processes/electromagnetic/standard/src/G4MscModel71.cc

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//
// $Id: G4MscModel71.cc,v 1.5 2007/05/22 17:34:36 vnivanch Exp $
// GEANT4 tag $Name: geant4-09-01-patch-01 $
//
// -------------------------------------------------------------------
//
// GEANT4 Class file
//
//
// File name:   G4MscModel71
//
// Author:      Laszlo Urban
//
// Creation date: 03.03.2001
//
// Modifications:
//
// 27-03-03 Move model part from G4MultipleScattering (V.Ivanchenko)
// 23-05-03 important change in angle distribution for muons/hadrons
//          the central part now is similar to the Highland parametrization +
//          minor correction in angle sampling algorithm (for all particles)
//          (L.Urban)
// 30-05-03 misprint in SampleCosineTheta corrected(L.Urban)
// 27-03-03 Rename (V.Ivanchenko)
// 05-08-03 angle distribution has been modified (L.Urban)
// 06-11-03 precision problems solved for high energy (PeV) particles
//          change in the tail of the angular distribution
//          highKinEnergy is set to 100 PeV (L.Urban) 
//
// 10-11-03 highKinEnergy is set back to 100 TeV, some tail tuning +
//          cleaning (L.Urban) 
// 26-11-03 correction in TrueStepLength : 
//          trueLength <= currentRange (L.Urban) 
// 01-03-04 signature changed in SampleCosineTheta,
//          energy dependence calculations has been simplified,
// 11-03-04 corrections in GeomPathLength,TrueStepLength,
//          SampleCosineTheta
// 23-04-04 true -> geom and geom -> true transformation has been
//          rewritten, changes in the angular distribution (L.Urban)
// 19-07-04 correction in SampleCosineTheta in order to avoid
//          num. precision problems at high energy/small step(L.Urban) 
// 17-08-04 changes in the angle distribution (slightly modified
//          Highland formula for the width of the central part,
//          changes in the numerical values of some other parameters)
//          ---> approximately step independent distribution (L.Urban)
// 21-09-04 change in the tail of the angular distribution (L.Urban)
//
// 03-11-04 precision problem for very high energy ions and small stepsize
//          solved in SampleCosineTheta (L.Urban).
// 15-04-05 optimize internal interface - add SampleSecondaries method (V.Ivanchenko)
// 03-10-05 Model is freezed with the name McsModel71 (V.Ivanchenko)
// 17-02-06 Save table of transport cross sections not mfp (V.Ivanchenko)
//

// Class Description:
//
// Implementation of the model of multiple scattering based on
// H.W.Lewis Phys Rev 78 (1950) 526 and others

// -------------------------------------------------------------------
//


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

#include "G4MscModel71.hh"
#include "Randomize.hh"
#include "G4Electron.hh"
#include "G4LossTableManager.hh"
#include "G4PhysicsTable.hh"
#include "G4ParticleChangeForMSC.hh"
#include "G4TransportationManager.hh"
#include "G4Navigator.hh"

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

using namespace std;

G4MscModel71::G4MscModel71(G4double& m_dtrl, G4double& m_NuclCorrPar,
                           G4double& m_FactPar, G4double& m_factail,
                       G4bool& m_samplez, const G4String& nam)
  : G4VEmModel(nam),
  taubig(8.0),
  tausmall(1.e-20),
  taulim(1.e-6),
  dtrl(m_dtrl),
  NuclCorrPar (m_NuclCorrPar),
  FactPar(m_FactPar),
  factail(m_factail),
  samplez(m_samplez),
  isInitialized(false)
{
  stepmin       = 1.e-6*mm;
  currentRange  = 0. ;
}

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

G4MscModel71::~G4MscModel71()
{}

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

void G4MscModel71::Initialise(const G4ParticleDefinition* p,
                              const G4DataVector&)
{
  if(isInitialized) return;
  // set values of some data members
  sigmafactor = twopi*classic_electr_radius*classic_electr_radius;
  particle = p;
  mass = particle->GetPDGMass();
  charge = particle->GetPDGCharge()/eplus;
  b = 1. ;
  xsi = 3.00 ;

  if(pParticleChange)
    fParticleChange = reinterpret_cast<G4ParticleChangeForMSC*>(pParticleChange);
  else
    fParticleChange = new G4ParticleChangeForMSC();

  navigator = G4TransportationManager::GetTransportationManager()
    ->GetNavigatorForTracking();
}

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

G4double G4MscModel71::ComputeCrossSectionPerAtom(
                             const G4ParticleDefinition* part,
                                   G4double KineticEnergy,
                                   G4double AtomicNumber,
                                   G4double AtomicWeight, 
                                   G4double,
                                   G4double)
{
  const G4double epsfactor = 2.*electron_mass_c2*electron_mass_c2*
                             Bohr_radius*Bohr_radius/(hbarc*hbarc);
  const G4double epsmin = 1.e-4 , epsmax = 1.e10;

  const G4double Zdat[15] = { 4., 6.,13.,20.,26.,29.,32.,38.,47.,
                             50.,56.,64.,74.,79.,82. };

  const G4double Tdat[23] = {0.0001*MeV,0.0002*MeV,0.0004*MeV,0.0007*MeV,
                             0.001*MeV,0.002*MeV,0.004*MeV,0.007*MeV,
                             0.01*MeV,0.02*MeV,0.04*MeV,0.07*MeV,
                             0.1*MeV,0.2*MeV,0.4*MeV,0.7*MeV,
                             1.*MeV,2.*MeV,4.*MeV,7.*MeV,10.*MeV,20.*MeV,
                             10000.0*MeV};

 // corr. factors for e-/e+ lambda
          G4double celectron[15][23] =
          {{1.125,1.072,1.051,1.047,1.047,1.050,1.052,1.054,
            1.054,1.057,1.062,1.069,1.075,1.090,1.105,1.111,
            1.112,1.108,1.100,1.093,1.089,1.087,0.7235     },
           {1.408,1.246,1.143,1.096,1.077,1.059,1.053,1.051,
            1.052,1.053,1.058,1.065,1.072,1.087,1.101,1.108,
            1.109,1.105,1.097,1.090,1.086,1.082,0.7925     },
           {2.833,2.268,1.861,1.612,1.486,1.309,1.204,1.156,
            1.136,1.114,1.106,1.106,1.109,1.119,1.129,1.132,
            1.131,1.124,1.113,1.104,1.099,1.098,0.9147     },
           {3.879,3.016,2.380,2.007,1.818,1.535,1.340,1.236,
            1.190,1.133,1.107,1.099,1.098,1.103,1.110,1.113,
            1.112,1.105,1.096,1.089,1.085,1.098,0.9700     },
           {6.937,4.330,2.886,2.256,1.987,1.628,1.395,1.265,
            1.203,1.122,1.080,1.065,1.061,1.063,1.070,1.073,
            1.073,1.070,1.064,1.059,1.056,1.056,1.0022     },
           {9.616,5.708,3.424,2.551,2.204,1.762,1.485,1.330,
            1.256,1.155,1.099,1.077,1.070,1.068,1.072,1.074,
            1.074,1.070,1.063,1.059,1.056,1.052,1.0158     },
           {11.72,6.364,3.811,2.806,2.401,1.884,1.564,1.386,
            1.300,1.180,1.112,1.082,1.073,1.066,1.068,1.069,
            1.068,1.064,1.059,1.054,1.051,1.050,1.0284     },
           {18.08,8.601,4.569,3.183,2.662,2.025,1.646,1.439,
            1.339,1.195,1.108,1.068,1.053,1.040,1.039,1.039,
            1.039,1.037,1.034,1.031,1.030,1.036,1.0515     },
           {18.22,10.48,5.333,3.713,3.115,2.367,1.898,1.631,
            1.498,1.301,1.171,1.105,1.077,1.048,1.036,1.033,
            1.031,1.028,1.024,1.022,1.021,1.024,1.0834     },
           {14.14,10.65,5.710,3.929,3.266,2.453,1.951,1.669,
            1.528,1.319,1.178,1.106,1.075,1.040,1.027,1.022,
            1.020,1.017,1.015,1.013,1.013,1.020,1.0937     },
           {14.11,11.73,6.312,4.240,3.478,2.566,2.022,1.720,
            1.569,1.342,1.186,1.102,1.065,1.022,1.003,0.997,
            0.995,0.993,0.993,0.993,0.993,1.011,1.1140     },
           {22.76,20.01,8.835,5.287,4.144,2.901,2.219,1.855,
            1.677,1.410,1.224,1.121,1.073,1.014,0.986,0.976,
            0.974,0.972,0.973,0.974,0.975,0.987,1.1410     },
           {50.77,40.85,14.13,7.184,5.284,3.435,2.520,2.059,
            1.837,1.512,1.283,1.153,1.091,1.010,0.969,0.954,
            0.950,0.947,0.949,0.952,0.954,0.963,1.1750     },
           {65.87,59.06,15.87,7.570,5.567,3.650,2.682,2.182,
            1.939,1.579,1.325,1.178,1.108,1.014,0.965,0.947,
            0.941,0.938,0.940,0.944,0.946,0.954,1.1922     },
           {55.60,47.34,15.92,7.810,5.755,3.767,2.760,2.239,
            1.985,1.609,1.343,1.188,1.113,1.013,0.960,0.939,
            0.933,0.930,0.933,0.936,0.939,0.949,1.2026     }};
           G4double cpositron[15][23] = {
           {2.589,2.044,1.658,1.446,1.347,1.217,1.144,1.110,
            1.097,1.083,1.080,1.086,1.092,1.108,1.123,1.131,
            1.131,1.126,1.117,1.108,1.103,1.100,0.7235     },
           {3.904,2.794,2.079,1.710,1.543,1.325,1.202,1.145,
            1.122,1.096,1.089,1.092,1.098,1.114,1.130,1.137,
            1.138,1.132,1.122,1.113,1.108,1.102,0.7925     },
           {7.970,6.080,4.442,3.398,2.872,2.127,1.672,1.451,
            1.357,1.246,1.194,1.179,1.178,1.188,1.201,1.205,
            1.203,1.190,1.173,1.159,1.151,1.145,0.9147     },
           {9.714,7.607,5.747,4.493,3.815,2.777,2.079,1.715,
            1.553,1.353,1.253,1.219,1.211,1.214,1.225,1.228,
            1.225,1.210,1.191,1.175,1.166,1.174,0.9700     },
           {17.97,12.95,8.628,6.065,4.849,3.222,2.275,1.820,
            1.624,1.382,1.259,1.214,1.202,1.202,1.214,1.219,
            1.217,1.203,1.184,1.169,1.160,1.151,1.0022     },
           {24.83,17.06,10.84,7.355,5.767,3.707,2.546,1.996,
            1.759,1.465,1.311,1.252,1.234,1.228,1.238,1.241,
            1.237,1.222,1.201,1.184,1.174,1.159,1.0158     },
           {23.26,17.15,11.52,8.049,6.375,4.114,2.792,2.155,
            1.880,1.535,1.353,1.281,1.258,1.247,1.254,1.256,
            1.252,1.234,1.212,1.194,1.183,1.170,1.0284     },
           {22.33,18.01,12.86,9.212,7.336,4.702,3.117,2.348,
            2.015,1.602,1.385,1.297,1.268,1.251,1.256,1.258,
            1.254,1.237,1.214,1.195,1.185,1.179,1.0515     },
           {33.91,24.13,15.71,10.80,8.507,5.467,3.692,2.808,
            2.407,1.873,1.564,1.425,1.374,1.330,1.324,1.320,
            1.312,1.288,1.258,1.235,1.221,1.205,1.0834     },
           {32.14,24.11,16.30,11.40,9.015,5.782,3.868,2.917,
            2.490,1.925,1.596,1.447,1.391,1.342,1.332,1.327,
            1.320,1.294,1.264,1.240,1.226,1.214,1.0937     },
           {29.51,24.07,17.19,12.28,9.766,6.238,4.112,3.066,
            2.602,1.995,1.641,1.477,1.414,1.356,1.342,1.336,
            1.328,1.302,1.270,1.245,1.231,1.233,1.1140     },
           {38.19,30.85,21.76,15.35,12.07,7.521,4.812,3.498,
            2.926,2.188,1.763,1.563,1.484,1.405,1.382,1.371,
            1.361,1.330,1.294,1.267,1.251,1.239,1.1410     },
           {49.71,39.80,27.96,19.63,15.36,9.407,5.863,4.155,
            3.417,2.478,1.944,1.692,1.589,1.480,1.441,1.423,
            1.409,1.372,1.330,1.298,1.280,1.258,1.1750     },
           {59.25,45.08,30.36,20.83,16.15,9.834,6.166,4.407,
            3.641,2.648,2.064,1.779,1.661,1.531,1.482,1.459,
            1.442,1.400,1.354,1.319,1.299,1.272,1.1922     },
           {56.38,44.29,30.50,21.18,16.51,10.11,6.354,4.542,
            3.752,2.724,2.116,1.817,1.692,1.554,1.499,1.474,
            1.456,1.412,1.364,1.328,1.307,1.282,1.2026     }};

  G4double sigma;
  if (part != particle ) {
    particle = part;
    mass = particle->GetPDGMass();
    charge = particle->GetPDGCharge()/eplus;
  }

  G4double Z23 = 2.*log(AtomicNumber)/3.; Z23 = exp(Z23);

  // correction if particle .ne. e-/e+
  // compute equivalent kinetic energy
  // lambda depends on p*beta ....

  G4double eKineticEnergy = KineticEnergy;

  if((particle->GetParticleName() != "e-") &&
     (particle->GetParticleName() != "e+") )
  {
     G4double TAU = KineticEnergy/mass ;
     G4double c = mass*TAU*(TAU+2.)/(electron_mass_c2*(TAU+1.)) ;
     G4double w = c-2. ;
     G4double tau = 0.5*(w+sqrt(w*w+4.*c)) ;
     eKineticEnergy = electron_mass_c2*tau ;
  }

  G4double ChargeSquare = charge*charge;

  G4double eTotalEnergy = eKineticEnergy + electron_mass_c2 ;
  G4double beta2 = eKineticEnergy*(eTotalEnergy+electron_mass_c2)
                                 /(eTotalEnergy*eTotalEnergy);
  G4double bg2   = eKineticEnergy*(eTotalEnergy+electron_mass_c2)
                                 /(electron_mass_c2*electron_mass_c2);

  G4double eps = epsfactor*bg2/Z23;

  if     (eps<epsmin)  sigma = 2.*eps*eps;
  else if(eps<epsmax)  sigma = log(1.+2.*eps)-2.*eps/(1.+2.*eps);
  else                 sigma = log(2.*eps)-1.+1./eps;

  sigma *= ChargeSquare*AtomicNumber*AtomicNumber/(beta2*bg2);

  // nuclear size effect correction for high energy
  // ( a simple approximation at present)
  G4double corrnuclsize,a,w1,w2,w;

  G4double x0 = 1. - NuclCorrPar*mass/(KineticEnergy*
               exp(log(AtomicWeight/(g/mole))/3.));
  if ( x0 < -1. || eKineticEnergy  <= 10.*MeV)
      {
        x0 = -1.;
        corrnuclsize = 1.;
      }
  else
      {
        a = 1.+1./eps;
        if (eps > epsmax) w1=log(2.*eps)+1./eps-3./(8.*eps*eps);
        else              w1=log((a+1.)/(a-1.))-2./(a+1.);
        w = 1./((1.-x0)*eps);
        if (w < epsmin)   w2=-log(w)-1.+2.*w-1.5*w*w;
        else              w2 = log((a-x0)/(a-1.))-(1.-x0)/(a-x0);
        corrnuclsize = w1/w2;
        corrnuclsize = exp(-FactPar*mass/KineticEnergy)*
                      (corrnuclsize-1.)+1.;
      }

  // interpolate in AtomicNumber and beta2
  // get bin number in Z
  G4int iZ = 14;
  while ((iZ>=0)&&(Zdat[iZ]>=AtomicNumber)) iZ -= 1;
  if (iZ==14)                               iZ = 13;
  if (iZ==-1)                               iZ = 0 ;

  G4double Z1 = Zdat[iZ];
  G4double Z2 = Zdat[iZ+1];
  G4double ratZ = (AtomicNumber-Z1)/(Z2-Z1);

  // get bin number in T (beta2)
  G4int iT = 22;
  while ((iT>=0)&&(Tdat[iT]>=eKineticEnergy)) iT -= 1;
  if(iT==22)                                  iT = 21;
  if(iT==-1)                                  iT = 0 ;

  //  calculate betasquare values
  G4double T = Tdat[iT],   E = T + electron_mass_c2;
  G4double b2small = T*(E+electron_mass_c2)/(E*E);
  T = Tdat[iT+1]; E = T + electron_mass_c2;
  G4double b2big = T*(E+electron_mass_c2)/(E*E);
  G4double ratb2 = (beta2-b2small)/(b2big-b2small);
  G4double c1,c2,cc1,cc2,corr;
  if (charge < 0.)
    {
       c1 = celectron[iZ][iT];
       c2 = celectron[iZ+1][iT];
       cc1 = c1+ratZ*(c2-c1);

       c1 = celectron[iZ][iT+1];
       c2 = celectron[iZ+1][iT+1];
       cc2 = c1+ratZ*(c2-c1);

       corr = cc1+ratb2*(cc2-cc1);
       sigma /= corr;
    }

  if (charge > 0.)
    {
       c1 = cpositron[iZ][iT];
       c2 = cpositron[iZ+1][iT];
       cc1 = c1+ratZ*(c2-c1);

       c1 = cpositron[iZ][iT+1];
       c2 = cpositron[iZ+1][iT+1];
       cc2 = c1+ratZ*(c2-c1);

       corr = cc1+ratb2*(cc2-cc1);
       sigma /= corr;
    }

  sigma *= sigmafactor;

  //  nucl. size correction for particles other than e+/e- only at present !!!!
  if((particle->GetParticleName() != "e-") &&
     (particle->GetParticleName() != "e+")   )
     sigma /= corrnuclsize;
  //  G4cout << "e= " << KineticEnergy << " sigma= " << sigma << G4endl;

  return sigma;
}

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

G4double G4MscModel71::GeomPathLength(
                          G4PhysicsTable* theLambdaTable,
                    const G4MaterialCutsCouple* couple,
                    const G4ParticleDefinition* theParticle,
                          G4double& T0,
                          G4double lambda,
                          G4double range,
                          G4double truePathLength)
{
  //  do the true -> geom transformation
  const G4double  ztmax = 101./103. ;
  if (theParticle != particle ) {
    particle = theParticle;
    mass = particle->GetPDGMass();
    charge = particle->GetPDGCharge()/eplus;
  }
  currentKinEnergy = T0;
  currentRange = range ;
  currentRadLength = couple->GetMaterial()->GetRadlen();

  lambda0 = lambda;
  par1 = -1. ;  
  par2 = par3 = 0. ;  
  tPathLength = truePathLength;

  // this correction needed to run MSC with eIoni and eBrem inactivated
  // and makes no harm for a normal run
  if(tPathLength > range)
    tPathLength = range ;

  G4double tau   = tPathLength/lambda0 ;

  if (tau <= tausmall) return tPathLength;

  G4double zmean = tPathLength;
  if (tPathLength < range*dtrl) {
    zmean = lambda0*(1.-exp(-tau));
    if(tau < taulim) zmean = tPathLength*(1.-0.5*tPathLength/lambda0) ;
  } else if(T0 < mass) {
    par1 = 1./range ;
    par2 = 1./(par1*lambda0) ;
    par3 = 1.+par2 ;
    zmean = (1.-exp(par3*log(1.-tPathLength/range)))/(par1*par3) ;
  } else {
    G4LossTableManager* theManager = G4LossTableManager::Instance();
    G4double T1 = theManager->GetEnergy(particle,range-tPathLength,couple);
    G4double lambda1 ;
    if (theLambdaTable) {
      G4bool bb;
      lambda1 = ((*theLambdaTable)[couple->GetIndex()])->GetValue(T1,bb);
    } else {
      lambda1 = CrossSection(couple,particle,T1,0.0,1.0);
    }
    lambda1 = 1.0/lambda1;
    par1 = (lambda0-lambda1)/(lambda0*tPathLength) ;
    par2 = 1./(par1*lambda0) ;
    par3 = 1.+par2 ;
    zmean = (1.-exp(par3*log(lambda1/lambda0)))/(par1*par3) ;
  }

  //  sample z
  G4double zPathLength = zmean ;
  G4double zt = zmean/tPathLength ;
  if (tPathLength >= stepmin && samplez && zt > 0.5 && zt < ztmax)
  {
    G4double cz = 0.5*(3.*zt-1.)/(1.-zt) ;
    G4double cz1 = 1.+cz ;
    G4double u0 = cz/cz1 ;
    G4double u,grej ;
    do {
        u = exp(log(G4UniformRand())/cz1) ;
        grej = exp(cz*log(u/u0))*(1.-u)/(1.-u0) ;
      } while (grej < G4UniformRand()) ;
   zPathLength = tPathLength*u ;
  }

  return zPathLength ;
}

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

G4double G4MscModel71::TrueStepLength(G4double geomStepLength)
{
  G4double trueLength = geomStepLength;
  trueLength = geomStepLength;
  if(geomStepLength > lambda0*tausmall)
  {
    if(par1 <  0.)
      trueLength = -lambda0*log(1.-geomStepLength/lambda0) ;
    else 
    {
      if(par1*par3*geomStepLength < 1.)
        trueLength = (1.-exp(log(1.-par1*par3*geomStepLength)/par3))/par1 ;
      else 
        trueLength = currentRange ;
    }  
  }

  if(trueLength > tPathLength) trueLength = tPathLength;
  if(trueLength > currentRange) trueLength = currentRange ;
  if(trueLength < geomStepLength) trueLength = geomStepLength;

  return trueLength;
}

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

void G4MscModel71::SampleSecondaries(std::vector<G4DynamicParticle*>*,
                                     const G4MaterialCutsCouple*,
                                     const G4DynamicParticle* dynParticle,
                                     G4double truestep,
                                     G4double safety)
{
  G4double kineticEnergy = dynParticle->GetKineticEnergy();
  if(kineticEnergy <= 0.0) return;

  G4double cth  = SampleCosineTheta(truestep,kineticEnergy);
  G4double sth  = sqrt((1.0 - cth)*(1.0 + cth));
  G4double phi  = twopi*G4UniformRand();
  G4double dirx = sth*cos(phi);
  G4double diry = sth*sin(phi);

  G4ThreeVector oldDirection = dynParticle->GetMomentumDirection();
  G4ThreeVector newDirection(dirx,diry,cth);
  newDirection.rotateUz(oldDirection);
  fParticleChange->ProposeMomentumDirection(newDirection);

  /*
    const G4ParticleDefinition* pd = dynParticle->GetDefinition();
    G4cout << "G4MscModel71: Sample secondary; E(MeV)= " << kineticEnergy/MeV
           << " MeV; step(mm)= " << truestep/mm
           << ", safety(mm)= " <<  safety/mm << " " << pd->GetParticleName()
           << G4endl;
  */

  if (latDisplasment && safety > 0.0) {

    G4double r = SampleDisplacement();
    if (r > safety) r = safety;

    // sample direction of lateral displacement
    G4double phi  = twopi*G4UniformRand();
    G4double dirx = std::cos(phi);
    G4double diry = std::sin(phi);

    G4ThreeVector newPosition(dirx,diry,0.0);
    newPosition.rotateUz(oldDirection);

    // compute new endpoint of the Step
    newPosition *= r;
    newPosition += *(fParticleChange->GetProposedPosition());

    navigator->LocateGlobalPointWithinVolume(newPosition);

    fParticleChange->ProposePosition(newPosition);
  }
}

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

G4double G4MscModel71::SampleCosineTheta(G4double trueStepLength, G4double KineticEnergy)
{
  G4double cth = 1. ;
  G4double tau = trueStepLength/lambda0 ;

  if(trueStepLength >= currentRange*dtrl)
    if(par1*trueStepLength < 1.)
      tau = -par2*log(1.-par1*trueStepLength) ;
    else
      tau = taubig ;

  currentTau = tau ;

  if(trueStepLength < stepmin)
    cth = exp(-tau) ;
  else
  {
    if (tau >= taubig) cth = -1.+2.*G4UniformRand();
    else if (tau >= tausmall)
    {
        G4double a ;

        // for all particles take the width of the central part
        //  from a  parametrization similar to the Highland formula
        // ( Highland formula: Particle Physics Booklet, July 2002, eq. 26.10)
        // here : theta0 = 13.6*MeV*Q*(t/X0)**0.555/(beta*cp) 
        const G4double c_highland = 13.6*MeV, corr_highland=0.555 ;
        G4double Q = std::abs(charge) ;
        G4double xx0 = trueStepLength/currentRadLength;
        G4double betacp = sqrt(currentKinEnergy*(currentKinEnergy+2.*mass)*
                               KineticEnergy*(KineticEnergy+2.*mass)/
                               ((currentKinEnergy+mass)*(KineticEnergy+mass))) ;
        G4double theta0 = c_highland*Q*exp(corr_highland*log(xx0))/betacp ;

        if(theta0 > taulim) a = 0.5/(1.-cos(theta0)) ;
        else                a = 1.0/(theta0*theta0) ;

        G4double xmeanth = exp(-tau);
        G4double xmeanth1 = 1.-xmeanth ;
        if(currentTau < taulim) xmeanth1 = tau ;          

        const G4double x1fac1 = exp(-xsi) ;
        const G4double x1fac2 = (1.-(1.+xsi)*x1fac1)/(1.-x1fac1) ;
        const G4double x1fac3 = 1.3      ; 

        G4double ea,eaa,xmean1 ;
        G4double c = 2.,b1 = 2., bx = 2.,
                 eb1 = b1, ebx = b1, xmean2 = 0. ;
        G4double prob = 1., qprob ;              
        G4double x0 = 1.-xsi/a;
        G4double oneminusx0=xsi/a ;
        G4double oneplusx0=2.+xsi/a ;

        G4double f1x0=1., f2x0=1. ;
        const G4double tau0 = 0.10 ;
        if(tau > tau0)
        {
         // 1 model function
          a = 1./xmeanth1 ;
          ea = exp(-2.*a) ;
          eaa= 1.-ea ;
          xmean1 = 1.-1./a+2.*ea/eaa ;
          prob = 1. ;
          qprob = 1. ;
        }
        else if (x0 <= -1.)
        {
          // 2 model fuctions only
          // in order to have xmean1 > xmeanth -> qprob < 1
          x0 = -1.;

          if( a < 1./xmeanth1)
            a = 1./xmeanth1 ;
          
          oneminusx0 = 1.-x0 ;
          oneplusx0 =  1.+x0 ;
          ea = exp(-a*oneminusx0);
          eaa = 1.-ea ;
          xmean1 = 1.-1./a+oneminusx0*ea/eaa ;
          qprob = xmeanth/xmean1 ;

        }
        else
        {
          // 3 model fuctions
          // in order to have xmean1 > xmeanth
          if((1.-x1fac2/a) < xmeanth)
          {
            a = x1fac3*x1fac2/xmeanth1 ;
            x0 = 1.-xsi/a ;
            oneminusx0=xsi/a ;
            oneplusx0=2.-xsi/a ;
          }

          ea = x1fac1 ;
          eaa = 1.-ea ;
          xmean1 = 1.-x1fac2/a ;

          const G4double fctail = factail*1.0 ;
          c = 2.+fctail*tau ;
          G4double c1 = c-1. ;
          G4double c2 = c-2. ;
          if(c2 == 0.) c2 = fctail*tausmall ;            

          b = 1.+(c-xsi)/a ;

          b1 = b+1. ;
          bx = c/a ;
          eb1=exp((c1)*log(b1)) ;
          ebx=exp((c1)*log(bx)) ;
          xmean2 = (x0*eb1+ebx-(eb1*bx-b1*ebx)/c2)/(eb1-ebx) ;

          f1x0 = a*ea/eaa ;
          f2x0 = c1*eb1*ebx/(eb1-ebx)/
                          exp(c*log(bx)) ;
          // from continuity at x=x0
          prob = f2x0/(f1x0+f2x0) ;
          // from xmean = xmeanth
          qprob = (f1x0+f2x0)*xmeanth/(f2x0*xmean1+f1x0*xmean2) ;

        }

        // sampling of costheta
        if (G4UniformRand() < qprob)
        {
          if (G4UniformRand() < prob)
             cth = 1.+log(ea+G4UniformRand()*eaa)/a ;
          else
             cth = b-b1*bx/exp(log(ebx-G4UniformRand()*(ebx-eb1))/(c-1.)) ;
        }
        else
        {
          cth = -1.+2.*G4UniformRand();
        }
    }
  }  

  return cth ;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....

G4double G4MscModel71::SampleDisplacement()
{
  const G4double kappa = 2.5;
  const G4double kappapl1 = kappa+1.;
  const G4double kappami1 = kappa-1.;
  G4double rmean = 0.0;
  if (currentTau >= tausmall) {
    if (currentTau < taulim) {
      rmean = kappa*currentTau*currentTau*currentTau*(1.-kappapl1*currentTau*0.25)/6. ;

    } else {
      G4double etau = 0.0;
      if (currentTau<taubig) etau = exp(-currentTau);
      rmean = -kappa*currentTau;
      rmean = -exp(rmean)/(kappa*kappami1);
      rmean += currentTau-kappapl1/kappa+kappa*etau/kappami1;
    }
    if (rmean>0.) rmean = 2.*lambda0*sqrt(rmean/3.0);
    else          rmean = 0.;
 }
  return rmean;
}

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

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