G4ecpssrBaseKxsModel Class Reference

#include <G4ecpssrBaseKxsModel.hh>

Inheritance diagram for G4ecpssrBaseKxsModel:

Public Member Functions
	G4ecpssrBaseKxsModel ()
	~G4ecpssrBaseKxsModel ()
G4double	CalculateCrossSection (G4int, G4double, G4double)
G4double	ExpIntFunction (G4int n, G4double x)
Public Member Functions inherited from G4VecpssrKModel
	G4VecpssrKModel ()
virtual	~G4VecpssrKModel ()

Detailed Description

Definition at line 38 of file G4ecpssrBaseKxsModel.hh.

Constructor & Destructor Documentation

G4ecpssrBaseKxsModel::G4ecpssrBaseKxsModel

(

)

Definition at line 45 of file G4ecpssrBaseKxsModel.cc.

References FatalException, G4Exception(), G4CrossSectionDataSet::LoadData(), and test::x.

{ 
    verboseLevel=0;
    
    // Storing C coefficients for high velocity formula

    G4String fileC1("pixe/uf/c1");
    tableC1 = new G4CrossSectionDataSet(new G4SemiLogInterpolation, 1.,1.);

    G4String fileC2("pixe/uf/c2");
    tableC2 = new G4CrossSectionDataSet(new G4SemiLogInterpolation, 1.,1.);

    G4String fileC3("pixe/uf/c3");
    tableC3 = new G4CrossSectionDataSet(new G4SemiLogInterpolation, 1.,1.);

    // Storing FK data needed for medium velocities region
    char *path = 0;

    path = getenv("G4LEDATA");
 
    if (!path) {
      G4Exception("G4ecpssrBaseKxsModel::G4ecpssrBaseKxsModel()", "em0006", FatalException,"G4LEDATA environment variable not set" );
      return;
    }

    std::ostringstream fileName;
    fileName << path << "/pixe/uf/FK.dat";
    std::ifstream FK(fileName.str().c_str());

    if (!FK) 
      G4Exception("G4ecpssrBaseKxsModel::G4ecpssrBaseKxsModel()", "em0003", FatalException,"error opening FK data file" );

    dummyVec.push_back(0.);

    while(!FK.eof())
    {
    double x;
    double y;
    
    FK>>x>>y;

    //  Mandatory vector initialization
        if (x != dummyVec.back()) 
        { 
          dummyVec.push_back(x); 
          aVecMap[x].push_back(-1.);
        }
      
        FK>>FKData[x][y];

        if (y != aVecMap[x].back()) aVecMap[x].push_back(y);
          
    }

    tableC1->LoadData(fileC1);
    tableC2->LoadData(fileC2);
    tableC3->LoadData(fileC3);

}

G4ecpssrBaseKxsModel::~G4ecpssrBaseKxsModel

(

)

Definition at line 113 of file G4ecpssrBaseKxsModel.cc.

{ 

  delete tableC1;
  delete tableC2;
  delete tableC3;

}

Member Function Documentation

G4double G4ecpssrBaseKxsModel::CalculateCrossSection ( G4int  zTarget, G4double  massIncident, G4double  energyIncident  )

virtual

Implements G4VecpssrKModel.

Definition at line 196 of file G4ecpssrBaseKxsModel.cc.

References G4Alpha::Alpha(), python.hepunit::amu_c2, python.hepunit::barn, G4AtomicShell::BindingEnergy(), python.hepunit::Bohr_radius, C1, C3, python.hepunit::electron_mass_c2, python.hepunit::eplus, python.hepunit::eV, ExpIntFunction(), G4CrossSectionDataSet::FindValue(), python.hepunit::fine_structure_const, G4cout, G4endl, G4NistManager::GetAtomicMassAmu(), G4ParticleDefinition::GetPDGCharge(), G4ParticleDefinition::GetPDGMass(), GT, G4AtomicTransitionManager::Instance(), G4NistManager::Instance(), python.hepunit::pi, G4Proton::Proton(), G4AtomicTransitionManager::Shell(), and test::x.

{

  // this K-CrossSection calculation method is done according to W.Brandt and G.Lapicki, Phys.Rev.A23(1981)//                                   
  
  G4NistManager* massManager = G4NistManager::Instance();   

  G4AtomicTransitionManager*  transitionManager =  G4AtomicTransitionManager::Instance();

  G4double  zIncident = 0; 
  G4Proton* aProtone = G4Proton::Proton();
  G4Alpha* aAlpha = G4Alpha::Alpha();

  if (massIncident == aProtone->GetPDGMass() )
  {
   zIncident = (aProtone->GetPDGCharge())/eplus; 
  }
  else
    {
      if (massIncident == aAlpha->GetPDGMass())
    {
      zIncident  = (aAlpha->GetPDGCharge())/eplus; 
    }
      else
    { 
      G4cout << "*** WARNING in G4ecpssrBaseKxsModel::CalculateCrossSection : we can treat only Proton or Alpha incident particles " << G4endl;
      return 0;
    }
  }
  
    if (verboseLevel>0) G4cout << "  massIncident=" << massIncident<< G4endl;

  G4double kBindingEnergy = transitionManager->Shell(zTarget,0)->BindingEnergy();

    if (verboseLevel>0) G4cout << "  kBindingEnergy=" << kBindingEnergy/eV<< G4endl;

  G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
    
    if (verboseLevel>0) G4cout << "  massTarget=" <<  massTarget<< G4endl;
 
  G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2; //the mass of the system (projectile, target) 
  
    if (verboseLevel>0) G4cout << "  systemMass=" <<  systemMass<< G4endl;

  const G4double zkshell= 0.3;
  // *** see Brandt, Phys Rev A23, p 1727

  G4double screenedzTarget = zTarget-zkshell; // screenedzTarget is the screened nuclear charge of the target
  // *** see Brandt, Phys Rev A23, p 1727

  const G4double rydbergMeV= 13.6056923e-6;
 
  G4double tetaK = kBindingEnergy/((screenedzTarget*screenedzTarget)*rydbergMeV);  //tetaK denotes the reduced binding energy of the electron
  // *** see Rice, ADANDT 20, p 504, f 2 
  
    if (verboseLevel>0) G4cout << "  tetaK=" <<  tetaK<< G4endl;

  G4double velocity =(2./(tetaK*screenedzTarget))*std::pow(((energyIncident*electron_mass_c2)/(massIncident*rydbergMeV)),0.5);
  // *** also called xiK
  // *** see Brandt, Phys Rev A23, p 1727
  // *** see Basbas, Phys Rev A17, p 1656, f4
    
    if (verboseLevel>0) G4cout << "  velocity=" << velocity<< G4endl;

  const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ;        
  
    if (verboseLevel>0) G4cout << "  bohrPow2Barn=" <<  bohrPow2Barn<< G4endl;

  G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);     //sigma0 is the initial cross section of K shell at stable state
  // *** see Benka, ADANDT 22, p 220, f2, for protons
  // *** see Basbas, Phys Rev A7, p 1000
   
    if (verboseLevel>0) G4cout << "  sigma0=" <<  sigma0<< G4endl;

  const G4double kAnalyticalApproximation= 1.5; 
  G4double x = kAnalyticalApproximation/velocity;
  // *** see Brandt, Phys Rev A23, p 1727
  // *** see Brandt, Phys Rev A20, p 469, f16 in expression of h
  
    if (verboseLevel>0) G4cout << "  x=" << x<< G4endl;

  G4double electrIonizationEnergy;                                         
  // *** see Basbas, Phys Rev A17, p1665, f27
  // *** see Brandt, Phys Rev A20, p469
  // *** see Liu, Comp Phys Comm 97, p325, f A5
                                        
  if ((0.< x) && (x <= 0.035))
    {
      electrIonizationEnergy= 0.75*pi*(std::log(1./(x*x))-1.);
    }
  else
    {
      if ( (0.035 < x) && (x <=3.))
    {
      electrIonizationEnergy =std::exp(-2.*x)/(0.031+(0.213*std::pow(x,0.5))+(0.005*x)-(0.069*std::pow(x,3./2.))+(0.324*x*x));
    }

      else
    {
      if ( (3.< x) && (x<=11.))
       {
         electrIonizationEnergy =2.*std::exp(-2.*x)/std::pow(x,1.6);
       }

      else electrIonizationEnergy =0.;
    }
    }

    if (verboseLevel>0) G4cout << "  electrIonizationEnergy=" << electrIonizationEnergy<< G4endl;

  G4double hFunction =(electrIonizationEnergy*2.)/(tetaK*std::pow(velocity,3)); //hFunction represents the correction for polarization effet
  // *** see Brandt, Phys Rev A20, p 469, f16
  
    if (verboseLevel>0) G4cout << "  hFunction=" << hFunction<< G4endl;
    
  G4double gFunction = (1.+(9.*velocity)+(31.*velocity*velocity)+(98.*std::pow(velocity,3.))+(12.*std::pow(velocity,4.))+(25.*std::pow(velocity,5.))
            +(4.2*std::pow(velocity,6.))+(0.515*std::pow(velocity,7.)))/std::pow(1.+velocity,9.); //gFunction represents the correction for binding effet
  // *** see Brandt, Phys Rev A20, p 469, f19
  
    if (verboseLevel>0) G4cout << "  gFunction=" << gFunction<< G4endl;
 
  //-----------------------------------------------------------------------------------------------------------------------------

  G4double sigmaPSS = 1.+(((2.*zIncident)/(screenedzTarget*tetaK))*(gFunction-hFunction)); //describes the perturbed stationnairy state of the affected atomic electon
  // *** also called dzeta
  // *** also called epsilon
  // *** see Basbas, Phys Rev A17, p1667, f45
      
    if (verboseLevel>0) G4cout << "  sigmaPSS=" << sigmaPSS<< G4endl;
    
    if (verboseLevel>0) G4cout << "  sigmaPSS*tetaK=" << sigmaPSS*tetaK<< G4endl;

  //----------------------------------------------------------------------------------------------------------------------------
  
  const G4double cNaturalUnit= 1/fine_structure_const;  // it's the speed of light according to Atomic-Unit-System
   
    if (verboseLevel>0) G4cout << "  cNaturalUnit=" << cNaturalUnit<< G4endl;
  
  G4double ykFormula=0.4*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocity/sigmaPSS);
  // *** also called yS
  // *** see Brandt, Phys Rev A20, p467, f6
  // *** see Brandt, Phys Rev A23, p1728
      
    if (verboseLevel>0) G4cout << "  ykFormula=" << ykFormula<< G4endl;
 
  G4double relativityCorrection = std::pow((1.+(1.1*ykFormula*ykFormula)),0.5)+ykFormula;// the relativistic correction parameter
  // *** also called mRS
  // *** see Brandt, Phys Rev A20, p467, f6
    
    if (verboseLevel>0) G4cout << "  relativityCorrection=" << relativityCorrection<< G4endl;

  G4double reducedVelocity = velocity*std::pow(relativityCorrection,0.5);  // presents the reduced collision velocity parameter 
  // *** also called xiR
  // *** see Brandt, Phys Rev A20, p468, f7
  // *** see Brandt, Phys Rev A23, p1728
      
    if (verboseLevel>0) G4cout << "  reducedVelocity=" << reducedVelocity<< G4endl;

  G4double etaOverTheta2 = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget)
                           /(sigmaPSS*tetaK)/(sigmaPSS*tetaK);
  // *** see Benka, ADANDT 22, p220, f4 for eta
  // then we use sigmaPSS*tetaK == epsilon*tetaK
    
    if (verboseLevel>0) G4cout << "  etaOverTheta2=" << etaOverTheta2<< G4endl;

  G4double universalFunction = 0;
  
  // low velocity formula
  // *****************  
   if ( velocity < 1. )
  // OR
  //if ( reducedVelocity/sigmaPSS < 1.)
  // *** see Brandt, Phys Rev A23, p1727
  // *** reducedVelocity/sigmaPSS is also called xiR/dzeta
  // *****************
    {
      if (verboseLevel>0) G4cout << "  Notice : FK is computed from low velocity formula" << G4endl;
      
      universalFunction = (std::pow(2.,9.)/45.)*std::pow(reducedVelocity/sigmaPSS,8.)*std::pow((1.+(1.72*(reducedVelocity/sigmaPSS)*(reducedVelocity/sigmaPSS))),-4.);// is the reduced universal cross section
      // *** see Brandt, Phys Rev A23, p1728
      
      if (verboseLevel>0) G4cout << "  universalFunction by Brandt 1981 =" << universalFunction<< G4endl;

    }

  else
    
  {
    
    if ( etaOverTheta2 > 86.6 && (sigmaPSS*tetaK) > 0.4 && (sigmaPSS*tetaK) < 2.9996 )
    {
      // High and medium energies. Method from Rice ADANDT 20, p506, 1977 on tables from Benka 1978
      
      if (verboseLevel>0) G4cout << "  Notice : FK is computed from high velocity formula" << G4endl;

      if (verboseLevel>0) G4cout << "  sigmaPSS*tetaK=" << sigmaPSS*tetaK << G4endl;
    
      G4double C1= tableC1->FindValue(sigmaPSS*tetaK);
      G4double C2= tableC2->FindValue(sigmaPSS*tetaK);
      G4double C3= tableC3->FindValue(sigmaPSS*tetaK);
      
        if (verboseLevel>0) G4cout << "  C1=" << C1 << G4endl;
        if (verboseLevel>0) G4cout << "  C2=" << C2 << G4endl;
        if (verboseLevel>0) G4cout << "  C3=" << C3 << G4endl;
   
      G4double etaK = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
      // *** see Benka, ADANDT 22, p220, f4 for eta
      
        if (verboseLevel>0) G4cout << "  etaK=" << etaK << G4endl;

      G4double etaT = (sigmaPSS*tetaK)*(sigmaPSS*tetaK)*(86.6); // at any theta, the largest tabulated etaOverTheta2 is 86.6
      // *** see Rice, ADANDT 20, p506
      
        if (verboseLevel>0) G4cout << "  etaT=" << etaT << G4endl;
    
      G4double fKT = FunctionFK((sigmaPSS*tetaK),86.6)*(etaT/(sigmaPSS*tetaK));
      // *** see Rice, ADANDT 20, p506

      if (FunctionFK((sigmaPSS*tetaK),86.6)<=0.) 
    {
        G4cout << 
        "*** WARNING in G4ecpssrBaseKxsModel::CalculateCrossSection : unable to interpolate FK function in high velocity region ! ***" << G4endl;
    return 0;
    }

        if (verboseLevel>0) G4cout << "  FunctionFK=" << FunctionFK((sigmaPSS*tetaK),86.6) << G4endl;
      
        if (verboseLevel>0) G4cout << "  fKT=" << fKT << G4endl;
    
      G4double GK = C2/(4*etaK) + C3/(32*etaK*etaK);
        
    if (verboseLevel>0) G4cout << "  GK=" << GK << G4endl;
      
      G4double GT = C2/(4*etaT) + C3/(32*etaT*etaT);
      
        if (verboseLevel>0) G4cout << "  GT=" << GT << G4endl;
    
      G4double DT = fKT - C1*std::log(etaT) + GT;
      
        if (verboseLevel>0) G4cout << "  DT=" << DT << G4endl;

      G4double fKK = C1*std::log(etaK) + DT - GK;
      
        if (verboseLevel>0) G4cout << "  fKK=" << fKK << G4endl;
    
      G4double universalFunction3= fKK/(etaK/tetaK);
      // *** see Rice, ADANDT 20, p505, f7
      
        if (verboseLevel>0) G4cout << "  universalFunction3=" << universalFunction3 << G4endl;

      universalFunction=universalFunction3;
    
    }
    
    else if ( etaOverTheta2 >= 1.e-3 && etaOverTheta2 <= 86.6 && (sigmaPSS*tetaK) >= 0.4 && (sigmaPSS*tetaK) <= 2.9996 )

    {
      // From Benka 1978
      
      if (verboseLevel>0) G4cout << "  Notice : FK is computed from INTERPOLATED data" << G4endl;
     
      G4double universalFunction2 = FunctionFK((sigmaPSS*tetaK),etaOverTheta2);

      if (universalFunction2<=0) 
      {
        G4cout << 
        "*** WARNING : G4ecpssrBaseKxsModel::CalculateCrossSection is unable to interpolate FK function in medium velocity region ! ***" << G4endl;
    return 0;
      }
      
      if (verboseLevel>0) G4cout << "  universalFunction2=" << universalFunction2 << " for theta=" << sigmaPSS*tetaK << " and etaOverTheta2=" << etaOverTheta2 << G4endl;
      
      universalFunction=universalFunction2;
    }
        
  }
  
  //----------------------------------------------------------------------------------------------------------------------

  G4double sigmaPSSR = (sigma0/(sigmaPSS*tetaK))*universalFunction; //sigmaPSSR is the straight-line K-shell ionization cross section
  // *** see Benka, ADANDT 22, p220, f1
  
    if (verboseLevel>0) G4cout << "  sigmaPSSR=" << sigmaPSSR<< G4endl;
  
  //-----------------------------------------------------------------------------------------------------------------------

  G4double pssDeltaK = (4./(systemMass*sigmaPSS*tetaK))*(sigmaPSS/velocity)*(sigmaPSS/velocity);
  // *** also called dzetaK*deltaK
  // *** see Brandt, Phys Rev A23, p1727, f B2
    
    if (verboseLevel>0) G4cout << "  pssDeltaK=" << pssDeltaK<< G4endl;

  if (pssDeltaK>1) return 0.;

  G4double energyLoss = std::pow(1-pssDeltaK,0.5); //energyLoss incorporates the straight-line energy-loss 
  // *** also called zK
  // *** see Brandt, Phys Rev A23, p1727, after f B2
    
    if (verboseLevel>0) G4cout << "  energyLoss=" << energyLoss<< G4endl;

  G4double energyLossFunction = (std::pow(2.,-9)/8.)*((((9.*energyLoss)-1.)*std::pow(1.+energyLoss,9.))+(((9.*energyLoss)+1.)*std::pow(1.-energyLoss,9.)));//energy loss function 
  // *** also called fs
  // *** see Brandt, Phys Rev A23, p1718, f7
    
    if (verboseLevel>0) G4cout << "  energyLossFunction=" <<  energyLossFunction<< G4endl;

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

  G4double coulombDeflection = (4.*pi*zIncident/systemMass)*std::pow(tetaK*sigmaPSS,-2.)*std::pow(velocity/sigmaPSS,-3.)*(zTarget/screenedzTarget); //incorporates Coulomb deflection parameter 
  // *** see Brandt, Phys Rev A23, p1727, f B3
 
    if (verboseLevel>0) G4cout << "  cParameter-short=" << coulombDeflection<< G4endl;

  G4double cParameter = 2.*coulombDeflection/(energyLoss*(energyLoss+1.));
  // *** see Brandt, Phys Rev A23, p1727, f B4
  
    if (verboseLevel>0) G4cout << "  cParameter-full=" << cParameter<< G4endl;

  G4double coulombDeflectionFunction = 9.*ExpIntFunction(10,cParameter);                         //this function describes Coulomb-deflection effect
  // *** see Brandt, Phys Rev A23, p1727
  
    if (verboseLevel>0) G4cout << "  ExpIntFunction(10,cParameter) =" << ExpIntFunction(10,cParameter) << G4endl;
    
    if (verboseLevel>0) G4cout << "  coulombDeflectionFunction =" << coulombDeflectionFunction << G4endl;

  //--------------------------------------------------------------------------------------------------------------------------------------------------
 
  G4double crossSection =  0;
  
  crossSection = energyLossFunction* coulombDeflectionFunction*sigmaPSSR;  //this ECPSSR cross section is estimated at perturbed-stationnairy-state(PSS)
                                                                           //and it's reduced by the energy-loss(E),the Coulomb deflection(C),
                                                                           //and the relativity(R) effects

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

  if (crossSection >= 0) {
    return crossSection * barn;
  }
  else {return 0;}

}

G4double G4ecpssrBaseKxsModel::ExpIntFunction	(	G4int	n,
		G4double	x
	)

Definition at line 124 of file G4ecpssrBaseKxsModel.cc.

References test::a, test::b, test::c, G4cout, G4endl, n, and test::x.

Referenced by CalculateCrossSection().

{
// this "ExpIntFunction" function allows fast evaluation of the n order exponential integral function En(x)

  G4int i;
  G4int ii;
  G4int nm1;
  G4double a;
  G4double b;
  G4double c;
  G4double d;
  G4double del;
  G4double fact;
  G4double h;
  G4double psi;
  G4double ans = 0;
  const G4double euler= 0.5772156649;
  const G4int maxit= 100;
  const G4double fpmin = 1.0e-30;
  const G4double eps = 1.0e-7;
  nm1=n-1;
  if (n<0 || x<0.0 || (x==0.0 && (n==0 || n==1))) {
    G4cout << "*** WARNING in G4ecpssrBaseKxsModel::ExpIntFunction: bad arguments in ExpIntFunction" << G4endl;
    G4cout << n << ", " << x << G4endl;
  }
  else {
       if (n==0) ans=std::exp(-x)/x;
        else {
           if (x==0.0) ans=1.0/nm1;
              else {
                   if (x > 1.0) {
                            b=x+n;
                            c=1.0/fpmin;
                            d=1.0/b;
                h=d;
                for (i=1;i<=maxit;i++) {
                  a=-i*(nm1+i);
                  b +=2.0;
                  d=1.0/(a*d+b);
                  c=b+a/c;
                  del=c*d;
                  h *=del;
                      if (std::fabs(del-1.0) < eps) {
                    ans=h*std::exp(-x);
                    return ans;
                      }
                }
           } else {
             ans = (nm1!=0 ? 1.0/nm1 : -std::log(x)-euler);
             fact=1.0;
             for (i=1;i<=maxit;i++) {
               fact *=-x/i;
               if (i !=nm1) del = -fact/(i-nm1);
               else {
             psi = -euler;
             for (ii=1;ii<=nm1;ii++) psi +=1.0/ii;
             del=fact*(-std::log(x)+psi);
               }
               ans += del;
               if (std::fabs(del) < std::fabs(ans)*eps) return ans;
             }
           }
          }
    }
  }
return ans;
}

---

The documentation for this class was generated from the following files:

• G4ecpssrBaseKxsModel.hh
• G4ecpssrBaseKxsModel.cc