G4BetaDecayCorrections Class Reference

#include <G4BetaDecayCorrections.hh>

Public Member Functions
	G4BetaDecayCorrections (const G4int Z, const G4int A)
	~G4BetaDecayCorrections ()
G4double	FermiFunction (const G4double &W)
G4double	ShapeFactor (const G4BetaDecayType &, const G4double &p_e, const G4double &e_nu)

Detailed Description

Definition at line 36 of file G4BetaDecayCorrections.hh.

Constructor & Destructor Documentation

G4BetaDecayCorrections()

G4BetaDecayCorrections::G4BetaDecayCorrections	(	const G4int	Z,
		const G4int	A )

Definition at line 33 of file G4BetaDecayCorrections.cc.

 : Z(theZ), A(theA)
{
  // alphaZ = fine_structure_const*std::abs(Z);
  alphaZ = fine_structure_const*Z;
 
  // Nuclear radius in units of hbar/m_e/c
  G4double a13 = G4Pow::GetInstance()->Z13(A);
  Rnuc = 0.5*fine_structure_const*a13;
 
  // Electron screening potential in units of electron mass
  V0 = 1.13*fine_structure_const*fine_structure_const
           *std::pow(std::abs(Z), 4./3.);
 
  gamma0 = std::sqrt(1. - alphaZ*alphaZ);
 
  // Largest allowed value of im argument in ModSquared
//  imMax = std::log(DBL_MAX)/pi;
  imMax = 200.;   // actual value = 225.931, but use 200 to be safe
//  G4cout << " imMax = " << imMax << G4endl; 
 
  // Coefficients for gamma function with real argument
  gc[0] = -0.1010678;
  gc[1] =  0.4245549;
  gc[2] = -0.6998588;
  gc[3] =  0.9512363;
  gc[4] = -0.5748646;
  gc[5] = 1.0;
}

~G4BetaDecayCorrections()

G4BetaDecayCorrections::~G4BetaDecayCorrections ( )

inline

Definition at line 41 of file G4BetaDecayCorrections.hh.

{};

Member Function Documentation

FermiFunction()

G4double G4BetaDecayCorrections::FermiFunction

(

const G4double &

W

)

Definition at line 64 of file G4BetaDecayCorrections.cc.

{
  // Calculate the relativistic Fermi function.  Argument W is the
  // total electron energy in units of electron mass.
  // Ref: E. Feenberg, G. Trigg, Reviews of Modern Physics, 22(1950)
 
  G4double Wprime;
  if (Z < 0) {
    Wprime = W + V0;
  } else {
    Wprime = W - V0;
//    if (Wprime < 1.) Wprime = W;
    if (Wprime <= 1.00001) Wprime = 1.00001;
  }
 
  G4double p_e = std::sqrt(Wprime*Wprime - 1.);
  G4double eta = alphaZ*Wprime/p_e;
  G4double epieta = std::exp(pi*eta);
  G4double realGamma = Gamma(2.*gamma0+1);
  G4double mod2Gamma = ModSquared(gamma0, eta);
 
  // Fermi function
  G4double factor1 = 2*(1+gamma0)*mod2Gamma/realGamma/realGamma;
  G4double factor2 = epieta*std::pow(2*p_e*Rnuc, 2*(gamma0-1) );
 
  // Electron screening factor
  G4double factor3 = (Wprime/W)*std::sqrt( (Wprime*Wprime - 1.)/(W*W - 1.) );
 
  return factor1*factor2*factor3;
}

ShapeFactor()

G4double G4BetaDecayCorrections::ShapeFactor	(	const G4BetaDecayType &	bdt,
		const G4double &	p_e,
		const G4double &	e_nu )

Definition at line 144 of file G4BetaDecayCorrections.cc.

{
  G4double twoPR = 2.*p_e*Rnuc;
  G4double factor(1.);
 
  switch (bdt)
  {
    case (allowed) :
      break;
 
    case (firstForbidden) :
      {
        // Parameters for 1st forbidden shape determined from 210Bi data
        // Not valid for other 1st forbidden nuclei
        G4double c1 = 0.578;
        G4double c2 = 28.466;
        G4double c3 = -0.658;
 
        G4double w = std::sqrt(1. + p_e*p_e);
        factor = 1. + c1*w + c2/w + c3*w*w;
      }
      break;
 
    case (uniqueFirstForbidden) :
      {
        G4double eta = alphaZ*std::sqrt(1. + p_e*p_e)/p_e;
        G4double gamma1 = std::sqrt(4. - alphaZ*alphaZ);
        G4double gamterm1 = Gamma(2.*gamma0+1.)/Gamma(2.*gamma1+1.);
        G4double term1 = e_nu*e_nu*(1. + gamma0)/6.;
        G4double term2 = 12.*(2. + gamma1)*p_e*p_e
                            *std::pow(twoPR, 2.*(gamma1-gamma0-1) )
                            *gamterm1*gamterm1
                            *ModSquared(gamma1, eta)/ModSquared(gamma0, eta);
        factor = term1 + term2;
      }
      break;
 
    case (secondForbidden) :
      break;
 
    case (uniqueSecondForbidden) :
      {
        G4double eta = alphaZ*std::sqrt(1. + p_e*p_e)/p_e;
        G4double gamma1 = std::sqrt(4. - alphaZ*alphaZ);
        G4double gamma2 = std::sqrt(9. - alphaZ*alphaZ);
        G4double gamterm0 = Gamma(2.*gamma0+1.);
        G4double gamterm1 = gamterm0/Gamma(2.*gamma1+1.);
        G4double gamterm2 = gamterm0/Gamma(2.*gamma2+1.);
        G4double term1 = e_nu*e_nu*e_nu*e_nu*(1. + gamma0)/60.;
 
        G4double term2 = 4.*(2. + gamma1)*e_nu*e_nu*p_e*p_e
                           *std::pow(twoPR, 2.*(gamma1-gamma0-1.) )
                           *gamterm1*gamterm1
                           *ModSquared(gamma1, eta)/ModSquared(gamma0, eta);
 
        G4double term3 = 180.*(3.+gamma2)*p_e*p_e*p_e*p_e
                             *std::pow(twoPR, 2.*(gamma2-gamma0-2) )
                             *gamterm2*gamterm2
                             *ModSquared(gamma2, eta)/ModSquared(gamma0, eta);
 
        factor = term1 + term2 + term3;
      }
      break;
 
    case (thirdForbidden) :
      break;
 
    case (uniqueThirdForbidden) :
      {
        G4double eta = alphaZ*std::sqrt(1. + p_e*p_e)/p_e;
        G4double gamma1 = std::sqrt(4. - alphaZ*alphaZ);
        G4double gamma2 = std::sqrt(9. - alphaZ*alphaZ);
        G4double gamma3 = std::sqrt(16. - alphaZ*alphaZ);
        G4double gamterm0 = Gamma(2.*gamma0+1.);
        G4double gamterm1 = gamterm0/Gamma(2.*gamma1+1.);
        G4double gamterm2 = gamterm0/Gamma(2.*gamma2+1.);
        G4double gamterm3 = gamterm0/Gamma(2.*gamma3+1.);
 
        G4double term1 = e_nu*e_nu*e_nu*e_nu*e_nu*e_nu*(1. + gamma0)/1260.;
 
        G4double term2 = 2.*(2. + gamma1)*e_nu*e_nu*e_nu*e_nu*p_e*p_e
                           *std::pow(twoPR, 2.*(gamma1-gamma0-1.) )
                           *gamterm1*gamterm1
                           *ModSquared(gamma1, eta)/ModSquared(gamma0, eta)/5.;
 
        G4double term3 = 60.*(3.+gamma2)*p_e*p_e*p_e*p_e*e_nu*e_nu
                             *std::pow(twoPR, 2.*(gamma2-gamma0-2.) )
                             *gamterm2*gamterm2
                             *ModSquared(gamma2, eta)/ModSquared(gamma0, eta);
 
        G4double term4 = 2240.*p_e*p_e*p_e*p_e*p_e*p_e*(4. + gamma3)
                             *std::pow(twoPR, 2.*(gamma3-gamma0-3.) )
                             *gamterm3*gamterm3
                             *ModSquared(gamma3, eta)/ModSquared(gamma0, eta);
 
        factor = term1 + term2 + term3 + term4;
      }
      break;
 
    default:
      G4Exception("G4BetaDecayCorrections::ShapeFactor()","HAD_RDM_010",
                  JustWarning,
                  "Transition not yet implemented - using allowed shape");
      break;
  }
 
  return factor;
}

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

• G4BetaDecayCorrections.hh
• G4BetaDecayCorrections.cc