#include <G4BraggModel.hh>

Inheritance diagram for G4BraggModel:

Collaboration diagram for G4BraggModel:

Public Member Functions
	G4BraggModel (const G4ParticleDefinition *p=nullptr, const G4String &nam="Bragg")

virtual	~G4BraggModel ()

virtual void	Initialise (const G4ParticleDefinition *, const G4DataVector &)

virtual G4double	ComputeCrossSectionPerElectron (const G4ParticleDefinition *, G4double kineticEnergy, G4double cutEnergy, G4double maxEnergy)

virtual G4double	ComputeCrossSectionPerAtom (const G4ParticleDefinition *, G4double kineticEnergy, G4double Z, G4double A, G4double cutEnergy, G4double maxEnergy)

virtual G4double	CrossSectionPerVolume (const G4Material , const G4ParticleDefinition , G4double kineticEnergy, G4double cutEnergy, G4double maxEnergy)

virtual G4double	ComputeDEDXPerVolume (const G4Material , const G4ParticleDefinition , G4double kineticEnergy, G4double cutEnergy)

virtual void	SampleSecondaries (std::vector< G4DynamicParticle > , const G4MaterialCutsCouple , const G4DynamicParticle , G4double tmin, G4double maxEnergy)

virtual G4double	GetChargeSquareRatio (const G4ParticleDefinition , const G4Material , G4double kineticEnergy)

virtual G4double	GetParticleCharge (const G4ParticleDefinition p, const G4Material mat, G4double kineticEnergy)

Public Member Functions inherited from G4VEmModel
	G4VEmModel (const G4String &nam)

virtual	~G4VEmModel ()

virtual void	InitialiseLocal (const G4ParticleDefinition , G4VEmModel masterModel)

virtual void	InitialiseForMaterial (const G4ParticleDefinition , const G4Material )

virtual void	InitialiseForElement (const G4ParticleDefinition *, G4int Z)

virtual G4double	GetPartialCrossSection (const G4Material , G4int, const G4ParticleDefinition , G4double)

virtual G4double	ComputeCrossSectionPerShell (const G4ParticleDefinition *, G4int Z, G4int shellIdx, G4double kinEnergy, G4double cutEnergy=0.0, G4double maxEnergy=DBL_MAX)

virtual G4double	ChargeSquareRatio (const G4Track &)

virtual void	StartTracking (G4Track *)

virtual void	CorrectionsAlongStep (const G4MaterialCutsCouple , const G4DynamicParticle , G4double &eloss, G4double &niel, G4double length)

virtual G4double	Value (const G4MaterialCutsCouple , const G4ParticleDefinition , G4double kineticEnergy)

virtual G4double	MinPrimaryEnergy (const G4Material , const G4ParticleDefinition , G4double cut=0.0)

virtual G4double	MinEnergyCut (const G4ParticleDefinition , const G4MaterialCutsCouple )

virtual void	SetupForMaterial (const G4ParticleDefinition , const G4Material , G4double kineticEnergy)

virtual void	DefineForRegion (const G4Region *)

virtual void	ModelDescription (std::ostream &outFile) const

void	InitialiseElementSelectors (const G4ParticleDefinition *, const G4DataVector &)

std::vector< G4EmElementSelector * > *	GetElementSelectors ()

void	SetElementSelectors (std::vector< G4EmElementSelector > )

G4double	ComputeDEDX (const G4MaterialCutsCouple , const G4ParticleDefinition , G4double kineticEnergy, G4double cutEnergy=DBL_MAX)

G4double	CrossSection (const G4MaterialCutsCouple , const G4ParticleDefinition , G4double kineticEnergy, G4double cutEnergy=0.0, G4double maxEnergy=DBL_MAX)

G4double	ComputeMeanFreePath (const G4ParticleDefinition , G4double kineticEnergy, const G4Material , G4double cutEnergy=0.0, G4double maxEnergy=DBL_MAX)

G4double	ComputeCrossSectionPerAtom (const G4ParticleDefinition , const G4Element , G4double kinEnergy, G4double cutEnergy=0.0, G4double maxEnergy=DBL_MAX)

G4int	SelectIsotopeNumber (const G4Element *)

const G4Element *	SelectRandomAtom (const G4MaterialCutsCouple , const G4ParticleDefinition , G4double kineticEnergy, G4double cutEnergy=0.0, G4double maxEnergy=DBL_MAX)

const G4Element *	SelectRandomAtom (const G4Material , const G4ParticleDefinition , G4double kineticEnergy, G4double cutEnergy=0.0, G4double maxEnergy=DBL_MAX)

G4int	SelectRandomAtomNumber (const G4Material *)

void	SetParticleChange (G4VParticleChange , G4VEmFluctuationModel f=0)

void	SetCrossSectionTable (G4PhysicsTable *, G4bool isLocal)

G4ElementData *	GetElementData ()

G4PhysicsTable *	GetCrossSectionTable ()

G4VEmFluctuationModel *	GetModelOfFluctuations ()

G4VEmAngularDistribution *	GetAngularDistribution ()

void	SetAngularDistribution (G4VEmAngularDistribution *)

G4double	HighEnergyLimit () const

G4double	LowEnergyLimit () const

G4double	HighEnergyActivationLimit () const

G4double	LowEnergyActivationLimit () const

G4double	PolarAngleLimit () const

G4double	SecondaryThreshold () const

G4bool	LPMFlag () const

G4bool	DeexcitationFlag () const

G4bool	ForceBuildTableFlag () const

G4bool	UseAngularGeneratorFlag () const

void	SetAngularGeneratorFlag (G4bool)

void	SetHighEnergyLimit (G4double)

void	SetLowEnergyLimit (G4double)

void	SetActivationHighEnergyLimit (G4double)

void	SetActivationLowEnergyLimit (G4double)

G4bool	IsActive (G4double kinEnergy)

void	SetPolarAngleLimit (G4double)

void	SetSecondaryThreshold (G4double)

void	SetLPMFlag (G4bool val)

void	SetDeexcitationFlag (G4bool val)

void	SetForceBuildTable (G4bool val)

void	SetMasterThread (G4bool val)

G4bool	IsMaster () const

G4double	MaxSecondaryKinEnergy (const G4DynamicParticle *dynParticle)

const G4String &	GetName () const

void	SetCurrentCouple (const G4MaterialCutsCouple *)

const G4Element *	GetCurrentElement () const

const G4Isotope *	GetCurrentIsotope () const

G4bool	IsLocked () const

void	SetLocked (G4bool)

Protected Member Functions
virtual G4double	MaxSecondaryEnergy (const G4ParticleDefinition *, G4double kinEnergy)

G4double	GetChargeSquareRatio () const

void	SetChargeSquareRatio (G4double val)

Protected Member Functions inherited from G4VEmModel
G4ParticleChangeForLoss *	GetParticleChangeForLoss ()

G4ParticleChangeForGamma *	GetParticleChangeForGamma ()

const G4MaterialCutsCouple *	CurrentCouple () const

void	SetCurrentElement (const G4Element *)

Private Member Functions
void	SetParticle (const G4ParticleDefinition *p)

G4bool	HasMaterial (const G4Material *material)

G4double	StoppingPower (const G4Material *material, G4double kineticEnergy)

G4double	ElectronicStoppingPower (G4double z, G4double kineticEnergy) const

G4double	DEDX (const G4Material *material, G4double kineticEnergy)

G4bool	MolecIsInZiegler1988 (const G4Material *material)

G4double	ChemicalFactor (G4double kineticEnergy, G4double eloss125) const

void	SetExpStopPower125 (G4double value)

G4BraggModel &	operator= (const G4BraggModel &right)

	G4BraggModel (const G4BraggModel &)

Private Attributes
G4EmCorrections *	corr

const G4ParticleDefinition *	particle

G4ParticleDefinition *	theElectron

G4ParticleChangeForLoss *	fParticleChange

const G4Material *	currentMaterial

G4double	mass

G4double	spin

G4double	chargeSquare

G4double	massRate

G4double	ratio

G4double	lowestKinEnergy

G4double	protonMassAMU

G4double	theZieglerFactor

G4double	expStopPower125

G4int	iMolecula

G4int	iPSTAR

G4bool	isIon

G4bool	isInitialised

Static Private Attributes
static G4PSTARStopping *	fPSTAR = 0

Additional Inherited Members
Protected Attributes inherited from G4VEmModel
G4ElementData *	fElementData

G4VParticleChange *	pParticleChange

G4PhysicsTable *	xSectionTable

const std::vector< G4double > *	theDensityFactor

const std::vector< G4int > *	theDensityIdx

size_t	idxTable

Static Protected Attributes inherited from G4VEmModel
static const G4double	inveplus = 1.0/CLHEP::eplus

Detailed Description

Definition at line 71 of file G4BraggModel.hh.

Constructor & Destructor Documentation

◆ G4BraggModel() [1/2]

G4BraggModel::G4BraggModel	(	const G4ParticleDefinition *	p = `nullptr`,
		const G4String &	nam = `"Bragg"`
	)

Definition at line 85 of file G4BraggModel.cc.

   : G4VEmModel(nam),
     particle(0),
     currentMaterial(0),
     protonMassAMU(1.007276),
     iMolecula(-1),
     iPSTAR(-1),
     isIon(false),
     isInitialised(false)
 {
   fParticleChange = 0;
   SetHighEnergyLimit(2.0*MeV);
 
   lowestKinEnergy  = 1.0*keV;
   theZieglerFactor = eV*cm2*1.0e-15;
   theElectron = G4Electron::Electron();
   expStopPower125 = 0.0;
 
   corr = G4LossTableManager::Instance()->EmCorrections();
   if(p) { SetParticle(p); }
   else  { SetParticle(theElectron); }
 }

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◆ ~G4BraggModel()

G4BraggModel::~G4BraggModel ( )

virtual

Definition at line 110 of file G4BraggModel.cc.

 {
   if(IsMaster()) { delete fPSTAR; fPSTAR = 0; }
 }

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◆ G4BraggModel() [2/2]

G4BraggModel::G4BraggModel ( const G4BraggModel & )

private

Member Function Documentation

◆ ChemicalFactor()

G4double G4BraggModel::ChemicalFactor	(	G4double	kineticEnergy,
		G4double	eloss125
	)		const

private

Definition at line 768 of file G4BraggModel.cc.

 {
   // Approximation of Chemical Factor according to
   // J.F.Ziegler and J.M.Manoyan, The stopping of ions in compaunds,
   // Nucl. Inst. & Meth. in Phys. Res. B35 (1988) 215-228.
   
   G4double gamma    = 1.0 + kineticEnergy/proton_mass_c2 ;    
   G4double gamma25  = 1.0 + 25.0*keV /proton_mass_c2 ;
   G4double gamma125 = 1.0 + 125.0*keV/proton_mass_c2 ;
   G4double beta     = sqrt(1.0 - 1.0/(gamma*gamma)) ;
   G4double beta25   = sqrt(1.0 - 1.0/(gamma25*gamma25)) ;
   G4double beta125  = sqrt(1.0 - 1.0/(gamma125*gamma125)) ;
   
   G4double factor = 1.0 + (expStopPower125/eloss125 - 1.0) *
                    (1.0 + G4Exp( 1.48 * ( beta125/beta25 - 7.0 ) ) ) /
                    (1.0 + G4Exp( 1.48 * ( beta/beta25    - 7.0 ) ) ) ;
 
   return factor ;
 }

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◆ ComputeCrossSectionPerAtom()

G4double G4BraggModel::ComputeCrossSectionPerAtom	(	const G4ParticleDefinition *	p,
		G4double	kineticEnergy,
		G4double	Z,
		G4double	A,
		G4double	cutEnergy,
		G4double	maxEnergy
	)

virtual

Reimplemented from G4VEmModel.

Definition at line 196 of file G4BraggModel.cc.

 {
   G4double cross = Z*ComputeCrossSectionPerElectron
                                          (p,kineticEnergy,cutEnergy,maxEnergy);
   return cross;
 }

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◆ ComputeCrossSectionPerElectron()

G4double G4BraggModel::ComputeCrossSectionPerElectron	(	const G4ParticleDefinition *	p,
		G4double	kineticEnergy,
		G4double	cutEnergy,
		G4double	maxEnergy
	)

virtual

Definition at line 167 of file G4BraggModel.cc.

 {
   G4double cross     = 0.0;
   G4double tmax      = MaxSecondaryEnergy(p, kineticEnergy);
   G4double maxEnergy = std::min(tmax,maxKinEnergy);
   if(cutEnergy < maxEnergy) {
 
     G4double energy  = kineticEnergy + mass;
     G4double energy2 = energy*energy;
     G4double beta2   = kineticEnergy*(kineticEnergy + 2.0*mass)/energy2;
     cross = (maxEnergy - cutEnergy)/(cutEnergy*maxEnergy) 
       - beta2*G4Log(maxEnergy/cutEnergy)/tmax;
 
     if( 0.0 < spin ) { cross += 0.5*(maxEnergy - cutEnergy)/energy2; }
 
     cross *= twopi_mc2_rcl2*chargeSquare/beta2;
   }
  //   G4cout << "BR: e= " << kineticEnergy << " tmin= " << cutEnergy 
  //          << " tmax= " << tmax << " cross= " << cross << G4endl;
  
   return cross;
 }

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◆ ComputeDEDXPerVolume()

G4double G4BraggModel::ComputeDEDXPerVolume	(	const G4Material *	material,
		const G4ParticleDefinition *	p,
		G4double	kineticEnergy,
		G4double	cutEnergy
	)

virtual

Reimplemented from G4VEmModel.

Definition at line 225 of file G4BraggModel.cc.

 {
   G4double tmax  = MaxSecondaryEnergy(p, kineticEnergy);
   G4double tkin  = kineticEnergy/massRate;
   G4double dedx  = 0.0;
 
   if(tkin < lowestKinEnergy) {
     dedx = DEDX(material, lowestKinEnergy)*sqrt(tkin/lowestKinEnergy);
   } else {
     dedx = DEDX(material, tkin); 
   }
 
   if (cutEnergy < tmax) {
 
     G4double tau   = kineticEnergy/mass;
     G4double gam   = tau + 1.0;
     G4double bg2   = tau * (tau+2.0);
     G4double beta2 = bg2/(gam*gam);
     G4double x     = cutEnergy/tmax;
 
     dedx += (G4Log(x) + (1.0 - x)*beta2) * twopi_mc2_rcl2
           * (material->GetElectronDensity())/beta2;
   }
 
   // now compute the total ionization loss
 
   if (dedx < 0.0) { dedx = 0.0; }
 
   dedx *= chargeSquare;
 
   //G4cout << "E(MeV)= " << tkin/MeV << " dedx= " << dedx 
   //         << "  " << material->GetName() << G4endl;
 
   return dedx;
 }

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◆ CrossSectionPerVolume()

G4double G4BraggModel::CrossSectionPerVolume	(	const G4Material *	material,
		const G4ParticleDefinition *	p,
		G4double	kineticEnergy,
		G4double	cutEnergy,
		G4double	maxEnergy
	)

virtual

Reimplemented from G4VEmModel.

Definition at line 210 of file G4BraggModel.cc.

 {
   G4double eDensity = material->GetElectronDensity();
   G4double cross = eDensity*ComputeCrossSectionPerElectron
                                          (p,kineticEnergy,cutEnergy,maxEnergy);
   return cross;
 }

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◆ DEDX()

G4double G4BraggModel::DEDX	(	const G4Material *	material,
		G4double	kineticEnergy
	)

private

Definition at line 594 of file G4BraggModel.cc.

 {
   G4double eloss = 0.0;
 
   // check DB
   if(material != currentMaterial) {
     currentMaterial = material;
     iPSTAR    = -1;
     iMolecula = -1;
     if( !HasMaterial(material) ) { iPSTAR = fPSTAR->GetIndex(material); }
 
     //G4cout << "%%% " <<material->GetName() << "  iMolecula= " 
     //           << iMolecula << "  iPSTAR= " << iPSTAR << G4endl; 
 
   }
 
   const G4int numberOfElements = material->GetNumberOfElements();
   const G4double* theAtomicNumDensityVector =
                                  material->GetAtomicNumDensityVector();
   
   if( iPSTAR >= 0 ) {
     return 
       fPSTAR->GetElectronicDEDX(iPSTAR, kineticEnergy)*material->GetDensity();
 
   } else if(iMolecula >= 0) {
 
     eloss = StoppingPower(material, kineticEnergy)*
                           material->GetDensity()/amu;
 
   // Pure material ICRU49 paralmeterisation
   } else if(1 == numberOfElements) {
 
     G4double z = material->GetZ();
     eloss = ElectronicStoppingPower(z, kineticEnergy)
                                * (material->GetTotNbOfAtomsPerVolume());
 
 
   // Experimental data exist only for kinetic energy 125 keV
   } else if( MolecIsInZiegler1988(material) ) { 
 
     // Loop over elements - calculation based on Bragg's rule 
     G4double eloss125 = 0.0 ;
     const G4ElementVector* theElementVector =
                            material->GetElementVector();
   
     //  Loop for the elements in the material
     for (G4int i=0; i<numberOfElements; i++) {
       const G4Element* element = (*theElementVector)[i] ;
       G4double z = element->GetZ() ;
       eloss    += ElectronicStoppingPower(z,kineticEnergy)
                                     * theAtomicNumDensityVector[i] ;
       eloss125 += ElectronicStoppingPower(z,125.0*keV)
                                     * theAtomicNumDensityVector[i] ;
     }      
 
     // Chemical factor is taken into account
     eloss *= ChemicalFactor(kineticEnergy, eloss125) ;
  
   // Brugg's rule calculation
   } else {
     const G4ElementVector* theElementVector =
                            material->GetElementVector() ;
   
     //  loop for the elements in the material
     for (G4int i=0; i<numberOfElements; i++)
     {
       const G4Element* element = (*theElementVector)[i] ;
       eloss   += ElectronicStoppingPower(element->GetZ(), kineticEnergy)
                                    * theAtomicNumDensityVector[i];
     }      
   }
   return eloss*theZieglerFactor;
 }

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◆ ElectronicStoppingPower()

G4double G4BraggModel::ElectronicStoppingPower	(	G4double	z,
		G4double	kineticEnergy
	)		const

private

Definition at line 449 of file G4BraggModel.cc.

 {
   G4double ionloss ;
   G4int i = G4lrint(z)-1 ;  // index of atom
   if(i < 0)  i = 0 ;
   if(i > 91) i = 91 ;
   
   // The data and the fit from: 
   // ICRU Report 49, 1993. Ziegler's type of parametrisations.
   // Proton kinetic energy for parametrisation (keV/amu)  
 
   G4double T = kineticEnergy/(keV*protonMassAMU) ; 
   
   static const G4double a[92][5] = {
    {1.254E+0, 1.440E+0, 2.426E+2, 1.200E+4, 1.159E-1},
    {1.229E+0, 1.397E+0, 4.845E+2, 5.873E+3, 5.225E-2},
    {1.411E+0, 1.600E+0, 7.256E+2, 3.013E+3, 4.578E-2},
    {2.248E+0, 2.590E+0, 9.660E+2, 1.538E+2, 3.475E-2},
    {2.474E+0, 2.815E+0, 1.206E+3, 1.060E+3, 2.855E-2},
    {2.631E+0, 2.601E+0, 1.701E+3, 1.279E+3, 1.638E-2},
    {2.954E+0, 3.350E+0, 1.683E+3, 1.900E+3, 2.513E-2},
    {2.652E+0, 3.000E+0, 1.920E+3, 2.000E+3, 2.230E-2},
    {2.085E+0, 2.352E+0, 2.157E+3, 2.634E+3, 1.816E-2},
    {1.951E+0, 2.199E+0, 2.393E+3, 2.699E+3, 1.568E-2},
        // Z= 11-20
    {2.542E+0, 2.869E+0, 2.628E+3, 1.854E+3, 1.472E-2},
    {3.791E+0, 4.293E+0, 2.862E+3, 1.009E+3, 1.397E-2},
    {4.154E+0, 4.739E+0, 2.766E+3, 1.645E+2, 2.023E-2},
    {4.914E+0, 5.598E+0, 3.193E+3, 2.327E+2, 1.419E-2},
    {3.232E+0, 3.647E+0, 3.561E+3, 1.560E+3, 1.267E-2},
    {3.447E+0, 3.891E+0, 3.792E+3, 1.219E+3, 1.211E-2},
    {5.301E+0, 6.008E+0, 3.969E+3, 6.451E+2, 1.183E-2},
    {5.731E+0, 6.500E+0, 4.253E+3, 5.300E+2, 1.123E-2},
    {5.152E+0, 5.833E+0, 4.482E+3, 5.457E+2, 1.129E-2},
    {5.521E+0, 6.252E+0, 4.710E+3, 5.533E+2, 1.112E-2},
        // Z= 21-30
    {5.201E+0, 5.884E+0, 4.938E+3, 5.609E+2, 9.995E-3},
    {4.858E+0, 5.489E+0, 5.260E+3, 6.511E+2, 8.930E-3},
    {4.479E+0, 5.055E+0, 5.391E+3, 9.523E+2, 9.117E-3},
    {3.983E+0, 4.489E+0, 5.616E+3, 1.336E+3, 8.413E-3},
    {3.469E+0, 3.907E+0, 5.725E+3, 1.461E+3, 8.829E-3},
    {3.519E+0, 3.963E+0, 6.065E+3, 1.243E+3, 7.782E-3},
    {3.140E+0, 3.535E+0, 6.288E+3, 1.372E+3, 7.361E-3},
    {3.553E+0, 4.004E+0, 6.205E+3, 5.551E+2, 8.763E-3},
    {3.696E+0, 4.194E+0, 4.649E+3, 8.113E+1, 2.242E-2},
    {4.210E+0, 4.750E+0, 6.953E+3, 2.952E+2, 6.809E-3},
        // Z= 31-40
    {5.041E+0, 5.697E+0, 7.173E+3, 2.026E+2, 6.725E-3},
    {5.554E+0, 6.300E+0, 6.496E+3, 1.100E+2, 9.689E-3},
    {5.323E+0, 6.012E+0, 7.611E+3, 2.925E+2, 6.447E-3},
    {5.874E+0, 6.656E+0, 7.395E+3, 1.175E+2, 7.684E-3},
    {6.658E+0, 7.536E+0, 7.694E+3, 2.223E+2, 6.509E-3},
    {6.413E+0, 7.240E+0, 1.185E+4, 1.537E+2, 2.880E-3},
    {5.694E+0, 6.429E+0, 8.478E+3, 2.929E+2, 6.087E-3},
    {6.339E+0, 7.159E+0, 8.693E+3, 3.303E+2, 6.003E-3},
    {6.407E+0, 7.234E+0, 8.907E+3, 3.678E+2, 5.889E-3},
    {6.734E+0, 7.603E+0, 9.120E+3, 4.052E+2, 5.765E-3},
        // Z= 41-50
    {6.901E+0, 7.791E+0, 9.333E+3, 4.427E+2, 5.587E-3},
    {6.424E+0, 7.248E+0, 9.545E+3, 4.802E+2, 5.376E-3},
    {6.799E+0, 7.671E+0, 9.756E+3, 5.176E+2, 5.315E-3},
    {6.109E+0, 6.887E+0, 9.966E+3, 5.551E+2, 5.151E-3},
    {5.924E+0, 6.677E+0, 1.018E+4, 5.925E+2, 4.919E-3},
    {5.238E+0, 5.900E+0, 1.038E+4, 6.300E+2, 4.758E-3},
    // {5.623,    6.354,    7160.0,   337.6,    0.013940}, // Ag Ziegler77
    {5.345E+0, 6.038E+0, 6.790E+3, 3.978E+2, 1.676E-2}, // Ag ICRU49
    {5.814E+0, 6.554E+0, 1.080E+4, 3.555E+2, 4.626E-3},
    {6.229E+0, 7.024E+0, 1.101E+4, 3.709E+2, 4.540E-3},
    {6.409E+0, 7.227E+0, 1.121E+4, 3.864E+2, 4.474E-3},
        // Z= 51-60
    {7.500E+0, 8.480E+0, 8.608E+3, 3.480E+2, 9.074E-3},
    {6.979E+0, 7.871E+0, 1.162E+4, 3.924E+2, 4.402E-3},
    {7.725E+0, 8.716E+0, 1.183E+4, 3.948E+2, 4.376E-3},
    {8.337E+0, 9.425E+0, 1.051E+4, 2.696E+2, 6.206E-3},
    {7.287E+0, 8.218E+0, 1.223E+4, 3.997E+2, 4.447E-3},
    {7.899E+0, 8.911E+0, 1.243E+4, 4.021E+2, 4.511E-3},
    {8.041E+0, 9.071E+0, 1.263E+4, 4.045E+2, 4.540E-3},
    {7.488E+0, 8.444E+0, 1.283E+4, 4.069E+2, 4.420E-3},
    {7.291E+0, 8.219E+0, 1.303E+4, 4.093E+2, 4.298E-3},
    {7.098E+0, 8.000E+0, 1.323E+4, 4.118E+2, 4.182E-3},
        // Z= 61-70
    {6.909E+0, 7.786E+0, 1.343E+4, 4.142E+2, 4.058E-3},
    {6.728E+0, 7.580E+0, 1.362E+4, 4.166E+2, 3.976E-3},
    {6.551E+0, 7.380E+0, 1.382E+4, 4.190E+2, 3.877E-3},
    {6.739E+0, 7.592E+0, 1.402E+4, 4.214E+2, 3.863E-3},
    {6.212E+0, 6.996E+0, 1.421E+4, 4.239E+2, 3.725E-3},
    {5.517E+0, 6.210E+0, 1.440E+4, 4.263E+2, 3.632E-3},
    {5.220E+0, 5.874E+0, 1.460E+4, 4.287E+2, 3.498E-3},
    {5.071E+0, 5.706E+0, 1.479E+4, 4.330E+2, 3.405E-3},
    {4.926E+0, 5.542E+0, 1.498E+4, 4.335E+2, 3.342E-3},
    {4.788E+0, 5.386E+0, 1.517E+4, 4.359E+2, 3.292E-3},
        // Z= 71-80
    {4.893E+0, 5.505E+0, 1.536E+4, 4.384E+2, 3.243E-3},
    {5.028E+0, 5.657E+0, 1.555E+4, 4.408E+2, 3.195E-3},
    {4.738E+0, 5.329E+0, 1.574E+4, 4.432E+2, 3.186E-3},
    {4.587E+0, 5.160E+0, 1.541E+4, 4.153E+2, 3.406E-3},
    {5.201E+0, 5.851E+0, 1.612E+4, 4.416E+2, 3.122E-3},
    {5.071E+0, 5.704E+0, 1.630E+4, 4.409E+2, 3.082E-3},
    {4.946E+0, 5.563E+0, 1.649E+4, 4.401E+2, 2.965E-3},
    {4.477E+0, 5.034E+0, 1.667E+4, 4.393E+2, 2.871E-3},
    //  {4.856,    5.460,    18320.0,  438.5,    0.002542}, //Ziegler77
    {4.844E+0, 5.458E+0, 7.852E+3, 9.758E+2, 2.077E-2}, //ICRU49
    {4.307E+0, 4.843E+0, 1.704E+4, 4.878E+2, 2.882E-3},
        // Z= 81-90
    {4.723E+0, 5.311E+0, 1.722E+4, 5.370E+2, 2.913E-3},
    {5.319E+0, 5.982E+0, 1.740E+4, 5.863E+2, 2.871E-3},
    {5.956E+0, 6.700E+0, 1.780E+4, 6.770E+2, 2.660E-3},
    {6.158E+0, 6.928E+0, 1.777E+4, 5.863E+2, 2.812E-3},
    {6.203E+0, 6.979E+0, 1.795E+4, 5.863E+2, 2.776E-3},
    {6.181E+0, 6.954E+0, 1.812E+4, 5.863E+2, 2.748E-3},
    {6.949E+0, 7.820E+0, 1.830E+4, 5.863E+2, 2.737E-3},
    {7.506E+0, 8.448E+0, 1.848E+4, 5.863E+2, 2.727E-3},
    {7.648E+0, 8.609E+0, 1.866E+4, 5.863E+2, 2.697E-3},
    {7.711E+0, 8.679E+0, 1.883E+4, 5.863E+2, 2.641E-3},
        // Z= 91-92
    {7.407E+0, 8.336E+0, 1.901E+4, 5.863E+2, 2.603E-3},
    {7.290E+0, 8.204E+0, 1.918E+4, 5.863E+2, 2.673E-3}
   };
 
   G4double fac = 1.0 ;
 
     // Carbon specific case for E < 40 keV
   if ( T < 40.0 && 5 == i) {
     fac = sqrt(T/40.0) ;
     T = 40.0 ;  
 
     // Free electron gas model
   } else if ( T < 10.0 ) { 
     fac = sqrt(T*0.1) ;
     T =10.0 ;
   }
 
   // Main parametrisation
   G4double slow  = a[i][1] * G4Exp(G4Log(T) * 0.45) ;
   G4double shigh = G4Log( 1.0 + a[i][3]/T + a[i][4]*T ) * a[i][2]/T ;
   ionloss = slow*shigh*fac / (slow + shigh) ;     
   
   if ( ionloss < 0.0) { ionloss = 0.0; }
   
   return ionloss;
 }

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◆ GetChargeSquareRatio() [1/2]

G4double G4BraggModel::GetChargeSquareRatio	(	const G4ParticleDefinition *	p,
		const G4Material *	mat,
		G4double	kineticEnergy
	)

virtual

Reimplemented from G4VEmModel.

Definition at line 145 of file G4BraggModel.cc.

 {
   // this method is called only for ions
   G4double q2 = corr->EffectiveChargeSquareRatio(p,mat,kineticEnergy);
   GetModelOfFluctuations()->SetParticleAndCharge(p, q2);
   return q2*corr->EffectiveChargeCorrection(p,mat,kineticEnergy);
 }

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◆ GetChargeSquareRatio() [2/2]

G4double G4BraggModel::GetChargeSquareRatio ( ) const

inlineprotected

Definition at line 193 of file G4BraggModel.hh.

 {
   return chargeSquare;
 }

◆ GetParticleCharge()

G4double G4BraggModel::GetParticleCharge	(	const G4ParticleDefinition *	p,
		const G4Material *	mat,
		G4double	kineticEnergy
	)

virtual

Reimplemented from G4VEmModel.

Reimplemented in G4BraggIonGasModel.

Definition at line 157 of file G4BraggModel.cc.

 {
   // this method is called only for ions, so no check if it is an ion 
   return corr->GetParticleCharge(p,mat,kineticEnergy);
 }

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◆ HasMaterial()

G4bool G4BraggModel::HasMaterial ( const G4Material * material )

private

Definition at line 356 of file G4BraggModel.cc.

 {
   return false;
   /*
   G4String chFormula = material->GetChemicalFormula();
   if("" == chFormula) { return false; }
 
   // ICRU Report N49, 1993. Power's model for H
   static const size_t numberOfMolecula = 11;
   static const G4String molName[numberOfMolecula] = {
     "Al_2O_3",                 "CO_2",                      "CH_4",
     "(C_2H_4)_N-Polyethylene", "(C_2H_4)_N-Polypropylene",  "(C_8H_8)_N",
     "C_3H_8",                  "SiO_2",                     "H_2O",
     "H_2O-Gas",                "Graphite" } ;
 
   // Search for the material in the table
   for (size_t i=0; i<numberOfMolecula; ++i) {
     if (chFormula == molName[i]) {
       iPSTAR = fPSTAR->GetIndex(matName[i]);  
       break;
     }
   }
   return (iPSTAR >= 0);
   */
 }

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◆ Initialise()

void G4BraggModel::Initialise	(	const G4ParticleDefinition *	p,
		const G4DataVector &
	)

virtual

Implements G4VEmModel.

Definition at line 117 of file G4BraggModel.cc.

 {
   if(p != particle) { SetParticle(p); }
 
   // always false before the run
   SetDeexcitationFlag(false);
 
   if(!isInitialised) {
     isInitialised = true;
 
     if(UseAngularGeneratorFlag() && !GetAngularDistribution()) {
       SetAngularDistribution(new G4DeltaAngle());
     }
     G4String pname = particle->GetParticleName();
     if(particle->GetParticleType() == "nucleus" && 
        pname != "deuteron" && pname != "triton" &&
        pname != "alpha+"   && pname != "helium" &&
        pname != "hydrogen") { isIon = true; }
 
     fParticleChange = GetParticleChangeForLoss();
     if(!fPSTAR) { fPSTAR = new G4PSTARStopping(); }
   }
   if(IsMaster() && particle->GetPDGMass() < GeV) { fPSTAR->Initialise(); }
 }

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◆ MaxSecondaryEnergy()

G4double G4BraggModel::MaxSecondaryEnergy	(	const G4ParticleDefinition *	pd,
		G4double	kinEnergy
	)

protectedvirtual

Reimplemented from G4VEmModel.

Definition at line 344 of file G4BraggModel.cc.

 {
   if(pd != particle) { SetParticle(pd); }
   G4double tau  = kinEnergy/mass;
   G4double tmax = 2.0*electron_mass_c2*tau*(tau + 2.) /
                   (1. + 2.0*(tau + 1.)*ratio + ratio*ratio);
   return tmax;
 }

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◆ MolecIsInZiegler1988()

G4bool G4BraggModel::MolecIsInZiegler1988 ( const G4Material * material )

private

Definition at line 670 of file G4BraggModel.cc.

 {
   // The list of molecules from
   // J.F.Ziegler and J.M.Manoyan, The stopping of ions in compaunds,
   // Nucl. Inst. & Meth. in Phys. Res. B35 (1988) 215-228.
   
   G4String myFormula = G4String(" ") ;
   const G4String chFormula = material->GetChemicalFormula() ;
   if (myFormula == chFormula ) { return false; }
   
   //  There are no evidence for difference of stopping power depended on
   //  phase of the compound except for water. The stopping power of the 
   //  water in gas phase can be predicted using Bragg's rule.
   //  
   //  No chemical factor for water-gas 
    
   myFormula = G4String("H_2O") ;
   const G4State theState = material->GetState() ;
   if( theState == kStateGas && myFormula == chFormula) return false ;
     
 
   // The coffecient from Table.4 of Ziegler & Manoyan
   static const G4double HeEff = 2.8735 ;
   
   static const size_t numberOfMolecula = 53;
   static const G4String nameOfMol[53] = {
     "H_2O",      "C_2H_4O",    "C_3H_6O",  "C_2H_2",             "C_H_3OH",
     "C_2H_5OH",  "C_3H_7OH",   "C_3H_4",   "NH_3",               "C_14H_10",
     "C_6H_6",    "C_4H_10",    "C_4H_6",   "C_4H_8O",            "CCl_4",
     "CF_4",      "C_6H_8",     "C_6H_12",  "C_6H_10O",           "C_6H_10",
     "C_8H_16",   "C_5H_10",    "C_5H_8",   "C_3H_6-Cyclopropane","C_2H_4F_2",
     "C_2H_2F_2", "C_4H_8O_2",  "C_2H_6",   "C_2F_6",             "C_2H_6O",
     "C_3H_6O",   "C_4H_10O",   "C_2H_4",   "C_2H_4O",            "C_2H_4S",
     "SH_2",      "CH_4",       "CCLF_3",   "CCl_2F_2",           "CHCl_2F",
     "(CH_3)_2S", "N_2O",       "C_5H_10O", "C_8H_6",             "(CH_2)_N",
     "(C_3H_6)_N","(C_8H_8)_N", "C_3H_8",   "C_3H_6-Propylene",   "C_3H_6O",
     "C_3H_6S",   "C_4H_4S",    "C_7H_8"
   };
 
   static const G4double expStopping[numberOfMolecula] = {
      66.1,  190.4, 258.7,  42.2, 141.5,
     210.9,  279.6, 198.8,  31.0, 267.5,
     122.8,  311.4, 260.3, 328.9, 391.3,
     206.6,  374.0, 422.0, 432.0, 398.0,
     554.0,  353.0, 326.0,  74.6, 220.5,
     197.4,  362.0, 170.0, 330.5, 211.3,
     262.3,  349.6,  51.3, 187.0, 236.9,
     121.9,   35.8, 247.0, 292.6, 268.0,
     262.3,   49.0, 398.9, 444.0,  22.91,
      68.0,  155.0,  84.0,  74.2, 254.7,
     306.8,  324.4, 420.0
   } ;
 
   static const G4double expCharge[53] = {
     HeEff, HeEff, HeEff,   1.0, HeEff,
     HeEff, HeEff, HeEff,   1.0,   1.0,
       1.0, HeEff, HeEff, HeEff, HeEff,
     HeEff, HeEff, HeEff, HeEff, HeEff,
     HeEff, HeEff, HeEff,   1.0, HeEff,
     HeEff, HeEff, HeEff, HeEff, HeEff,
     HeEff, HeEff,   1.0, HeEff, HeEff,
     HeEff,   1.0, HeEff, HeEff, HeEff,
     HeEff,   1.0, HeEff, HeEff,   1.0,
       1.0,   1.0,   1.0,   1.0, HeEff,
     HeEff, HeEff, HeEff
   } ;
 
   static const G4double numberOfAtomsPerMolecula[53] = {
     3.0,  7.0, 10.0,  4.0,  6.0,
     9.0, 12.0,  7.0,  4.0, 24.0,
     12.0, 14.0, 10.0, 13.0,  5.0,
     5.0, 14.0, 18.0, 17.0, 17.0,
     24.0, 15.0, 13.0,  9.0,  8.0,
     6.0, 14.0,  8.0,  8.0,  9.0,
     10.0, 15.0,  6.0,  7.0,  7.0,
     3.0,  5.0,  5.0,  5.0,  5.0,
     9.0,  3.0, 16.0, 14.0,  3.0,
     9.0, 16.0, 11.0,  9.0, 10.0,
     10.0,  9.0, 15.0
   } ;
 
   // Search for the compaund in the table
   for (size_t i=0; i<numberOfMolecula; i++)
     {
       if(chFormula == nameOfMol[i]) {
         G4double exp125 = expStopping[i] *
                           (material->GetTotNbOfAtomsPerVolume()) /
                           (expCharge[i] * numberOfAtomsPerMolecula[i]) ;
         SetExpStopPower125(exp125);
         return true;
       }
     }
   
   return false;
 }

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◆ operator=()

G4BraggModel& G4BraggModel::operator= ( const G4BraggModel & right )

private

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◆ SampleSecondaries()

void G4BraggModel::SampleSecondaries	(	std::vector< G4DynamicParticle >	vdp,
		const G4MaterialCutsCouple *	couple,
		const G4DynamicParticle *	dp,
		G4double	tmin,
		G4double	maxEnergy
	)

virtual

Implements G4VEmModel.

Definition at line 266 of file G4BraggModel.cc.

 {
   G4double tmax = MaxSecondaryKinEnergy(dp);
   G4double xmax = std::min(tmax, maxEnergy);
   if(xmin >= xmax) { return; }
 
   G4double kineticEnergy = dp->GetKineticEnergy();
   G4double energy  = kineticEnergy + mass;
   G4double energy2 = energy*energy;
   G4double beta2   = kineticEnergy*(kineticEnergy + 2.0*mass)/energy2;
   G4double grej    = 1.0;
   G4double deltaKinEnergy, f;
 
   CLHEP::HepRandomEngine* rndmEngineMod = G4Random::getTheEngine();
   G4double rndm[2];
 
   // sampling follows ...
   do {
     rndmEngineMod->flatArray(2, rndm);
     deltaKinEnergy = xmin*xmax/(xmin*(1.0 - rndm[0]) + xmax*rndm[0]);
 
     f = 1.0 - beta2*deltaKinEnergy/tmax;
 
     if(f > grej) {
         G4cout << "G4BraggModel::SampleSecondary Warning! "
                << "Majorant " << grej << " < "
                << f << " for e= " << deltaKinEnergy
                << G4endl;
     }
 
     // Loop checking, 03-Aug-2015, Vladimir Ivanchenko
   } while( grej*rndm[1] >= f );
 
   G4ThreeVector deltaDirection;
 
   if(UseAngularGeneratorFlag()) {
     const G4Material* mat =  couple->GetMaterial();
     G4int Z = SelectRandomAtomNumber(mat);
 
     deltaDirection = 
       GetAngularDistribution()->SampleDirection(dp, deltaKinEnergy, Z, mat);
 
   } else {
  
     G4double deltaMomentum =
       sqrt(deltaKinEnergy * (deltaKinEnergy + 2.0*electron_mass_c2));
     G4double cost = deltaKinEnergy * (energy + electron_mass_c2) /
       (deltaMomentum * dp->GetTotalMomentum());
     if(cost > 1.0) { cost = 1.0; }
     G4double sint = sqrt((1.0 - cost)*(1.0 + cost));
 
     G4double phi = twopi*rndmEngineMod->flat();
 
     deltaDirection.set(sint*cos(phi),sint*sin(phi), cost) ;
     deltaDirection.rotateUz(dp->GetMomentumDirection());
   }  
 
   // create G4DynamicParticle object for delta ray
   G4DynamicParticle* delta = 
     new G4DynamicParticle(theElectron,deltaDirection,deltaKinEnergy);
 
   // Change kinematics of primary particle
   kineticEnergy -= deltaKinEnergy;
   G4ThreeVector finalP = dp->GetMomentum() - delta->GetMomentum();
   finalP               = finalP.unit();
   
   fParticleChange->SetProposedKineticEnergy(kineticEnergy);
   fParticleChange->SetProposedMomentumDirection(finalP);
 
   vdp->push_back(delta);
 }

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◆ SetChargeSquareRatio()

void G4BraggModel::SetChargeSquareRatio ( G4double val )

inlineprotected

Definition at line 198 of file G4BraggModel.hh.

 {
   chargeSquare = val;
 }

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◆ SetExpStopPower125()

void G4BraggModel::SetExpStopPower125 ( G4double value )

inlineprivate

Definition at line 149 of file G4BraggModel.hh.

149 {expStopPower125 = value;};

G4BraggModel::expStopPower125

G4double expStopPower125

Definition: G4BraggModel.hh:172

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◆ SetParticle()

void G4BraggModel::SetParticle ( const G4ParticleDefinition * p )

inlineprivate

Definition at line 182 of file G4BraggModel.hh.

 {
   particle = p;
   mass = particle->GetPDGMass();
   spin = particle->GetPDGSpin();
   G4double q = particle->GetPDGCharge()/CLHEP::eplus;
   chargeSquare = q*q;
   massRate     = mass/CLHEP::proton_mass_c2;
   ratio = CLHEP::electron_mass_c2/mass;
 }

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◆ StoppingPower()

G4double G4BraggModel::StoppingPower	(	const G4Material *	material,
		G4double	kineticEnergy
	)

private

Definition at line 384 of file G4BraggModel.cc.

 {
   G4double ionloss = 0.0 ;
 
   if (iMolecula >= 0) {
   
     // The data and the fit from: 
     // ICRU Report N49, 1993. Ziegler's model for protons.
     // Proton kinetic energy for parametrisation (keV/amu)  
 
     G4double T = kineticEnergy/(keV*protonMassAMU) ; 
 
     static const G4double a[11][5] = {
    {1.187E+1, 1.343E+1, 1.069E+4, 7.723E+2, 2.153E-2},
    {7.802E+0, 8.814E+0, 8.303E+3, 7.446E+2, 7.966E-3}, 
    {7.294E+0, 8.284E+0, 5.010E+3, 4.544E+2, 8.153E-3}, 
    {8.646E+0, 9.800E+0, 7.066E+3, 4.581E+2, 9.383E-3}, 
    {1.286E+1, 1.462E+1, 5.625E+3, 2.621E+3, 3.512E-2}, 
    {3.229E+1, 3.696E+1, 8.918E+3, 3.244E+3, 1.273E-1}, 
    {1.604E+1, 1.825E+1, 6.967E+3, 2.307E+3, 3.775E-2}, 
    {8.049E+0, 9.099E+0, 9.257E+3, 3.846E+2, 1.007E-2},
    {4.015E+0, 4.542E+0, 3.955E+3, 4.847E+2, 7.904E-3}, 
    {4.571E+0, 5.173E+0, 4.346E+3, 4.779E+2, 8.572E-3},
    {2.631E+0, 2.601E+0, 1.701E+3, 1.279E+3, 1.638E-2} };
 
     static const G4double atomicWeight[11] = {
     101.96128, 44.0098, 16.0426, 28.0536, 42.0804,
     104.1512, 44.665, 60.0843, 18.0152, 18.0152, 12.0};       
 
     if ( T < 10.0 ) {
       ionloss = a[iMolecula][0] * sqrt(T) ;
     
     } else if ( T < 10000.0 ) {
       G4double slow  = a[iMolecula][1] * G4Exp(G4Log(T)* 0.45);
       G4double shigh = G4Log( 1.0 + a[iMolecula][3]/T  
                      + a[iMolecula][4]*T ) * a[iMolecula][2]/T ;
       ionloss = slow*shigh / (slow + shigh) ;     
     } 
 
     if ( ionloss < 0.0) ionloss = 0.0 ;
     if ( 10 == iMolecula ) { 
       if (T < 100.0) {
         ionloss *= (1.0+0.023+0.0066*G4Log(T)*invLog10);  
       }
       else if (T < 700.0) {   
         ionloss *=(1.0+0.089-0.0248*G4Log(T-99.)*invLog10);
       } 
       else if (T < 10000.0) {    
         ionloss *=(1.0+0.089-0.0248*G4Log(700.-99.)*invLog10);
       }
     }
     ionloss /= atomicWeight[iMolecula];
 
   // pure material (normally not the case for this function)
   } else if(1 == (material->GetNumberOfElements())) {
     G4double z = material->GetZ() ;
     ionloss = ElectronicStoppingPower( z, kineticEnergy ) ;  
   }
   
   return ionloss;
 }

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Member Data Documentation

◆ chargeSquare

G4double G4BraggModel::chargeSquare

private

Definition at line 166 of file G4BraggModel.hh.

◆ corr

G4EmCorrections* G4BraggModel::corr

private

Definition at line 155 of file G4BraggModel.hh.

◆ currentMaterial

const G4Material* G4BraggModel::currentMaterial

private

Definition at line 162 of file G4BraggModel.hh.

◆ expStopPower125

G4double G4BraggModel::expStopPower125

private

Definition at line 172 of file G4BraggModel.hh.

◆ fParticleChange

G4ParticleChangeForLoss* G4BraggModel::fParticleChange

private

Definition at line 159 of file G4BraggModel.hh.

◆ fPSTAR

G4PSTARStopping * G4BraggModel::fPSTAR = 0

staticprivate

Definition at line 160 of file G4BraggModel.hh.

◆ iMolecula

G4int G4BraggModel::iMolecula

private

Definition at line 174 of file G4BraggModel.hh.

◆ iPSTAR

G4int G4BraggModel::iPSTAR

private

Definition at line 175 of file G4BraggModel.hh.

◆ isInitialised

G4bool G4BraggModel::isInitialised

private

Definition at line 177 of file G4BraggModel.hh.

◆ isIon

G4bool G4BraggModel::isIon

private

Definition at line 176 of file G4BraggModel.hh.

◆ lowestKinEnergy

G4double G4BraggModel::lowestKinEnergy

private

Definition at line 169 of file G4BraggModel.hh.

◆ mass

G4double G4BraggModel::mass

private

Definition at line 164 of file G4BraggModel.hh.

◆ massRate

G4double G4BraggModel::massRate

private

Definition at line 167 of file G4BraggModel.hh.

◆ particle

const G4ParticleDefinition* G4BraggModel::particle

private

Definition at line 157 of file G4BraggModel.hh.

◆ protonMassAMU

G4double G4BraggModel::protonMassAMU

private

Definition at line 170 of file G4BraggModel.hh.

◆ ratio

G4double G4BraggModel::ratio

private

Definition at line 168 of file G4BraggModel.hh.

◆ spin

G4double G4BraggModel::spin

private

Definition at line 165 of file G4BraggModel.hh.

◆ theElectron

G4ParticleDefinition* G4BraggModel::theElectron

private

Definition at line 158 of file G4BraggModel.hh.

◆ theZieglerFactor

G4double G4BraggModel::theZieglerFactor

private

Definition at line 171 of file G4BraggModel.hh.

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

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ G4BraggModel() [1/2]

◆ ~G4BraggModel()

◆ G4BraggModel() [2/2]

Member Function Documentation

◆ ChemicalFactor()

◆ ComputeCrossSectionPerAtom()

◆ ComputeCrossSectionPerElectron()

◆ ComputeDEDXPerVolume()

◆ CrossSectionPerVolume()

◆ DEDX()

◆ ElectronicStoppingPower()

◆ GetChargeSquareRatio() [1/2]

◆ GetChargeSquareRatio() [2/2]

◆ GetParticleCharge()

◆ HasMaterial()

◆ Initialise()

◆ MaxSecondaryEnergy()

◆ MolecIsInZiegler1988()

◆ operator=()

◆ SampleSecondaries()

◆ SetChargeSquareRatio()

◆ SetExpStopPower125()

◆ SetParticle()

◆ StoppingPower()

Member Data Documentation

◆ chargeSquare

◆ corr

◆ currentMaterial

◆ expStopPower125

◆ fParticleChange

◆ fPSTAR

◆ iMolecula

◆ iPSTAR

◆ isInitialised

◆ isIon

◆ lowestKinEnergy

◆ mass

◆ massRate

◆ particle

◆ protonMassAMU

◆ ratio

◆ spin

◆ theElectron

◆ theZieglerFactor