BetheBlochModel Class Reference

Bethe-Bloch model for Muon Ionization as described in: W.Lohmann, R.Kopp and R.Voss, Energy Loss of Muons in the Energy Range 1-10000 GeV, CERN 85-03. More...

#include <BetheBlochModel.h>

Inheritance diagram for BetheBlochModel:

List of all members.

Public Member Functions
	BetheBlochModel ()
	BetheBlochModel (const Material &material)
	~BetheBlochModel ()
double	dE_dx (double E) const
ValidityRange_t	ValidityRange (void) const
Private Member Functions
double	MaximumEnergyTransfer (double E) const
double	DensityCorrectionFactor (double E) const

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Detailed Description

Bethe-Bloch model for Muon Ionization as described in: W.Lohmann, R.Kopp and R.Voss, Energy Loss of Muons in the Energy Range 1-10000 GeV, CERN 85-03.

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Id

BetheBlochModel.cxx,v 1.2 2004/01/05 16:11:12 costas Exp

MuELoss

Costas Andreopoulos <C.V.Andreopoulos@rl.ac.uk> CCLRC, Rutherford Lab. December 10, 2003 _________________________________________________________________________________________

Definition at line 22 of file BetheBlochModel.h.

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Constructor & Destructor Documentation

BetheBlochModel::BetheBlochModel (   )

Definition at line 26 of file BetheBlochModel.cxx. 00026 : 00027 ProcessModel() 00028 { 00029 00030 } //_________________________________________________________________________________________

BetheBlochModel::BetheBlochModel (  const Material &  material  )

Definition at line 32 of file BetheBlochModel.cxx. 00032 : 00033 ProcessModel(material, Process::eIonization) 00034 { 00035 00036 } //_________________________________________________________________________________________

BetheBlochModel::~BetheBlochModel (   )

Definition at line 38 of file BetheBlochModel.cxx. { }

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Member Function Documentation

double BetheBlochModel::dE_dx (  double  E  )  const [virtual]

Implements ProcessModel. Definition at line 53 of file BetheBlochModel.cxx. References Material::A(), Utils::BetaFactor(), DensityCorrectionFactor(), Utils::GammaFactor(), Material::IonPotential(), MaximumEnergyTransfer(), and Material::Z(). { // Calculates ionization dE/dx for muons via Bethe-Bloch formula in MeV / (gr/cm^2) // Input : E, muon energy in MeV double a_2 = MuELoss::a_2; double pi = MuELoss::pi; double Na = MuELoss::Na; // in 10^-23 double lamda_2 = MuELoss::Le_2; // in 10^22 cm^2 double Z_A = fMaterial.Z() / fMaterial.A(); // in mol/gr double me = MuELoss::Me; // in MeV double beta = Utils::BetaFactor(MuELoss::Mm, E); double beta_2 = beta*beta; double gamma = Utils::GammaFactor(MuELoss::Mm, E); double gamma_2 = gamma*gamma; double I = 1e-6 * fMaterial.IonPotential(); // in MeV (ionization potential) double I_2 = I*I; // in MeV^2 double Em = MaximumEnergyTransfer(E); // in MeV^2 double Em_2 = Em*Em; // in MeV^2 double E_2 = E*E; // in MeV^2 double d = DensityCorrectionFactor(E); double de_dx = a_2 * 2*pi * Na * lamda_2 * Z_A * (me / beta_2) * ( log( 2*me*beta_2*gamma_2*Em/I_2 ) - 2*beta_2 + 0.25*(Em_2/E_2) - d ); // fix units... Compton wavelength ^2 is multiplied by 10^22 cm^2, // Avogadro's number is in 10^-23. // need to multiply by 10 return 10*de_dx; // in MeV/(gr/cm^2) }

double BetheBlochModel::DensityCorrectionFactor (  double  E  )  const [private]

Definition at line 100 of file BetheBlochModel.cxx. References Material::a(), Utils::BetaFactor(), Material::C(), Utils::GammaFactor(), Material::m(), Material::X0(), and Material::X1(). Referenced by dE_dx(). { // Calculates the density correction factor delta // Input : muon energy (MeV) // Looking at R.M.Sternheimer (BNL), Density Effect for the BetheBlochModel Loss in Various // Materials, Phys. Rev. 103, 511 (1956): // For Fe: X1 = 3, X0 = 0.10. a = 0.127, m = 3.29, C = -4.62 // Also Table 1, at YR. const double X0 = fMaterial.X0(); const double X1 = fMaterial.X1(); const double a = fMaterial.a(); const double m = fMaterial.m(); const double C = fMaterial.C(); const double beta = Utils::BetaFactor(MuELoss::Mm, E); const double gamma = Utils::GammaFactor(MuELoss::Mm, E); const double X = log10( beta*gamma ); if(X0 < X && X < X1) return ( 4.6052 * X + a * pow(X1-X,m) + C ); // X e (X0, X1) if(X > X1) return ( 4.6052 * X + C); // X e (X1, oo) return 0; // presumably valid in case X < X0 }

double BetheBlochModel::MaximumEnergyTransfer (  double  E  )  const [private]

Definition at line 85 of file BetheBlochModel.cxx. References Utils::E2P(). Referenced by dE_dx(). { // Calculates the maximum energy transfer to the electron (in MeV) // Input : muon energy (MeV) double me = MuELoss::Me; double me_2 = MuELoss::Me_2; double mm = MuELoss::Mm; double mm_2 = MuELoss::Mm_2; double p = Utils::E2P(mm, E); double p_2 = p*p; return 2 * me * p_2 / ( me_2 + mm_2 + 2*me*E ); }

ValidityRange_t BetheBlochModel::ValidityRange (  void   )  const [virtual]

Implements ProcessModel. Definition at line 43 of file BetheBlochModel.cxx. References ValidityRange::Emax, ValidityRange::Emin, and ValidityRange_t. { ValidityRange_t validity_range; validity_range.Emin = 0; validity_range.Emax = 10000000.; // MeV return validity_range; }

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

• BetheBlochModel.h
• BetheBlochModel.cxx

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