G4GoudsmitSaundersonMscModel.cc

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//
// ----------------------------------------------------------------------------
//
// GEANT4 Class implementation file
//
// File name:     G4GoudsmitSaundersonMscModel
//
// Author:        Mihaly Novak / (Omrane Kadri)
//
// Creation date: 20.02.2009
//
// Modifications:
// 04.03.2009 V.Ivanchenko cleanup and format according to Geant4 EM style
// 12.05.2010 O.Kadri: adding Qn1 and Qn12 as private doubles
// 18.05.2015 M. Novak provide PRELIMINARY verison of the revised class
//            This class has been revised and updated, new methods added.
//            A new version of Kawrakow-Bielajew Goudsmit-Saunderson MSC model
//            based on the screened Rutherford DCS for elastic scattering of
//            electrons/positrons has been introduced[1,2]. The corresponding MSC
//            angular distributions over a 2D parameter grid have been recomputed
//            and the CDFs are now stored in a variable transformed (smooth) form[2,3]
//            together with the corresponding rational interpolation parameters.
//            These angular distributions are handled by the new
//            G4GoudsmitSaundersonTable class that is responsible to sample if
//            it was no, single, few or multiple scattering case and delivers the
//            angular deflection (i.e. cos(theta) and sin(theta)).
//            Two screening options are provided:
//             - if fIsUsePWATotalXsecData=TRUE i.e. SetOptionPWAScreening(TRUE)
//               was called before initialisation: screening parameter value A is
//               determined such that the first transport coefficient G1(A)
//               computed according to the screened Rutherford DCS for elastic
//               scattering will reproduce the one computed from the PWA elastic
//               and first transport mean free paths[4].
//             - if fIsUsePWATotalXsecData=FALSE i.e. default value or
//               SetOptionPWAScreening(FALSE) was called before initialisation:
//               screening parameter value A is computed according to Moliere's
//               formula (by using material dependent parameters \chi_cc2 and b_c
//               precomputed for each material used at initialization in
//               G4GoudsmitSaundersonTable) [3]
//            Elastic and first trasport mean free paths are used consistently.
//            The new version is self-consistent, several times faster, more
//            robust and accurate compared to the earlier version.
//            Spin effects as well as a more accurate energy loss correction and
//            computations of Lewis moments will be implemented later on.
// 02.09.2015 M. Novak: first version of new step limit is provided.
//            fUseSafetyPlus corresponds to Urban fUseSafety (default)
//            fUseDistanceToBoundary corresponds to Urban fUseDistanceToBoundary
//            fUseSafety  corresponds to EGSnrc error-free stepping algorithm
//            Range factor can be significantly higher at each case than in Urban.
// 23.08.2017 M. Novak: added corrections to account spin effects (Mott-correction).
//            It can be activated by setting the fIsMottCorrection flag to be true
//            before initialization using the SetOptionMottCorrection() public method.
//            The fMottCorrection member is responsible to handle pre-computed Mott
//            correction (rejection) functions obtained by numerically computing
//            Goudsmit-Saunderson agnular distributions based on a DCS accounting spin
//            effects and screening corrections. The DCS used to compute the accurate
//            GS angular distributions is: DCS_{cor} = DCS_{SR}x[ DCS_{R}/DCS_{Mott}] where :
//               # DCS_{SR} is the relativistic Screened-Rutherford DCS (first Born approximate
//                 solution of the Klein-Gordon i.e. relativistic Schrodinger equation =>
//                 scattering of spinless e- on exponentially screened Coulomb potential)
//                 note: the default (without using Mott-correction) GS angular distributions
//                 are based on this DCS_{SR} with Moliere's screening parameter!
//               # DCS_{R} is the Rutherford DCS which is the same as above but without
//                 screening
//               # DCS_{Mott} is the Mott DCS i.e. solution of the Dirac equation with a bare
//                 Coulomb potential i.e. scattering of particles with spin (e- or e+) on a
//                 point-like unscreened Coulomb potential
//               # moreover, the screening parameter of the DCS_{cor} was determined such that
//                 the DCS_{cor} with this corrected screening parameter reproduce the first
//                 transport cross sections obtained from the corresponding most accurate DCS
//                 (i.e. from elsepa [4])
//            Unlike the default GS, the Mott-corrected angular distributions are particle type
//            (different for e- and e+ <= the DCS_{Mott} and the screening correction) and target
//            (Z and material) dependent.
// 27.10.2017 M. Novak:
//            - Mott-correction flag is set now through the G4EmParameters
//            - new form of PWA correction to integrated quantities and screening (default)
//            - changed step limit flag conventions:
//               # fUseSafety corresponds to Urban's fUseSafety
//               # fUseDistanceToBoundary corresponds to Urban's fUseDistanceToBoundary
//               # fUseSafetyPlus corresponds to the error-free stepping algorithm
// 02.02.2018 M. Novak: implemented CrossSectionPerVolume interface method (used only for testing)
//
// Class description:
//   Kawrakow-Bielajew Goudsmit-Saunderson MSC model based on the screened Rutherford DCS
//   for elastic scattering of e-/e+. Option, to include (Mott) correction (see above), is
//   also available now (SetOptionMottCorrection(true)). An EGSnrc like error-free stepping
//   algorithm (UseSafety) is available beyond the usual Geant4 step limitation algorithms
//   and true to geomerty and geometry to true step length computations that were adopted
//   from the Urban model[5]. The most accurate setting: error-free stepping i.e. the
//   UseSafetyPlus MSC step limit with Mott-correction (SetOptionMottCorrection(true)). Both
//   are expected to be set through the G4EmParameters singleton before initialisation:
//    # G4EmParameters::Instance()->SetMscStepLimitType(fUseSafetyPlus);
//    # G4EmParameters::Instance()->SetUseMottCorrection(true);
//
//
// References:
//   [1] A.F.Bielajew, NIMB 111 (1996) 195-208
//   [2] I.Kawrakow, A.F.Bielajew, NIMB 134(1998) 325-336
//   [3] I.Kawrakow, E.Mainegra-Hing, D.W.O.Rogers, F.Tessier,B.R.B.Walters, NRCC
//       Report PIRS-701 (2013)
//   [4] F.Salvat, A.Jablonski, C.J. Powell, CPC 165(2005) 157-190
//   [5] L.Urban, Preprint CERN-OPEN-2006-077 (2006)
//
// -----------------------------------------------------------------------------
 
 
#include "G4GoudsmitSaundersonMscModel.hh"
 
#include "G4GoudsmitSaundersonTable.hh"
#include "G4GSPWACorrections.hh"
 
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
 
#include "G4ParticleChangeForMSC.hh"
#include "G4DynamicParticle.hh"
#include "G4Electron.hh"
#include "G4Positron.hh"
 
#include "G4LossTableManager.hh"
#include "G4EmParameters.hh"
#include "G4Track.hh"
#include "G4PhysicsTable.hh"
#include "Randomize.hh"
#include "G4Log.hh"
#include "G4Exp.hh"
#include "G4Pow.hh"
#include <fstream>
 
 
// set accurate energy loss and dispalcement sampling to be always on now
G4bool G4GoudsmitSaundersonMscModel::gIsUseAccurate    = true;
// set the usual optimization to be always active now
G4bool G4GoudsmitSaundersonMscModel::gIsOptimizationOn = true;
 
 
G4GoudsmitSaundersonMscModel::G4GoudsmitSaundersonMscModel(const G4String& nam)
  : G4VMscModel(nam) {
  charge                 = 0;
  currentMaterialIndex   = -1;
  //
  fr                     = 0.1;
  rangeinit              = 1.e+21;
  geombig                = 1.e+50*mm;
  geomlimit              = geombig;
  tgeom                  = geombig;
  tlimit                 = 1.e+10*mm;
  presafety              = 0.*mm;
  //
  particle               = nullptr;
  theManager             = G4LossTableManager::Instance();
  firstStep              = true;
  currentKinEnergy       = 0.0;
  currentRange           = 0.0;
  //
  tlimitminfix2          = 1.*nm;
  tausmall               = 1.e-16;
  mass                   = electron_mass_c2;
  taulim                 = 1.e-6;
  //
  currentCouple          = nullptr;
  fParticleChange        = nullptr;
  //
  fZeff                  = 1.;
  //
  par1                   = 0.;
  par2                   = 0.;
  par3                   = 0.;
  //
  // Moliere screeing parameter will be used and (by default) corrections are
  // appalied to the integrated quantities (screeing parameter, elastic mfp, first
  // and second moments) derived from the corresponding PWA quantities
  // this PWA correction is ignored if Mott-correction is set to true because
  // Mott-correction contains all these corrections as well
  fIsUsePWACorrection    = true;
  //
  fIsUseMottCorrection   = false;
  //
  fLambda0               = 0.0; // elastic mean free path
  fLambda1               = 0.0; // first transport mean free path
  fScrA                  = 0.0; // screening parameter
  fG1                    = 0.0; // first transport coef.
  //
  fMCtoScrA              = 1.0;
  fMCtoQ1                = 1.0;
  fMCtoG2PerG1           = 1.0;
  //
  fTheTrueStepLenght     = 0.;
  fTheTransportDistance  = 0.;
  fTheZPathLenght        = 0.;
  //
  fTheDisplacementVector.set(0.,0.,0.);
  fTheNewDirection.set(0.,0.,1.);
  //
  fIsEverythingWasDone   = false;
  fIsMultipleSacettring  = false;
  fIsSingleScattering    = false;
  fIsEndedUpOnBoundary   = false;
  fIsNoScatteringInMSC   = false;
  fIsNoDisplace          = false;
  fIsInsideSkin          = false;
  fIsWasOnBoundary       = false;
  fIsFirstRealStep       = false;
  rndmEngineMod          = G4Random::getTheEngine();
  //
  fGSTable               = nullptr;
  fPWACorrection         = nullptr;
}
 
 
G4GoudsmitSaundersonMscModel::~G4GoudsmitSaundersonMscModel() {
  if (IsMaster()) {
    if (fGSTable) {
      delete fGSTable;
      fGSTable = nullptr;
    }
    if (fPWACorrection) {
      delete fPWACorrection;
      fPWACorrection = nullptr;
    }
  }
}
 
 
void G4GoudsmitSaundersonMscModel::Initialise(const G4ParticleDefinition* p, const G4DataVector&) {
  SetParticle(p);
  InitialiseParameters(p);
  // -create GoudsmitSaundersonTable and init its Mott-correction member if
  //  Mott-correction was required
  if (IsMaster()) {
    // get the Mott-correction flag from EmParameters
    if (G4EmParameters::Instance()->UseMottCorrection()) {
      fIsUseMottCorrection = true;
    }
    // Mott-correction includes other way of PWA x-section corrections so deactivate it even if it was true
    // when Mott-correction is activated by the user
    if (fIsUseMottCorrection) {
      fIsUsePWACorrection = false;
    }
    // clear GS-table
    if (fGSTable) {
      delete fGSTable;
      fGSTable = nullptr;
    }
    // clear PWA corrections table if any
    if (fPWACorrection) {
      delete fPWACorrection;
      fPWACorrection = nullptr;
    }
    // create GS-table
    G4bool isElectron = true;
    if (p->GetPDGCharge()>0.) {
      isElectron = false;
    }
    fGSTable = new G4GoudsmitSaundersonTable(isElectron);
    // G4GSTable will be initialised:
    // - Screened-Rutherford DCS based GS angular distributions will be loaded only if they are not there yet
    // - Mott-correction will be initialised if Mott-correction was requested to be used
    fGSTable->SetOptionMottCorrection(fIsUseMottCorrection);
    // - set PWA correction (correction to integrated quantites from Dirac-PWA)
    fGSTable->SetOptionPWACorrection(fIsUsePWACorrection);
    // init
    fGSTable->Initialise(LowEnergyLimit(),HighEnergyLimit());
    // create PWA corrections table if it was requested (and not disactivated because active Mott-correction)
    if (fIsUsePWACorrection) {
      fPWACorrection = new G4GSPWACorrections(isElectron);
      fPWACorrection->Initialise();
    }
  }
  fParticleChange = GetParticleChangeForMSC(p);
}
 
 
void G4GoudsmitSaundersonMscModel::InitialiseLocal(const G4ParticleDefinition*, G4VEmModel* masterModel) {
   fGSTable               = static_cast<G4GoudsmitSaundersonMscModel*>(masterModel)->GetGSTable();
   fIsUseMottCorrection   = static_cast<G4GoudsmitSaundersonMscModel*>(masterModel)->GetOptionMottCorrection();
   fIsUsePWACorrection    = static_cast<G4GoudsmitSaundersonMscModel*>(masterModel)->GetOptionPWACorrection();
   fPWACorrection         = static_cast<G4GoudsmitSaundersonMscModel*>(masterModel)->GetPWACorrection();
}
 
 
// computes macroscopic first transport cross section: used only in testing not during mc transport
G4double G4GoudsmitSaundersonMscModel::CrossSectionPerVolume(const G4Material* mat,
                                         const G4ParticleDefinition*,
                                         G4double kineticEnergy,
                                         G4double,
                                         G4double) {
  G4double xsecTr1  = 0.; // cross section per volume i.e. macroscopic 1st transport cross section
  // 
  fLambda0 = 0.0; // elastic mean free path
  fLambda1 = 0.0; // first transport mean free path
  fScrA    = 0.0; // screening parameter
  fG1      = 0.0; // first transport coef.
  // use Moliere's screening (with Mott-corretion if it was requested)
  G4double efEnergy = std::max(kineticEnergy, 10.*CLHEP::eV);
  // total mometum square
  G4double pt2     = efEnergy*(efEnergy+2.0*electron_mass_c2);
  // beta square
  G4double beta2   = pt2/(pt2+electron_mass_c2*electron_mass_c2);
  // current material index
  G4int    matindx = (G4int)mat->GetIndex();
  // Moliere's b_c
  G4double bc      = fGSTable->GetMoliereBc(matindx);
  // get the Mott-correcton factors if Mott-correcton was requested by the user
  fMCtoScrA       = 1.0;
  fMCtoQ1         = 1.0;
  fMCtoG2PerG1    = 1.0;
  G4double scpCor = 1.0;
  if (fIsUseMottCorrection) {
    fGSTable->GetMottCorrectionFactors(G4Log(efEnergy), beta2, matindx, fMCtoScrA, fMCtoQ1, fMCtoG2PerG1);
    // ! no scattering power correction since the current couple is not set before this interface method is called
    // scpCor = fGSTable->ComputeScatteringPowerCorrection(currentCouple, efEnergy);
  } else if (fIsUsePWACorrection) {
    fPWACorrection->GetPWACorrectionFactors(G4Log(efEnergy), beta2, matindx, fMCtoScrA, fMCtoQ1, fMCtoG2PerG1);
    // scpCor = fGSTable->ComputeScatteringPowerCorrection(currentCouple, efEnergy);
  }
  // screening parameter:
  // - if Mott-corretioncorrection: the Screened-Rutherford times Mott-corretion DCS with this
  //   screening parameter gives back the (elsepa) PWA first transport cross section
  // - if PWA correction: he Screened-Rutherford DCS with this screening parameter
  //   gives back the (elsepa) PWA first transport cross section
  fScrA    = fGSTable->GetMoliereXc2(matindx)/(4.0*pt2*bc)*fMCtoScrA;
  // elastic mean free path in Geant4 internal lenght units: the neglected (1+screening parameter) term is corrected
  // (if Mott-corretion: the corrected screening parameter is used for this (1+A) correction + Moliere b_c is also
  // corrected with the screening parameter correction)
  fLambda0 = beta2*(1.+fScrA)*fMCtoScrA/bc/scpCor;
  // first transport coefficient (if Mott-corretion: the corrected screening parameter is used (it will be fully
  // consistent with the one used during the pre-computation of the Mott-correted GS angular distributions))
  fG1      = 2.0*fScrA*((1.0+fScrA)*G4Log(1.0/fScrA+1.0)-1.0);
  // first transport mean free path
  fLambda1 = fLambda0/fG1;
  xsecTr1  = 1./fLambda1;
  return xsecTr1;
}
 
 
// gives back the first transport mean free path in internal G4 units
G4double
G4GoudsmitSaundersonMscModel::GetTransportMeanFreePath(const G4ParticleDefinition* /*partdef*/,
                                                       G4double kineticEnergy) {
  // kinetic energy is assumed to be in Geant4 internal energy unit which is MeV
  G4double efEnergy = kineticEnergy;
  //
  const G4Material*  mat = currentCouple->GetMaterial();
  //
  fLambda0 = 0.0; // elastic mean free path
  fLambda1 = 0.0; // first transport mean free path
  fScrA    = 0.0; // screening parameter
  fG1      = 0.0; // first transport coef.
 
  // use Moliere's screening (with Mott-corretion if it was requested)
  if  (efEnergy<10.*CLHEP::eV) efEnergy = 10.*CLHEP::eV;
  // total mometum square
  G4double pt2     = efEnergy*(efEnergy+2.0*electron_mass_c2);
  // beta square
  G4double beta2   = pt2/(pt2+electron_mass_c2*electron_mass_c2);
  // current material index
  G4int    matindx = (G4int)mat->GetIndex();
  // Moliere's b_c
  G4double bc      = fGSTable->GetMoliereBc(matindx);
  // get the Mott-correcton factors if Mott-correcton was requested by the user
  fMCtoScrA       = 1.0;
  fMCtoQ1         = 1.0;
  fMCtoG2PerG1    = 1.0;
  G4double scpCor = 1.0;
  if (fIsUseMottCorrection) {
    fGSTable->GetMottCorrectionFactors(G4Log(efEnergy), beta2, matindx, fMCtoScrA, fMCtoQ1, fMCtoG2PerG1);
    scpCor = fGSTable->ComputeScatteringPowerCorrection(currentCouple, efEnergy);
  } else if (fIsUsePWACorrection) {
    fPWACorrection->GetPWACorrectionFactors(G4Log(efEnergy), beta2, matindx, fMCtoScrA, fMCtoQ1, fMCtoG2PerG1);
    // scpCor = fGSTable->ComputeScatteringPowerCorrection(currentCouple, efEnergy);
  }
  // screening parameter:
  // - if Mott-corretioncorrection: the Screened-Rutherford times Mott-corretion DCS with this
  //   screening parameter gives back the (elsepa) PWA first transport cross section
  // - if PWA correction: he Screened-Rutherford DCS with this screening parameter
  //   gives back the (elsepa) PWA first transport cross section
  fScrA    = fGSTable->GetMoliereXc2(matindx)/(4.0*pt2*bc)*fMCtoScrA;
  // elastic mean free path in Geant4 internal lenght units: the neglected (1+screening parameter) term is corrected
  // (if Mott-corretion: the corrected screening parameter is used for this (1+A) correction + Moliere b_c is also
  // corrected with the screening parameter correction)
  fLambda0 = beta2*(1.+fScrA)*fMCtoScrA/bc/scpCor;
  // first transport coefficient (if Mott-corretion: the corrected screening parameter is used (it will be fully
  // consistent with the one used during the pre-computation of the Mott-correted GS angular distributions))
  fG1      = 2.0*fScrA*((1.0+fScrA)*G4Log(1.0/fScrA+1.0)-1.0);
  // first transport mean free path
  fLambda1 = fLambda0/fG1;
 
  return fLambda1;
}
 
 
G4double
G4GoudsmitSaundersonMscModel::GetTransportMeanFreePathOnly(const G4ParticleDefinition* /*partdef*/,
                                                       G4double kineticEnergy) {
  // kinetic energy is assumed to be in Geant4 internal energy unit which is MeV
  G4double efEnergy = kineticEnergy;
  //
  const G4Material*  mat = currentCouple->GetMaterial();
  //
  G4double lambda0 = 0.0; // elastc mean free path
  G4double lambda1 = 0.0; // first transport mean free path
  G4double scrA    = 0.0; // screening parametr
  G4double g1      = 0.0; // first transport mean free path
 
  // use Moliere's screening (with Mott-corretion if it was requested)
  if  (efEnergy<10.*CLHEP::eV) efEnergy = 10.*CLHEP::eV;
  // total mometum square in Geant4 internal energy2 units which is MeV2
  G4double pt2     = efEnergy*(efEnergy+2.0*electron_mass_c2);
  G4double beta2   = pt2/(pt2+electron_mass_c2*electron_mass_c2);
  G4int    matindx = (G4int)mat->GetIndex();
  G4double bc      = fGSTable->GetMoliereBc(matindx);
  // get the Mott-correcton factors if Mott-correcton was requested by the user
  G4double mctoScrA    = 1.0;
  G4double mctoQ1      = 1.0;
  G4double mctoG2PerG1 = 1.0;
  G4double scpCor      = 1.0;
  if (fIsUseMottCorrection) {
    fGSTable->GetMottCorrectionFactors(G4Log(efEnergy), beta2, matindx, mctoScrA, mctoQ1, mctoG2PerG1);
    scpCor = fGSTable->ComputeScatteringPowerCorrection(currentCouple, efEnergy);
  } else if (fIsUsePWACorrection) {
    fPWACorrection->GetPWACorrectionFactors(G4Log(efEnergy), beta2, matindx, mctoScrA, mctoQ1, mctoG2PerG1);
    // scpCor = fGSTable->ComputeScatteringPowerCorrection(currentCouple, efEnergy);
  }
  scrA    = fGSTable->GetMoliereXc2(matindx)/(4.0*pt2*bc)*mctoScrA;
  // total elastic mean free path in Geant4 internal lenght units
  lambda0 = beta2*(1.+scrA)*mctoScrA/bc/scpCor;
  g1      = 2.0*scrA*((1.0+scrA)*G4Log(1.0/scrA+1.0)-1.0);
  lambda1 = lambda0/g1;
 
  return lambda1;
}
 
 
void G4GoudsmitSaundersonMscModel::StartTracking(G4Track* track) {
  SetParticle(track->GetDynamicParticle()->GetDefinition());
  firstStep = true;
  tlimit    = tgeom = rangeinit = geombig;
  rangeinit = 1.e+21;
}
 
 
G4double G4GoudsmitSaundersonMscModel::ComputeTruePathLengthLimit(const G4Track& track,
                                                                        G4double& currentMinimalStep) {
  G4double skindepth = 0.;
  //
  const G4DynamicParticle* dp = track.GetDynamicParticle();
  G4StepPoint* sp             = track.GetStep()->GetPreStepPoint();
  G4StepStatus stepStatus     = sp->GetStepStatus();
  currentCouple               = track.GetMaterialCutsCouple();
  SetCurrentCouple(currentCouple);
  currentMaterialIndex        = (G4int)currentCouple->GetMaterial()->GetIndex();
  currentKinEnergy            = dp->GetKineticEnergy();
  currentRange                = GetRange(particle,currentKinEnergy,currentCouple,
                                         dp->GetLogKineticEnergy());
  // elastic and first transport mfp, screening parameter and G1 are also set
  // (Mott-correction will be used if it was requested by the user)
  fLambda1 = GetTransportMeanFreePath(particle,currentKinEnergy);
  // Set initial values:
  //  : lengths are initialised to currentMinimalStep  which is the true, minimum
  //    step length from all other physics
  fTheTrueStepLenght    = currentMinimalStep;
  fTheTransportDistance = currentMinimalStep;
  fTheZPathLenght       = currentMinimalStep;  // will need to be converted
  fTheDisplacementVector.set(0.,0.,0.);
  fTheNewDirection.set(0.,0.,1.);
 
  // Can everything be done in the step limit phase ?
  fIsEverythingWasDone  = false;
  // Multiple scattering needs to be sample ?
  fIsMultipleSacettring = false;
  // Single scattering needs to be sample ?
  fIsSingleScattering   = false;
  // Was zero deflection in multiple scattering sampling ?
  fIsNoScatteringInMSC  = false;
  // Do not care about displacement in MSC sampling
  // ( used only in the case of gIsOptimizationOn = true)
  fIsNoDisplace = false;
  // get pre-step point safety
  presafety = sp->GetSafety();
  //
  fZeff = currentCouple->GetMaterial()->GetIonisation()->GetZeffective();
  // distance will take into account max-fluct.
  G4double distance = currentRange;
  distance *= (1.20-fZeff*(1.62e-2-9.22e-5*fZeff));
  //
  // Possible optimization : if the distance is samller than the safety -> the
  // particle will never leave this volume -> dispalcement
  // as the effect of multiple elastic scattering can be skipped
  // Important : this optimization can cause problems if one does scoring
  // in a bigger volume since MSC won't be done deep inside the volume when
  // distance < safety so don't use optimized-mode in such case.
  if (gIsOptimizationOn && (distance<presafety)) {
     // Indicate that we need to do MSC after transportation and no dispalcement.
     fIsMultipleSacettring = true;
     fIsNoDisplace = true;
  } else if (steppingAlgorithm==fUseDistanceToBoundary) {
    //Compute geomlimit (and presafety) :
    // - geomlimit will be:
    //    == the straight line distance to the boundary if currentRange is
    //       longer than that
    //    == a big value [geombig = 1.e50*mm] if currentRange is shorter than
    //       the straight line distance to the boundary
    // - presafety will be updated as well
    // So the particle can travell 'gemlimit' distance (along a straight
    // line!) in its current direction:
    //  (1) before reaching a boundary (geomlimit < geombig) OR
    //  (2) before reaching its current range (geomlimit == geombig)
    geomlimit = ComputeGeomLimit(track, presafety, currentRange);
    // Record that the particle is on a boundary
    if ( (stepStatus==fGeomBoundary) || (stepStatus==fUndefined && presafety==0.0)) {
      fIsWasOnBoundary = true;
    }
    // Set skin depth = skin x elastic_mean_free_path
    skindepth     = skin*fLambda0;
    // Init the flag that indicates that the particle are within a skindepth
    // distance from a boundary
    fIsInsideSkin = false;
    // Check if we can try Single Scattering because we are within skindepth
    // distance from/to a boundary OR the current minimum true-step-length is
    // shorter than skindepth. NOTICE: the latest has only efficieny reasons
    // because the MSC angular sampling is fine for any short steps but much
    // faster to try single scattering in case of short steps.
    if ((stepStatus==fGeomBoundary) || (presafety<skindepth) || (fTheTrueStepLenght<skindepth)) {
      // check if we are within skindepth distance from a boundary
      if ((stepStatus == fGeomBoundary) || (presafety < skindepth)) {
        fIsInsideSkin    = true;
        fIsWasOnBoundary = true;
      }
      //Try single scattering:
      // - sample distance to next single scattering interaction (sslimit)
      // - compare to current minimum length
      //      == if sslimit is the shorter:
      //          - set the step length to sslimit
      //          - indicate that single scattering needs to be done
      //      == else : nothing to do
      //- in both cases, the step length was very short so geometrical and
      //  true path length are the same
      G4double sslimit = -1.*fLambda0*G4Log(G4UniformRand());
      // compare to current minimum step length
      if (sslimit<fTheTrueStepLenght) {
        fTheTrueStepLenght  = sslimit;
        fIsSingleScattering = true;
      }
      // short step -> true step length equal to geometrical path length
      fTheZPathLenght       = fTheTrueStepLenght;
      // Set taht everything is done in step-limit phase so no MSC call
      // We will check if we need to perform the single-scattering angular
      // sampling i.e. if single elastic scattering was the winer!
      fIsEverythingWasDone  = true;
    } else {
      // After checking we know that we cannot try single scattering so we will
      // need to make an MSC step
      // Indicate that we need to make and MSC step. We do not check if we can
      // do it now i.e. if presafety>final_true_step_length so we let the
      // fIsEverythingWasDone = false which indicates that we will perform
      // MSC after transportation.
      fIsMultipleSacettring = true;
      // Init the first-real-step falg: it will indicate if we do the first
      // non-single scattering step in this volume with this particle
      fIsFirstRealStep      = false;
      // If previously the partcile was on boundary it was within skin as
      // well. When it is not within skin anymore it has just left the skin
      // so we make the first real MSC step with the particle.
      if (fIsWasOnBoundary && !fIsInsideSkin) {
        // reset the 'was on boundary' indicator flag
        fIsWasOnBoundary  = false;
        fIsFirstRealStep  = true;
      }
      // If this is the first-real msc step (the partcile has just left the
      // skin) or this is the first step with the particle (was born or
      // primary):
      //   - set the initial range that will be used later to limit its step
      //     (only in this volume, because after boundary crossing at the
      //     first-real MSC step we will reset)
      //  - don't let the partcile to cross the volume just in one step
      if (firstStep || fIsFirstRealStep || rangeinit>1.e+20) {
        rangeinit = currentRange;
        // If geomlimit < geombig than the particle might reach the boundary
        // along its initial direction before losing its energy (in this step)
        // Otherwise we can be sure that the particle will lose it energy
        // before reaching the boundary along a starigth line so there is no
        // geometrical limit appalied. [However, tgeom is set only in the
        // first or the first-real MSC step. After the first or first real
        // MSC step the direction will change tgeom won't guaranty anything!
        // But we will try to end up within skindepth from the boundary using
        // the actual value of geomlimit(See later at step reduction close to
        // boundary).]
        if (geomlimit<geombig) {
          // transfrom straight line distance to the boundary to real step
          // length based on the mean values (using the prestep point
          // first-transport mean free path i.e. no energy loss correction)
          if ((1.-geomlimit/fLambda1)> 0.) {
            geomlimit = -fLambda1*G4Log(1.-geomlimit/fLambda1);
          }
          // the 2-different case that could lead us here
          if (firstStep) {
            tgeom = 2.*geomlimit/facgeom;
          } else {
            tgeom = geomlimit/facgeom;
          }
        } else {
          tgeom = geombig;
        }
      }
      // True step length limit from range factor. Noteice, that the initial
      // range is used that was set at the first step or first-real MSC step
      // in this volume with this particle.
      tlimit = facrange*rangeinit;
      // Take the minimum of the true step length limits coming from
      // geometrical constraint or range-factor limitation
      tlimit = std::min(tlimit,tgeom);
      // Step reduction close to boundary: we try to end up within skindepth
      // from the boundary ( Notice: in case of mag. field it might not work
      // because geomlimit is the straigth line distance to the boundary in
      // the currect direction (if geomlimit<geombig) and mag. field can
      // change the initial direction. So te particle might hit some boundary
      // before in a different direction. However, here we restrict the true
      // path length to this (straight line) lenght so the corresponding
      // transport distance (straight line) will be even shorter than
      // geomlimit-0.999*skindepth after the change of true->geom.
      if (geomlimit<geombig) {
        tlimit = std::min(tlimit, geomlimit-0.999*skindepth);
      }
      // randomize 1st step or 1st 'normal' step in volume
      if (firstStep || fIsFirstRealStep) {
        fTheTrueStepLenght = std::min(fTheTrueStepLenght, Randomizetlimit());
      } else {
        fTheTrueStepLenght = std::min(fTheTrueStepLenght, tlimit);
      }
    }
  } else if (steppingAlgorithm==fUseSafetyPlus) { // THE ERROR_FREE stepping alg.
    presafety =  ComputeSafety(sp->GetPosition(),fTheTrueStepLenght);
    geomlimit = presafety;
    // Set skin depth = skin x elastic_mean_free_path
    skindepth = skin*fLambda0;
    // Check if we can try Single Scattering because we are within skindepth
    // distance from/to a boundary OR the current minimum true-step-length is
    // shorter than skindepth. NOTICE: the latest has only efficieny reasons
    // because the MSC angular sampling is fine for any short steps but much
    // faster to try single scattering in case of short steps.
    if ((stepStatus==fGeomBoundary) || (presafety<skindepth) || (fTheTrueStepLenght<skindepth)) {
      //Try single scattering:
      // - sample distance to next single scattering interaction (sslimit)
      // - compare to current minimum length
      //      == if sslimit is the shorter:
      //          - set the step length to sslimit
      //          - indicate that single scattering needs to be done
      //      == else : nothing to do
      //- in both cases, the step length was very short so geometrical and
      //  true path length are the same
      G4double sslimit = -1.*fLambda0*G4Log(G4UniformRand());
      // compare to current minimum step length
      if (sslimit<fTheTrueStepLenght) {
        fTheTrueStepLenght  = sslimit;
        fIsSingleScattering = true;
      }
      // short step -> true step length equal to geometrical path length
      fTheZPathLenght       = fTheTrueStepLenght;
      // Set taht everything is done in step-limit phase so no MSC call
      // We will check if we need to perform the single-scattering angular
      // sampling i.e. if single elastic scattering was the winer!
      fIsEverythingWasDone  = true;
    } else {
      // After checking we know that we cannot try single scattering so we will
      // need to make an MSC step
      // Indicate that we need to make and MSC step.
      fIsMultipleSacettring = true;
      fIsEverythingWasDone  = true;
      // limit from range factor
      fTheTrueStepLenght    = std::min(fTheTrueStepLenght, facrange*currentRange);
      // never let the particle go further than the safety if we are out of the skin
      // if we are here we are out of the skin, presafety > 0.
      if (fTheTrueStepLenght>presafety) {
        fTheTrueStepLenght = std::min(fTheTrueStepLenght, presafety);
      }
      // make sure that we are still within the aplicability of condensed histry model
      // i.e. true step length is not longer than first transport mean free path.
      // We schould take into account energy loss along 0.5x lambda_transport1
      // step length as well. So let it 0.5 x lambda_transport1
      fTheTrueStepLenght = std::min(fTheTrueStepLenght, fLambda1*0.5);
    }
  } else {
    // This is the default stepping algorithm: the fastest but the least
    // accurate that corresponds to fUseSafety in Urban model. Note, that GS
    // model can handle any short steps so we do not need the minimum limits
    //
    // NO single scattering in case of skin or short steps (by defult the MSC
    // model will be single or even no scattering in case of short steps
    // compared to the elastic mean free path.)
    //
    // indicate that MSC needs to be done (always and always after transportation)
    fIsMultipleSacettring = true;
    if (stepStatus!=fGeomBoundary) {
      presafety = ComputeSafety(sp->GetPosition(),fTheTrueStepLenght);
    }
    // Far from boundary-> in optimized mode do not sample dispalcement.
    if ((distance<presafety) && (gIsOptimizationOn)) {
      fIsNoDisplace = true;
    } else {
      // Urban like
      if (firstStep || (stepStatus==fGeomBoundary) || rangeinit>1.e+20) {
        rangeinit = currentRange;
        fr        = facrange;
// We don't use this: we won't converge to the single scattering results with
//                    decreasing range-factor.
//              rangeinit = std::max(rangeinit, fLambda1);
//              if(fLambda1 > lambdalimit) {
//                fr *= (0.75+0.25*fLambda1/lambdalimit);
//              }
 
      }
      //step limit
      tlimit = std::max(fr*rangeinit, facsafety*presafety);
      // first step randomization
      if (firstStep || stepStatus==fGeomBoundary) {
        fTheTrueStepLenght = std::min(fTheTrueStepLenght, Randomizetlimit());
      } else {
        fTheTrueStepLenght = std::min(fTheTrueStepLenght, tlimit);
      }
    }
  }
  //
  // unset first-step
  firstStep =false;
  // performe single scattering, multiple scattering if this later can be done safely here
  if (fIsEverythingWasDone) {
    if (fIsSingleScattering) {
      // sample single scattering
      //G4double ekin   = 0.5*(currentKinEnergy + GetEnergy(particle,currentRange-fTheTrueStepLenght,currentCouple));
      G4double lekin  = G4Log(currentKinEnergy);
      G4double pt2    = currentKinEnergy*(currentKinEnergy+2.0*CLHEP::electron_mass_c2);
      G4double beta2  = pt2/(pt2+CLHEP::electron_mass_c2*CLHEP::electron_mass_c2);
      G4double cost   = fGSTable->SingleScattering(1., fScrA, lekin, beta2, currentMaterialIndex);
      // protection
      if (cost<-1.) cost = -1.;
      if (cost> 1.) cost =  1.;
      // compute sint
      G4double dum    = 1.-cost;
      G4double sint   = std::sqrt(dum*(2.-dum));
      G4double phi    = CLHEP::twopi*G4UniformRand();
      G4double sinPhi = std::sin(phi);
      G4double cosPhi = std::cos(phi);
      fTheNewDirection.set(sint*cosPhi,sint*sinPhi,cost);
    } else if (fIsMultipleSacettring) {
      // sample multiple scattering
      SampleMSC(); // fTheZPathLenght, fTheDisplacementVector and fTheNewDirection will be set
    } // and if single scattering but it was longer => nothing to do
  } //else { do nothing here but after transportation
  //
  return ConvertTrueToGeom(fTheTrueStepLenght,currentMinimalStep);
}
 
 
G4double G4GoudsmitSaundersonMscModel::ComputeGeomPathLength(G4double) {
  // convert true ->geom
  // It is called from the step limitation ComputeTruePathLengthLimit if
  // !fIsEverythingWasDone but protect:
  par1 = -1.;
  par2 = par3 = 0.;
  // if fIsEverythingWasDone = TRUE  => fTheZPathLenght is already set
  // so return with the already known value
  // Otherwise:
  if (!fIsEverythingWasDone) {
    // this correction needed to run MSC with eIoni and eBrem inactivated
    // and makes no harm for a normal run
    fTheTrueStepLenght = std::min(fTheTrueStepLenght,currentRange);
    //  do the true -> geom transformation
    fTheZPathLenght = fTheTrueStepLenght;
    // z = t for very small true-path-length
    if (fTheTrueStepLenght<tlimitminfix2) {
      return fTheZPathLenght;
    }
    G4double tau = fTheTrueStepLenght/fLambda1;
    if (tau<=tausmall) {
      fTheZPathLenght = std::min(fTheTrueStepLenght, fLambda1);
    } else  if (fTheTrueStepLenght<currentRange*dtrl) {
      if (tau<taulim) fTheZPathLenght = fTheTrueStepLenght*(1.-0.5*tau) ;
      else            fTheZPathLenght = fLambda1*(1.-G4Exp(-tau));
    } else if (currentKinEnergy<mass || fTheTrueStepLenght==currentRange)  {
      par1 = 1./currentRange ;     // alpha =1/range_init for Ekin<mass
      par2 = 1./(par1*fLambda1) ;  // 1/(alphaxlambda01)
      par3 = 1.+par2 ;             // 1+1/
      if (fTheTrueStepLenght<currentRange) {
        fTheZPathLenght = 1./(par1*par3) * (1.-std::pow(1.-par1*fTheTrueStepLenght,par3));
      } else {
        fTheZPathLenght = 1./(par1*par3);
      }
    } else {
      G4double rfin    = std::max(currentRange-fTheTrueStepLenght, 0.01*currentRange);
      G4double T1      = GetEnergy(particle,rfin,currentCouple);
      G4double lambda1 = GetTransportMeanFreePathOnly(particle,T1);
      //
      par1 = (fLambda1-lambda1)/(fLambda1*fTheTrueStepLenght);  // alpha
      par2 = 1./(par1*fLambda1);
      par3 = 1.+par2 ;
      G4Pow *g4calc = G4Pow::GetInstance();
      fTheZPathLenght = 1./(par1*par3) * (1.-g4calc->powA(1.-par1*fTheTrueStepLenght,par3));
    }
  }
  fTheZPathLenght = std::min(fTheZPathLenght, fLambda1);
  //
  return fTheZPathLenght;
}
 
 
G4double G4GoudsmitSaundersonMscModel::ComputeTrueStepLength(G4double geomStepLength) {
  // init
  fIsEndedUpOnBoundary = false;
  // step defined other than transportation
  if (geomStepLength==fTheZPathLenght) {
    return fTheTrueStepLenght;
  }
  // else ::
  // - set the flag that transportation was the winer so DoNothin in DOIT !!
  // - convert geom -> true by using the mean value
  fIsEndedUpOnBoundary = true; // OR LAST STEP
  fTheZPathLenght      = geomStepLength;
  // was a short single scattering step
  if (fIsEverythingWasDone && !fIsMultipleSacettring) {
    fTheTrueStepLenght = geomStepLength;
    return fTheTrueStepLenght;
  }
  // t = z for very small step
  if (geomStepLength<tlimitminfix2) {
    fTheTrueStepLenght = geomStepLength;
  // recalculation
  } else {
    G4double tlength = geomStepLength;
    if (geomStepLength>fLambda1*tausmall) {
      if (par1< 0.) {
        tlength = -fLambda1*G4Log(1.-geomStepLength/fLambda1) ;
      } else {
        if (par1*par3*geomStepLength<1.) {
          G4Pow *g4calc = G4Pow::GetInstance();
          tlength = (1.-g4calc->powA( 1.-par1*par3*geomStepLength,1./par3))/par1;
        } else {
          tlength = currentRange;
        }
      }
      if (tlength<geomStepLength || tlength>fTheTrueStepLenght) {
        tlength = geomStepLength;
      }
    }
    fTheTrueStepLenght = tlength;
  }
  //
  return fTheTrueStepLenght;
}
 
G4ThreeVector&
G4GoudsmitSaundersonMscModel::SampleScattering(const G4ThreeVector& oldDirection, G4double) {
  if (steppingAlgorithm==fUseDistanceToBoundary && fIsEverythingWasDone && fIsSingleScattering) {
    // single scattering was and scattering happend
    fTheNewDirection.rotateUz(oldDirection);
    fParticleChange->ProposeMomentumDirection(fTheNewDirection);
    return fTheDisplacementVector;
  } else if (steppingAlgorithm==fUseSafetyPlus) {  // error-free stepping
    if (fIsEndedUpOnBoundary) { // do nothing on the boundary
      return fTheDisplacementVector;
    } else if (fIsEverythingWasDone) { // evrything is done if not optimizations case !!!
      // check single scattering and see if it happened
      if (fIsSingleScattering) {
        fTheNewDirection.rotateUz(oldDirection);
        fParticleChange->ProposeMomentumDirection(fTheNewDirection);
        return fTheDisplacementVector;
      }
      // check if multiple scattering happened and do things only if scattering was really happening
      if (fIsMultipleSacettring && !fIsNoScatteringInMSC) {
           fTheNewDirection.rotateUz(oldDirection);
           fTheDisplacementVector.rotateUz(oldDirection);
           fParticleChange->ProposeMomentumDirection(fTheNewDirection);
      }
      // The only thing that could happen if we are here (fUseSafety and fIsEverythingWasDone)
      // is that  single scattering was tried but did not win so scattering did not happen.
      // So no displacement and no scattering
      return fTheDisplacementVector;
    }
    //
    // The only thing that could still happen with fUseSafetyPlus is that we are in the
    // optimization branch: so sample MSC angle here (no displacement)
  }
  //else MSC needs to be done here
  SampleMSC();
  if (!fIsNoScatteringInMSC) {
    fTheNewDirection.rotateUz(oldDirection);
    fParticleChange->ProposeMomentumDirection(fTheNewDirection);
    if (!fIsNoDisplace) {
      fTheDisplacementVector.rotateUz(oldDirection);
    }
  }
  //
  return fTheDisplacementVector;
}
 
 
void G4GoudsmitSaundersonMscModel::SampleMSC() {
  fIsNoScatteringInMSC = false;
  // kinetic energy is assumed to be in Geant4 internal energy unit which is MeV
  G4double kineticEnergy = currentKinEnergy;
  //
  // Energy loss correction: 2 version
  G4double eloss  = 0.0;
//  if (fTheTrueStepLenght > currentRange*dtrl) {
  eloss = kineticEnergy - GetEnergy(particle,currentRange-fTheTrueStepLenght,currentCouple);
//  } else {
//    eloss = fTheTrueStepLenght*GetDEDX(particle,kineticEnergy,currentCouple);
//  }
 
  G4double tau  = 0.;//    = kineticEnergy/electron_mass_c2; // where kinEnergy is the mean kinetic energy
  G4double tau2 = 0.;//   = tau*tau;
  G4double eps0 = 0.;//   = eloss/kineticEnergy0; // energy loss fraction to the begin step energy
  G4double epsm = 0.;//   = eloss/kineticEnergy;  // energy loss fraction to the mean step energy
 
  // - init.
  G4double efEnergy = kineticEnergy;
  G4double efStep   = fTheTrueStepLenght;
 
  G4double kineticEnergy0 = kineticEnergy;
  if (gIsUseAccurate) {    // - use accurate energy loss correction
    kineticEnergy  -= 0.5*eloss;  // mean energy along the full step
    // other parameters for energy loss corrections
    tau             = kineticEnergy/electron_mass_c2; // where kinEnergy is the mean kinetic energy
    tau2            = tau*tau;
    eps0            = eloss/kineticEnergy0; // energy loss fraction to the begin step energy
    epsm            = eloss/kineticEnergy;  // energy loss fraction to the mean step energy
 
    efEnergy        = kineticEnergy * (1.-epsm*epsm*(6.+10.*tau+5.*tau2)/(24.*tau2+48.*tau+72.));
    G4double dum    = 0.166666*(4.+tau*(6.+tau*(7.+tau*(4.+tau))))*(epsm/((tau+1.)*(tau+2.)))*(epsm/((tau+1.)*(tau+2.)));
    efStep          = fTheTrueStepLenght*(1.-dum);
  } else {                              // - take only mean energy
    kineticEnergy  -= 0.5*eloss;  // mean energy along the full step
    efEnergy        = kineticEnergy;
    G4double factor = 1./(1.+0.9784671*kineticEnergy); //0.9784671 = 1/(2*m_e)
    eps0            = eloss/kineticEnergy0;
    epsm            = eps0/(1.-0.5*eps0);
    G4double temp   = 0.3*(1 -factor*(1.-0.333333*factor))*eps0*eps0;
    efStep          = fTheTrueStepLenght*(1.+temp);
  }
  //
  // compute elastic mfp, first transport mfp, screening parameter, and G1 (with Mott-correction
  // if it was requested by the user)
  fLambda1 = GetTransportMeanFreePath(particle, efEnergy);
  // s/lambda_el
  G4double lambdan=0.;
  if (fLambda0>0.0) {
    lambdan=efStep/fLambda0;
  }
  if (lambdan<=1.0e-12) {
      if (fIsEverythingWasDone) {
        fTheZPathLenght = fTheTrueStepLenght;
      }
    fIsNoScatteringInMSC = true;
    return;
  }
  // first moment: 2.* lambdan *scrA*((1.+scrA)*log(1.+1./scrA)-1.);
  G4double Qn1 = lambdan *fG1;
  // sample scattering angles
  // new direction, relative to the orriginal one is in {uss,vss,wss}
  G4double cosTheta1 = 1.0, sinTheta1 = 0.0, cosTheta2 = 1.0, sinTheta2 = 0.0;
  G4double cosPhi1   = 1.0, sinPhi1   = 0.0, cosPhi2   = 1.0, sinPhi2   = 0.0;
  G4double uss       = 0.0, vss       = 0.0, wss       = 1.0;
  G4double x_coord   = 0.0, y_coord   = 0.0, z_coord   = 1.0;
  G4double u2 = 0.0, v2 = 0.0;
  // if we are above the upper grid limit with lambdaxG1=true-length/first-trans-mfp
  // => izotropic distribution: lambG1_max =7.992 but set it to 7
  if (0.5*Qn1 > 7.0){
    cosTheta1 = 1.-2.*G4UniformRand();
    sinTheta1 = std::sqrt((1.-cosTheta1)*(1.+cosTheta1));
    cosTheta2 = 1.-2.*G4UniformRand();
    sinTheta2 = std::sqrt((1.-cosTheta2)*(1.+cosTheta2));
  } else {
     // sample 2 scattering cost1, sint1, cost2 and sint2 for half path
     G4double lekin  = G4Log(efEnergy);
     G4double pt2    = efEnergy*(efEnergy+2.0*CLHEP::electron_mass_c2);
     G4double beta2  = pt2/(pt2+CLHEP::electron_mass_c2*CLHEP::electron_mass_c2);
     // backup GS angular dtr pointer (kinetic energy and delta index in case of Mott-correction)
     // if the first was an msc sampling (the same will be used if the second is also an msc step)
     G4GoudsmitSaundersonTable::GSMSCAngularDtr *gsDtr = nullptr;
     G4int mcEkinIdx    = -1;
     G4int mcDeltIdx    = -1;
     G4double transfPar = 0.;
     G4bool isMsc = fGSTable->Sampling(0.5*lambdan, 0.5*Qn1, fScrA, cosTheta1, sinTheta1, lekin, beta2,
                                       currentMaterialIndex, &gsDtr, mcEkinIdx, mcDeltIdx, transfPar,
                                       true);
     fGSTable->Sampling(0.5*lambdan, 0.5*Qn1, fScrA, cosTheta2, sinTheta2, lekin, beta2,
                        currentMaterialIndex, &gsDtr, mcEkinIdx, mcDeltIdx, transfPar, !isMsc);
     if (cosTheta1+cosTheta2==2.) { // no scattering happened
        if (fIsEverythingWasDone)
           fTheZPathLenght = fTheTrueStepLenght;
        fIsNoScatteringInMSC = true;
        return;
     }
  }
  // sample 2 azimuthal angles
  G4double phi1 = CLHEP::twopi*G4UniformRand();
  sinPhi1 = std::sin(phi1);
  cosPhi1 = std::cos(phi1);
  G4double phi2 = CLHEP::twopi*G4UniformRand();
  sinPhi2 = std::sin(phi2);
  cosPhi2 = std::cos(phi2);
 
  // compute final direction realtive to z-dir
  u2  = sinTheta2*cosPhi2;
  v2  = sinTheta2*sinPhi2;
  G4double u2p = cosTheta1*u2 + sinTheta1*cosTheta2;
  uss  = u2p*cosPhi1 - v2*sinPhi1;
  vss  = u2p*sinPhi1 + v2*cosPhi1;
  wss  = cosTheta1*cosTheta2 - sinTheta1*u2;
 
  // set new direction (is scattering frame)
  fTheNewDirection.set(uss,vss,wss);
 
  // set the fTheZPathLenght if we don't sample displacement and
  // we should do everything at the step-limit-phase before we return
  if(fIsNoDisplace && fIsEverythingWasDone)
    fTheZPathLenght = fTheTrueStepLenght;
 
  // in optimized-mode if the current-safety > current-range we do not use dispalcement
  if(fIsNoDisplace)
    return;
 
  //////////////////////////////////////////////////////////////////////
  // Compute final position
  Qn1 *=  fMCtoQ1;
  if (gIsUseAccurate) {
     // correction parameter
     G4double par =1.;
     if(Qn1<0.7) par = 1.;
     else if (Qn1<7.0) par = -0.031376*Qn1+1.01356;
     else par = 0.79;
 
     // Moments with energy loss correction
     // --first the uncorrected (for energy loss) values of gamma, eta, a1=a2=0.5*(1-eta), delta
     // gamma = G_2/G_1 based on G2 computed from A by using the Wentzel DCS form of G2
     G4double loga   = G4Log(1.0+1.0/fScrA);
     G4double gamma  = 6.0*fScrA*(1.0 + fScrA)*(loga*(1.0 + 2.0*fScrA) - 2.0)/fG1;
     gamma *= fMCtoG2PerG1;
     // sample eta from p(eta)=2*eta i.e. P(eta) = eta_square ;-> P(eta) = rand --> eta = sqrt(rand)
     G4double eta    = std::sqrt(G4UniformRand());
     G4double eta1   = 0.5*(1 - eta);  // used  more than once
     // 0.5 +sqrt(6)/6 = 0.9082483;
     // 1/(4*sqrt(6))  = 0.1020621;
     // (4-sqrt(6)/(24*sqrt(6))) = 0.026374715
     // delta = 0.9082483-(0.1020621-0.0263747*gamma)*Qn1 without energy loss cor.
     G4double delta  = 0.9082483-(0.1020621-0.0263747*gamma)*Qn1;
 
     // compute alpha1 and alpha2 for energy loss correction
     G4double temp1 = 2.0 + tau;
     G4double temp  = (2.0+tau*temp1)/((tau+1.0)*temp1);
     //Take logarithmic dependence
     temp = temp - (tau+1.0)/((tau+2.0)*(loga*(1.0+fScrA)-1.0));
     temp = temp * epsm;
     temp1 = 1.0 - temp;
     delta = delta + 0.40824829*(eps0*(tau+1.0)/((tau+2.0)*
             (loga*(1.0+fScrA)-1.0)*(loga*(1.0+2.0*fScrA)-2.0)) - 0.25*temp*temp);
     G4double b      = eta*delta;
     G4double c      = eta*(1.0-delta);
 
     //Calculate transport direction cosines:
     // ut,vt,wt is the final position divided by the true step length
     G4double w1v2 = cosTheta1*v2;
     G4double ut   = b*sinTheta1*cosPhi1 + c*(cosPhi1*u2 - sinPhi1*w1v2) + eta1*uss*temp1;
     G4double vt   = b*sinTheta1*sinPhi1 + c*(sinPhi1*u2 + cosPhi1*w1v2) + eta1*vss*temp1;
     G4double wt   = eta1*(1+temp) +       b*cosTheta1 +  c*cosTheta2    + eta1*wss*temp1;
 
     // long step correction
     ut *=par;
     vt *=par;
     wt *=par;
 
     // final position relative to the pre-step point in the scattering frame
     // ut = x_f/s so needs to multiply by s
     x_coord = ut*fTheTrueStepLenght;
     y_coord = vt*fTheTrueStepLenght;
     z_coord = wt*fTheTrueStepLenght;
 
     if(fIsEverythingWasDone){
       // We sample in the step limit so set fTheZPathLenght = transportDistance
       // and lateral displacement (x_coord,y_coord,z_coord-transportDistance)
       //Calculate transport distance
       G4double transportDistance  = std::sqrt(x_coord*x_coord+y_coord*y_coord+z_coord*z_coord);
       // protection
       if(transportDistance>fTheTrueStepLenght)
          transportDistance = fTheTrueStepLenght;
       fTheZPathLenght = transportDistance;
     }
     // else:: we sample in the DoIt so
     //       the fTheZPathLenght was already set and was taken as transport along zet
     fTheDisplacementVector.set(x_coord,y_coord,z_coord-fTheZPathLenght);
  } else {
     // compute zz = <z>/tPathLength
     // s -> true-path-length
     // z -> geom-path-length:: when PRESTA is used z =(def.) <z>
     // r -> lateral displacement = s/2 sin(theta)  => x_f = r cos(phi); y_f = r sin(phi)
     G4double zz = 0.0;
     if(fIsEverythingWasDone){
        // We sample in the step limit so set fTheZPathLenght = transportDistance
        // and lateral displacement (x_coord,y_coord,z_coord-transportDistance)
        if(Qn1<0.1) { // use 3-order Taylor approximation of (1-exp(-x))/x around x=0
          zz = 1.0 - Qn1*(0.5 - Qn1*(0.166666667 - 0.041666667*Qn1)); // 1/6 =0.166..7 ; 1/24=0.041..
        } else {
          zz = (1.-G4Exp(-Qn1))/Qn1;
        }
     } else {
        // we sample in the DoIt so
        // the fTheZPathLenght was already set and was taken as transport along zet
        zz = fTheZPathLenght/fTheTrueStepLenght;
     }
 
     G4double rr = (1.-zz*zz)/(1.-wss*wss); // s^2 >= <z>^2+r^2  :: where r^2 = s^2/4 sin^2(theta)
     if(rr >= 0.25) rr = 0.25;            // (1-<z>^2/s^2)/sin^2(theta) >= r^2/(s^2 sin^2(theta)) = 1/4 must hold
     G4double rperp = fTheTrueStepLenght*std::sqrt(rr);  // this is r/sint
     x_coord  = rperp*uss;
     y_coord  = rperp*vss;
     z_coord  = zz*fTheTrueStepLenght;
 
     if(fIsEverythingWasDone){
       G4double transportDistance = std::sqrt(x_coord*x_coord + y_coord*y_coord + z_coord*z_coord);
       fTheZPathLenght = transportDistance;
     }
 
     fTheDisplacementVector.set(x_coord,y_coord,z_coord- fTheZPathLenght);
   }
}