G4ecpssrBaseLixsModel Class Reference

#include <G4ecpssrBaseLixsModel.hh>

Inheritance diagram for G4ecpssrBaseLixsModel:

Public Member Functions
	G4ecpssrBaseLixsModel ()
	~G4ecpssrBaseLixsModel ()
G4double	CalculateL1CrossSection (G4int zTarget, G4double massIncident, G4double energyIncident)
G4double	CalculateL2CrossSection (G4int zTarget, G4double massIncident, G4double energyIncident)
G4double	CalculateL3CrossSection (G4int zTarget, G4double massIncident, G4double energyIncident)
G4double	CalculateVelocity (G4int subShell, G4int zTarget, G4double massIncident, G4double energyIncident)
G4double	ExpIntFunction (G4int n, G4double x)
Public Member Functions inherited from G4VecpssrLiModel
	G4VecpssrLiModel ()
virtual	~G4VecpssrLiModel ()
virtual G4double	CalculateL1CrossSection (G4int zTarget, G4double massIncident, G4double energyIncident)=0
virtual G4double	CalculateL2CrossSection (G4int zTarget, G4double massIncident, G4double energyIncident)=0
virtual G4double	CalculateL3CrossSection (G4int zTarget, G4double massIncident, G4double energyIncident)=0

Detailed Description

Definition at line 55 of file G4ecpssrBaseLixsModel.hh.

Constructor & Destructor Documentation

G4ecpssrBaseLixsModel()

G4ecpssrBaseLixsModel::G4ecpssrBaseLixsModel

(

)

Definition at line 43 of file G4ecpssrBaseLixsModel.cc.

{
  verboseLevel=0;
 
  // Storing FLi data needed for 0.2 to 3.0  velocities region
 
  char *path = std::getenv("G4LEDATA");
    
  if (!path) {
    G4Exception("G4ecpssrLCrossSection::G4ecpssrBaseLixsModel()","em0006", FatalException ,"G4LEDATA environment variable not set");
    return;
  }
  std::ostringstream fileName1;
  std::ostringstream fileName2;
 
  fileName1 << path << "/pixe/uf/FL1.dat";
  fileName2 << path << "/pixe/uf/FL2.dat";
 
  // Reading of FL1.dat
 
  std::ifstream FL1(fileName1.str().c_str());
  if (!FL1) G4Exception("G4ecpssrLCrossSection::G4ecpssrBaseLixsModel()","em0003",FatalException, "error opening FL1 data file");
 
  dummyVec1.push_back(0.);
 
  while(!FL1.eof())
    {
      double x1;
      double y1;
 
      FL1>>x1>>y1;
 
      //  Mandatory vector initialization
      if (x1 != dummyVec1.back())
        {
          dummyVec1.push_back(x1);
          aVecMap1[x1].push_back(-1.);
        }
 
      FL1>>FL1Data[x1][y1];
 
      if (y1 != aVecMap1[x1].back()) aVecMap1[x1].push_back(y1);
    }
 
  // Reading of FL2.dat
 
  std::ifstream FL2(fileName2.str().c_str());
  if (!FL2) G4Exception("G4ecpssrLCrossSection::G4ecpssrBaseLixsModel()","em0003", FatalException," error opening FL2 data file");
 
  dummyVec2.push_back(0.);
  
  while(!FL2.eof())
    {
      double x2;
      double y2;
 
      FL2>>x2>>y2;
 
      //  Mandatory vector initialization
      if (x2 != dummyVec2.back())
        {
          dummyVec2.push_back(x2);
          aVecMap2[x2].push_back(-1.);
        }
 
      FL2>>FL2Data[x2][y2];
 
      if (y2 != aVecMap2[x2].back()) aVecMap2[x2].push_back(y2);
    }
}

~G4ecpssrBaseLixsModel()

G4ecpssrBaseLixsModel::~G4ecpssrBaseLixsModel

(

)

Definition at line 116 of file G4ecpssrBaseLixsModel.cc.

{}

Member Function Documentation

CalculateL1CrossSection()

G4double G4ecpssrBaseLixsModel::CalculateL1CrossSection ( G4int  zTarget, G4double  massIncident, G4double  energyIncident  )

virtual

Implements G4VecpssrLiModel.

Definition at line 191 of file G4ecpssrBaseLixsModel.cc.

{
 
  if (zTarget <=4) return 0.;
 
  //this L1-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
  //and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
 
  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 G4ecpssrBaseLixsModel::CalculateL1CrossSection : Proton or Alpha incident particles only. " << G4endl;
      G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
      return 0;
    }
    }
 
  G4double l1BindingEnergy = transitionManager->Shell(zTarget,1)->BindingEnergy(); //Observed binding energy of L1-subshell
  G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
  G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2; //Mass of the system (projectile, target)
  static const G4double zlshell= 4.15;
  // *** see Benka, ADANDT 22, p 223
  G4double screenedzTarget = zTarget-zlshell; //Effective nuclear charge as seen by electrons in L1-sub shell
  static const G4double rydbergMeV= 13.6056923e-6;
 
  static const G4double nl= 2.;
  // *** see Benka, ADANDT 22, p 220, f3
  G4double tetal1 = (l1BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV); //Screening parameter
  // *** see Benka, ADANDT 22, p 220, f3
 
  if (verboseLevel>0) G4cout << "  tetal1=" <<  tetal1<< G4endl;
 
  G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
  // *** also called etaS
  // *** see Benka, ADANDT 22, p 220, f3
 
  static const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ; //Bohr radius of hydrogen
 
  G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
  // *** see Benka, ADANDT 22, p 220, f2, for protons
  // *** see Basbas, Phys Rev A7, p 1000
 
  G4double velocityl1 = CalculateVelocity(1, zTarget, massIncident, energyIncident); // Scaled velocity
 
  if (verboseLevel>0) G4cout << "  velocityl1=" << velocityl1<< G4endl;
 
  static const G4double l1AnalyticalApproximation= 1.5;
  G4double x1 =(nl*l1AnalyticalApproximation)/velocityl1;
  // *** 1.5 is cK = cL1 (it is 1.25 for L2 & L3)
  // *** see Brandt, Phys Rev A20, p 469, f16 in expression of h
 
  if (verboseLevel>0) G4cout << "  x1=" << x1<< G4endl;
 
  G4double electrIonizationEnergyl1=0.;
  // *** see Basbas, Phys Rev A17, p1665, f27
  // *** see Brandt, Phys Rev A20, p469
  // *** see Liu, Comp Phys Comm 97, p325, f A5
 
  if ( x1<=0.035)  electrIonizationEnergyl1= 0.75*pi*(std::log(1./(x1*x1))-1.);
  else
    {
      if ( x1<=3.)
        electrIonizationEnergyl1 =G4Exp(-2.*x1)/(0.031+(0.213*std::pow(x1,0.5))+(0.005*x1)-(0.069*std::pow(x1,3./2.))+(0.324*x1*x1));
      else
    {if ( x1<=11.) electrIonizationEnergyl1 =2.*G4Exp(-2.*x1)/std::pow(x1,1.6);}
    }
 
  G4double hFunctionl1 =(electrIonizationEnergyl1*2.*nl)/(tetal1*std::pow(velocityl1,3)); //takes into account the polarization effect
  // *** see Brandt, Phys Rev A20, p 469, f16
 
  if (verboseLevel>0) G4cout << "  hFunctionl1=" << hFunctionl1<< G4endl;
 
  G4double gFunctionl1 = (1.+(9.*velocityl1)+(31.*velocityl1*velocityl1)+(49.*std::pow(velocityl1,3.))+(162.*std::pow(velocityl1,4.))+(63.*std::pow(velocityl1,5.))+(18.*std::pow(velocityl1,6.))+(1.97*std::pow(velocityl1,7.)))/std::pow(1.+velocityl1,9.);//takes into account the reduced binding effect
  // *** see Brandt, Phys Rev A20, p 469, f19
 
  if (verboseLevel>0) G4cout << "  gFunctionl1=" << gFunctionl1<< G4endl;
 
  G4double sigmaPSS_l1 = 1.+(((2.*zIncident)/(screenedzTarget*tetal1))*(gFunctionl1-hFunctionl1)); //Binding-polarization factor
  // *** also called dzeta
  // *** also called epsilon
  // *** see Basbas, Phys Rev A17, p1667, f45
 
  if (verboseLevel>0) G4cout << "sigmaPSS_l1 =" << sigmaPSS_l1<< G4endl;
 
  const G4double cNaturalUnit= 137.;
 
  G4double yl1Formula=0.4*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(nl*velocityl1/sigmaPSS_l1);
  // *** also called yS
  // *** see Brandt, Phys Rev A20, p467, f6
  // *** see Brandt, Phys Rev A23, p1728
 
  G4double l1relativityCorrection = std::pow((1.+(1.1*yl1Formula*yl1Formula)),0.5)+yl1Formula; // Relativistic correction parameter
  // *** also called mRS
  // *** see Brandt, Phys Rev A20, p467, f6
 
  //G4double reducedVelocity_l1 = velocityl1*std::pow(l1relativityCorrection,0.5); //Reduced velocity parameter
 
  G4double L1etaOverTheta2;
 
  G4double  universalFunction_l1 = 0.;
 
  G4double sigmaPSSR_l1;
 
  // low velocity formula
  // *****************
  if ( velocityl1 <20.  )
  {
 
    L1etaOverTheta2 =(reducedEnergy* l1relativityCorrection)/((tetal1*sigmaPSS_l1)*(tetal1*sigmaPSS_l1));
    // *** 1) RELATIVISTIC CORRECTION ADDED
    // *** 2) sigma_PSS_l1 ADDED
    // *** reducedEnergy is etaS, l1relativityCorrection is mRS
    // *** see Phys Rev A20, p468, top
 
    if ( ((tetal1*sigmaPSS_l1) >=0.2) && ((tetal1*sigmaPSS_l1) <=2.6670) && (L1etaOverTheta2>=0.1e-3) && (L1etaOverTheta2<=0.866e2) )
      universalFunction_l1 = FunctionFL1((tetal1*sigmaPSS_l1),L1etaOverTheta2);
 
    if (verboseLevel>0) G4cout << "at low velocity range, universalFunction_l1  =" << universalFunction_l1 << G4endl;
 
    sigmaPSSR_l1 = (sigma0/(tetal1*sigmaPSS_l1))*universalFunction_l1;// Plane-wave Born -Aproximation L1-subshell ionisation Cross Section
  // *** see Benka, ADANDT 22, p220, f1
 
    if (verboseLevel>0) G4cout << "  at low velocity range, sigma PWBA L1 CS  = " << sigmaPSSR_l1<< G4endl;
  }
  else
  {
    L1etaOverTheta2 = reducedEnergy/(tetal1*tetal1);
    // Medium & high velocity
    // *** 1) NO RELATIVISTIC CORRECTION
    // *** 2) NO sigma_PSS_l1
    // *** see Benka, ADANDT 22, p223
 
    if ( (tetal1 >=0.2) && (tetal1 <=2.6670) && (L1etaOverTheta2>=0.1e-3) && (L1etaOverTheta2<=0.866e2) )
      universalFunction_l1 = FunctionFL1(tetal1,L1etaOverTheta2);
 
    if (verboseLevel>0) G4cout << "at medium and high velocity range, universalFunction_l1  =" << universalFunction_l1 << G4endl;
 
    sigmaPSSR_l1 = (sigma0/tetal1)*universalFunction_l1;// Plane-wave Born -Aproximation L1-subshell ionisation Cross Section
  // *** see Benka, ADANDT 22, p220, f1
 
    if (verboseLevel>0) G4cout << "  sigma PWBA L1 CS at medium and high velocity range = " << sigmaPSSR_l1<< G4endl;
  }
 
  G4double pssDeltal1 = (4./(systemMass *sigmaPSS_l1*tetal1))*(sigmaPSS_l1/velocityl1)*(sigmaPSS_l1/velocityl1);
  // *** also called dzeta*delta
  // *** see Brandt, Phys Rev A23, p1727, f B2
 
  if (verboseLevel>0) G4cout << "  pssDeltal1=" << pssDeltal1<< G4endl;
 
  if (pssDeltal1>1) return 0.;
 
  G4double energyLossl1 = std::pow(1-pssDeltal1,0.5);
  // *** also called z
  // *** see Brandt, Phys Rev A23, p1727, after f B2
 
  if (verboseLevel>0) G4cout << "  energyLossl1=" << energyLossl1<< G4endl;
 
  G4double coulombDeflectionl1 =
   (8.*pi*zIncident/systemMass)*std::pow(tetal1*sigmaPSS_l1,-2.)*std::pow(velocityl1/sigmaPSS_l1,-3.)*(zTarget/screenedzTarget);
  // *** see Brandt, Phys Rev A20, v2s and f2 and B2
  // *** with factor n2 compared to Brandt, Phys Rev A23, p1727, f B3
 
  G4double cParameterl1 =2.* coulombDeflectionl1/(energyLossl1*(energyLossl1+1.));
  // *** see Brandt, Phys Rev A23, p1727, f B4
 
  G4double coulombDeflectionFunction_l1 = 9.*ExpIntFunction(10,cParameterl1); //Coulomb-deflection effect correction
 
  if (verboseLevel>0) G4cout << "  coulombDeflectionFunction_l1 =" << coulombDeflectionFunction_l1 << G4endl;
 
  G4double crossSection_L1 = coulombDeflectionFunction_l1 * sigmaPSSR_l1;
 
  //ECPSSR L1 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
  //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
 
  if (verboseLevel>0) G4cout << "  crossSection_L1 =" << crossSection_L1 << G4endl;
 
  if (crossSection_L1 >= 0)
  {
    return crossSection_L1 * barn;
  }
 
  else {return 0;}
}

CalculateL2CrossSection()

G4double G4ecpssrBaseLixsModel::CalculateL2CrossSection ( G4int  zTarget, G4double  massIncident, G4double  energyIncident  )

virtual

Implements G4VecpssrLiModel.

Definition at line 394 of file G4ecpssrBaseLixsModel.cc.

{
  if (zTarget <=13 ) return 0.;
 
  // this L2-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
  // and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
 
  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 G4ecpssrBaseLixsModel::CalculateL2CrossSection : Proton or Alpha incident particles only. " << G4endl;
      G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
      return 0;
    }
    }
 
  G4double l2BindingEnergy = transitionManager->Shell(zTarget,2)->BindingEnergy(); //Observed binding energy of L2-subshell
 
  G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
 
  G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2; //Mass of the system (projectile, target)
 
  const G4double zlshell= 4.15;
 
  G4double screenedzTarget = zTarget-zlshell; //Effective nuclear charge as seen by electrons in L2-subshell
 
  const G4double rydbergMeV= 13.6056923e-6;
 
  const G4double nl= 2.;
 
  G4double tetal2 = (l2BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV); //Screening parameter
 
  if (verboseLevel>0) G4cout << "  tetal2=" <<  tetal2<< G4endl;
 
  G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
 
  const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ; //Bohr radius of hydrogen
 
  G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
 
  G4double velocityl2 = CalculateVelocity(2,  zTarget, massIncident, energyIncident); // Scaled velocity
 
  if (verboseLevel>0) G4cout << "  velocityl2=" << velocityl2<< G4endl;
 
  const G4double l23AnalyticalApproximation= 1.25;
 
  G4double x2 = (nl*l23AnalyticalApproximation)/velocityl2;
 
  if (verboseLevel>0) G4cout << "  x2=" << x2<< G4endl;
 
  G4double electrIonizationEnergyl2=0.;
 
  if ( x2<=0.035)  electrIonizationEnergyl2= 0.75*pi*(std::log(1./(x2*x2))-1.);
  else
    {
      if ( x2<=3.)
        electrIonizationEnergyl2 =G4Exp(-2.*x2)/(0.031+(0.213*std::pow(x2,0.5))+(0.005*x2)-(0.069*std::pow(x2,3./2.))+(0.324*x2*x2));
      else
        {if ( x2<=11.) electrIonizationEnergyl2 =2.*G4Exp(-2.*x2)/std::pow(x2,1.6);  }
    }
 
  G4double hFunctionl2 =(electrIonizationEnergyl2*2.*nl)/(tetal2*std::pow(velocityl2,3)); //takes into account  the polarization effect
 
  if (verboseLevel>0) G4cout << "  hFunctionl2=" << hFunctionl2<< G4endl;
 
  G4double gFunctionl2 = (1.+(10.*velocityl2)+(45.*velocityl2*velocityl2)+(102.*std::pow(velocityl2,3.))+(331.*std::pow(velocityl2,4.))+(6.7*std::pow(velocityl2,5.))+(58.*std::pow(velocityl2,6.))+(7.8*std::pow(velocityl2,7.))+ (0.888*std::pow(velocityl2,8.)) )/std::pow(1.+velocityl2,10.);
  //takes into account the reduced binding effect
 
  if (verboseLevel>0) G4cout << "  gFunctionl2=" << gFunctionl2<< G4endl;
 
  G4double sigmaPSS_l2 = 1.+(((2.*zIncident)/(screenedzTarget*tetal2))*(gFunctionl2-hFunctionl2)); //Binding-polarization factor
 
  if (verboseLevel>0) G4cout << "  sigmaPSS_l2=" << sigmaPSS_l2<< G4endl;
 
  const G4double cNaturalUnit= 137.;
 
  G4double yl2Formula=0.15*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocityl2/sigmaPSS_l2);
 
  G4double l2relativityCorrection = std::pow((1.+(1.1*yl2Formula*yl2Formula)),0.5)+yl2Formula; // Relativistic correction parameter
 
  G4double L2etaOverTheta2;
 
  G4double  universalFunction_l2 = 0.;
 
  G4double sigmaPSSR_l2 ;
 
  if ( velocityl2 < 20. )
  {
 
    L2etaOverTheta2 = (reducedEnergy*l2relativityCorrection)/((sigmaPSS_l2*tetal2)*(sigmaPSS_l2*tetal2));
 
    if ( (tetal2*sigmaPSS_l2>=0.2) && (tetal2*sigmaPSS_l2<=2.6670) && (L2etaOverTheta2>=0.1e-3) && (L2etaOverTheta2<=0.866e2) )
      universalFunction_l2 = FunctionFL2((tetal2*sigmaPSS_l2),L2etaOverTheta2);
 
    sigmaPSSR_l2 = (sigma0/(tetal2*sigmaPSS_l2))*universalFunction_l2;
 
    if (verboseLevel>0) G4cout << "  sigma PWBA L2 CS at low velocity range = " << sigmaPSSR_l2<< G4endl;
  }
  else
  {
 
    L2etaOverTheta2 = reducedEnergy /(tetal2*tetal2);
 
    if ( (tetal2>=0.2) && (tetal2<=2.6670) && (L2etaOverTheta2>=0.1e-3) && (L2etaOverTheta2<=0.866e2) )
      universalFunction_l2 = FunctionFL2((tetal2),L2etaOverTheta2);
 
    sigmaPSSR_l2 = (sigma0/tetal2)*universalFunction_l2;
 
    if (verboseLevel>0) G4cout << "  sigma PWBA L2 CS at medium and high velocity range = " << sigmaPSSR_l2<< G4endl;
 
  }
 
  G4double pssDeltal2 = (4./(systemMass*sigmaPSS_l2*tetal2))*(sigmaPSS_l2/velocityl2)*(sigmaPSS_l2/velocityl2);
 
  if (pssDeltal2>1) return 0.;
 
  G4double energyLossl2 = std::pow(1-pssDeltal2,0.5);
 
    if (verboseLevel>0) G4cout << "  energyLossl2=" << energyLossl2<< G4endl;
 
  G4double coulombDeflectionl2
    =(8.*pi*zIncident/systemMass)*std::pow(tetal2*sigmaPSS_l2,-2.)*std::pow(velocityl2/sigmaPSS_l2,-3.)*(zTarget/screenedzTarget);
 
  G4double cParameterl2 = 2.*coulombDeflectionl2/(energyLossl2*(energyLossl2+1.));
 
  G4double coulombDeflectionFunction_l2 = 11.*ExpIntFunction(12,cParameterl2); //Coulomb-deflection effect correction
  // *** see Brandt, Phys Rev A10, p477, f25
 
  if (verboseLevel>0) G4cout << "  coulombDeflectionFunction_l2 =" << coulombDeflectionFunction_l2 << G4endl;
 
  G4double crossSection_L2 = coulombDeflectionFunction_l2 * sigmaPSSR_l2;
  //ECPSSR L2 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
  //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
 
  if (verboseLevel>0) G4cout << "  crossSection_L2 =" << crossSection_L2 << G4endl;
 
  if (crossSection_L2 >= 0)
  {
     return crossSection_L2 * barn;
  }
  else {return 0;}
}

CalculateL3CrossSection()

G4double G4ecpssrBaseLixsModel::CalculateL3CrossSection ( G4int  zTarget, G4double  massIncident, G4double  energyIncident  )

virtual

Implements G4VecpssrLiModel.

Definition at line 557 of file G4ecpssrBaseLixsModel.cc.

{
  if (zTarget <=13) return 0.;
 
  //this L3-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
  //and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
 
  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 G4ecpssrBaseLixsModel::CalculateL3CrossSection : Proton or Alpha incident particles only. " << G4endl;
      G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
      return 0;
    }
    }
 
  G4double l3BindingEnergy = transitionManager->Shell(zTarget,3)->BindingEnergy();
 
  G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
 
  G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2;//Mass of the system (projectile, target)
 
  const G4double zlshell= 4.15;
 
  G4double screenedzTarget = zTarget-zlshell;//Effective nuclear charge as seen by electrons in L3-subshell
 
  const G4double rydbergMeV= 13.6056923e-6;
 
  const G4double nl= 2.;
 
  G4double tetal3 = (l3BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV);//Screening parameter
 
    if (verboseLevel>0) G4cout << "  tetal3=" <<  tetal3<< G4endl;
 
  G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
 
  const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ;//Bohr radius of hydrogen
 
  G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
 
  G4double velocityl3 = CalculateVelocity(3, zTarget, massIncident, energyIncident);// Scaled velocity
 
    if (verboseLevel>0) G4cout << "  velocityl3=" << velocityl3<< G4endl;
 
  const G4double l23AnalyticalApproximation= 1.25;
 
  G4double x3 = (nl*l23AnalyticalApproximation)/velocityl3;
 
    if (verboseLevel>0) G4cout << "  x3=" << x3<< G4endl;
 
  G4double electrIonizationEnergyl3=0.;
 
  if ( x3<=0.035)  electrIonizationEnergyl3= 0.75*pi*(std::log(1./(x3*x3))-1.);
    else
    {
      if ( x3<=3.) electrIonizationEnergyl3 =G4Exp(-2.*x3)/(0.031+(0.213*std::pow(x3,0.5))+(0.005*x3)-(0.069*std::pow(x3,3./2.))+(0.324*x3*x3));
      else
    {
      if ( x3<=11.) electrIonizationEnergyl3 =2.*G4Exp(-2.*x3)/std::pow(x3,1.6);}
    }
 
  G4double hFunctionl3 =(electrIonizationEnergyl3*2.*nl)/(tetal3*std::pow(velocityl3,3));//takes into account the polarization effect
 
    if (verboseLevel>0) G4cout << "  hFunctionl3=" << hFunctionl3<< G4endl;
 
  G4double gFunctionl3 = (1.+(10.*velocityl3)+(45.*velocityl3*velocityl3)+(102.*std::pow(velocityl3,3.))+(331.*std::pow(velocityl3,4.))+(6.7*std::pow(velocityl3,5.))+(58.*std::pow(velocityl3,6.))+(7.8*std::pow(velocityl3,7.))+ (0.888*std::pow(velocityl3,8.)) )/std::pow(1.+velocityl3,10.);
  //takes into account the reduced binding effect
 
    if (verboseLevel>0) G4cout << "  gFunctionl3=" << gFunctionl3<< G4endl;
 
  G4double sigmaPSS_l3 = 1.+(((2.*zIncident)/(screenedzTarget*tetal3))*(gFunctionl3-hFunctionl3));//Binding-polarization factor
 
    if (verboseLevel>0) G4cout << "sigmaPSS_l3 =" << sigmaPSS_l3<< G4endl;
 
  const G4double cNaturalUnit= 137.;
 
  G4double yl3Formula=0.15*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocityl3/sigmaPSS_l3);
 
  G4double l3relativityCorrection = std::pow((1.+(1.1*yl3Formula*yl3Formula)),0.5)+yl3Formula; // Relativistic correction parameter
 
  G4double L3etaOverTheta2;
 
  G4double  universalFunction_l3 = 0.;
 
  G4double sigmaPSSR_l3;
 
  if ( velocityl3 < 20. )
  {
 
    L3etaOverTheta2 = (reducedEnergy* l3relativityCorrection)/((sigmaPSS_l3*tetal3)*(sigmaPSS_l3*tetal3));
 
    if ( (tetal3*sigmaPSS_l3>=0.2) && (tetal3*sigmaPSS_l3<=2.6670) && (L3etaOverTheta2>=0.1e-3) && (L3etaOverTheta2<=0.866e2) )
 
      universalFunction_l3 = 2.*FunctionFL2((tetal3*sigmaPSS_l3), L3etaOverTheta2  );
 
    sigmaPSSR_l3 = (sigma0/(tetal3*sigmaPSS_l3))*universalFunction_l3;
 
    if (verboseLevel>0) G4cout << "  sigma PWBA L3 CS at low velocity range = " << sigmaPSSR_l3<< G4endl;
 
  }
 
  else
 
  {
 
    L3etaOverTheta2 = reducedEnergy/(tetal3*tetal3);
 
    if ( (tetal3>=0.2) && (tetal3<=2.6670) && (L3etaOverTheta2>=0.1e-3) && (L3etaOverTheta2<=0.866e2) )
 
      universalFunction_l3 = 2.*FunctionFL2(tetal3, L3etaOverTheta2  );
 
    sigmaPSSR_l3 = (sigma0/tetal3)*universalFunction_l3;
 
      if (verboseLevel>0) G4cout << "  sigma PWBA L3 CS at medium and high velocity range = " << sigmaPSSR_l3<< G4endl;
  }
 
  G4double pssDeltal3 = (4./(systemMass*sigmaPSS_l3*tetal3))*(sigmaPSS_l3/velocityl3)*(sigmaPSS_l3/velocityl3);
 
    if (verboseLevel>0) G4cout << "  pssDeltal3=" << pssDeltal3<< G4endl;
 
  if (pssDeltal3>1) return 0.;
 
  G4double energyLossl3 = std::pow(1-pssDeltal3,0.5);
 
  if (verboseLevel>0) G4cout << "  energyLossl3=" << energyLossl3<< G4endl;
 
  G4double coulombDeflectionl3 =
    (8.*pi*zIncident/systemMass)*std::pow(tetal3*sigmaPSS_l3,-2.)*std::pow(velocityl3/sigmaPSS_l3,-3.)*(zTarget/screenedzTarget);
 
  G4double cParameterl3 = 2.*coulombDeflectionl3/(energyLossl3*(energyLossl3+1.));
 
  G4double coulombDeflectionFunction_l3 = 11.*ExpIntFunction(12,cParameterl3);//Coulomb-deflection effect correction
  // *** see Brandt, Phys Rev A10, p477, f25
 
    if (verboseLevel>0) G4cout << "  coulombDeflectionFunction_l3 =" << coulombDeflectionFunction_l3 << G4endl;
 
  G4double crossSection_L3 =  coulombDeflectionFunction_l3 * sigmaPSSR_l3;
  //ECPSSR L3 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
  //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
 
    if (verboseLevel>0) G4cout << "  crossSection_L3 =" << crossSection_L3 << G4endl;
 
  if (crossSection_L3 >= 0)
  {
    return crossSection_L3 * barn;
  }
  else {return 0;}
}

CalculateVelocity()

G4double G4ecpssrBaseLixsModel::CalculateVelocity	(	G4int	subShell,
		G4int	zTarget,
		G4double	massIncident,
		G4double	energyIncident
	)

Definition at line 727 of file G4ecpssrBaseLixsModel.cc.

{
 
  G4AtomicTransitionManager*  transitionManager =  G4AtomicTransitionManager::Instance();
 
  G4double liBindingEnergy = transitionManager->Shell(zTarget,subShell)->BindingEnergy();
 
  G4Proton* aProtone = G4Proton::Proton();
  G4Alpha* aAlpha = G4Alpha::Alpha();
 
  if (!((massIncident == aProtone->GetPDGMass()) || (massIncident == aAlpha->GetPDGMass())))
    {
      G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateVelocity : Proton or Alpha incident particles only. " << G4endl;
      G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
      return 0;
    }
 
  const G4double zlshell= 4.15;
 
  G4double screenedzTarget = zTarget- zlshell;
 
  const G4double rydbergMeV= 13.6056923e-6;
 
  const G4double nl= 2.;
 
  G4double tetali = (liBindingEnergy*nl*nl)/(screenedzTarget*screenedzTarget*rydbergMeV);
 
  G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
 
  G4double velocity = 2.*nl*std::pow(reducedEnergy,0.5)/tetali;
  // *** see Brandt, Phys Rev A10, p10, f4
 
  return velocity;
}

Referenced by CalculateL1CrossSection(), CalculateL2CrossSection(), and CalculateL3CrossSection().

ExpIntFunction()

G4double G4ecpssrBaseLixsModel::ExpIntFunction	(	G4int	n,
		G4double	x
	)

Definition at line 121 of file G4ecpssrBaseLixsModel.cc.

{
// this 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;
  static const G4double euler= 0.5772156649;
  static const G4int maxit= 100;
  static const G4double fpmin = 1.0e-30;
  static 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 G4ecpssrBaseLixsModel::ExpIntFunction: bad arguments in ExpIntFunction"
         << G4endl;
  else {
    if (n==0) ans=G4Exp(-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*G4Exp(-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;
}

Referenced by CalculateL1CrossSection(), CalculateL2CrossSection(), and CalculateL3CrossSection().

---

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

• G4ecpssrBaseLixsModel.hh
• G4ecpssrBaseLixsModel.cc