= e2*targetZ/(mu_rel*gamma*beta*beta);
  G4double fatt2=fatt*fatt;
  total/=fatt2;

  G4double R=0;
  if (coeffb[0][0]!=0){
    //   cout<<" Mott....targetZ "<< targetZ<<endl;      
    R=RatioMottRutherford(anglein);
  } else if (coeffb[0][0]==0){
    // cout<<" McF.... targetZ "<< targetZ<<endl;
    R=McFcorrection(anglein);
  }

  G4double y=twopi*sin(anglein)*R*FormFactor2ExpHof(anglein)/
    ( (2*As+2.*fG4pow->powN(sin(anglein*0.5),2))*(2.*As+2.*fG4pow->powN(sin(anglein*0.5),2)) );

  return y/total;
}

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

G4double G4ScreeningMottCrossSection::GetScatteringAngle()
{
  //    cout<<"................ tkinLab  "<< G4BestUnit(tkinLab,"Energy") << " anglemin=  "<<anglemin<<endl;
  //cout<<"anglemax=  "<<anglemax<<endl;
  G4double r =G4UniformRand();
  
  G4double scattangle=0;
  G4double y=0;
  G4double dy=0;
  G4double area=0;

  for(G4int i=0; i<DIM; ++i){
    
    y+=AngleDistribution(tet[i])*dangle[i];
    dy= y-area ;
    area=y;

    if(r >=y-dy && r<=y+dy ){   
      scattangle= angle[i] +G4UniformRand()*dangle[i];
      //cout<<"y "<<y <<" r  "<< r  << " y/r "<<y/r << endl;
      break;
    }                   
  }
  return scattangle;
}

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

G4ThreeVector G4ScreeningMottCrossSection::GetNewDirection(){

  G4ThreeVector dir(0.0,0.0,1.0);
        
  G4double z1=GetScatteringAngle();
  
  G4double sint = sin(z1);
  G4double cost = sqrt(1.0 - sint*sint);
  G4double phi  = twopi* G4UniformRand();
  G4double dirx = sint*cos(phi);
  G4double diry = sint*sin(phi);
  G4double dirz = cost;

  //.......set Trc
  G4double etot=tkinLab+mass;
  G4double mass2=targetMass;
  Trec=(1.0 - cost)* mass2*(etot*etot - mass*mass )/
    (mass*mass + mass2*mass2+ 2.*mass2*etot);
       
  dir.set(dirx,diry,dirz);

  return dir;
}