KokoulinPetrukhinModel Class Reference

Kokoulin-Petrukhin model for direct e+e- pair production by muons 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 <KokoulinPetrukhinModel.h>

Inheritance diagram for KokoulinPetrukhinModel:

List of all members.

Public Member Functions
	KokoulinPetrukhinModel ()
	KokoulinPetrukhinModel (const Material &material)
	~KokoulinPetrukhinModel ()
double	dE_dx (double E) const
ValidityRange_t	ValidityRange (void) const
Private Member Functions
double	bpair (double E) const
double	V_min (double E) const
double	V_max (double E) const
double	P_max (double v, double E) const
double	d2s_dvdp (double v, double p, double E) const
double	FIe (double v, double p, double E) const
double	FIm (double v, double p, double E) const
double	Le (double v, double p, double E) const
double	Lm (double v, double p, double E) const
double	Ye (double v, double p) const
double	Ym (double v, double p) const

---

Detailed Description

Kokoulin-Petrukhin model for direct e+e- pair production by muons as described in: W.Lohmann, R.Kopp and R.Voss, Energy Loss of Muons in the Energy Range 1-10000 GeV, CERN 85-03.

________________________________________________________________________________________

Id

KokoulinPetrukhinModel.cxx,v 1.2 2004/01/05 16:11:13 costas Exp

MuELoss

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

Definition at line 22 of file KokoulinPetrukhinModel.h.

---

Constructor & Destructor Documentation

KokoulinPetrukhinModel::KokoulinPetrukhinModel (   )

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

KokoulinPetrukhinModel::KokoulinPetrukhinModel (  const Material &  material  )

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

KokoulinPetrukhinModel::~KokoulinPetrukhinModel (   )

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

---

Member Function Documentation

double KokoulinPetrukhinModel::bpair (  double  E  )  const [private]

Definition at line 61 of file KokoulinPetrukhinModel.cxx. References Material::A(), d2s_dvdp(), Integrator::Instance(), P_max(), Integrator::Simpson(), V_max(), and V_min(). Referenced by dE_dx(). { // Purpose: get the b factor for e+e- pair production from muons ( -dE/dx = b*E ) // Input : E, muon energy in MeV // Output : b factor in cm^2 / gr const int kNV = 300; const int kNP = 300; assert(E>=0); Integrator * integrator = Integrator::Instance(); double Vmin = V_min(E); double Vmax = V_max(E); double dV = (Vmax-Vmin)/kNV; double * vds_dv = new double[kNV]; for(int iv = 0; iv < kNV; iv++) { double v = Vmin + (iv+1) * dV; double Pmin = 0; double Pmax = P_max(v, E); if(Pmax < 0) return 0; // put this here for now so as not to hit an assert() below... // Eventually I need to solve Pmax(E) > 0 for E, and combine it // with the E limit from Vmax in the validity range of the model double dP = (Pmax-Pmin)/kNP; double * d2s = new double[kNP]; for(int ip = 0; ip < kNP; ip++) d2s[ip] = d2s_dvdp(v, (Pmin + (ip+1) * dP) ,E); vds_dv[iv] = v * integrator->Simpson(d2s, kNP, dP); delete [] d2s; } // v double integral = integrator->Simpson(vds_dv, kNV, dV); delete [] vds_dv; // factor 10 is for dimensions: // 10 : v*ds/dv(integral) in 10^22 cm2 -- N->N*10^(-23) -> b in 0.1 cm2/gr return 10* ( 2*MuELoss::Na / fMaterial.A() ) * integral; }

double KokoulinPetrukhinModel::d2s_dvdp (  double  v, double  p, double  E )  const [private]

Definition at line 113 of file KokoulinPetrukhinModel.cxx. References FIe(), FIm(), and Material::Z(). Referenced by bpair(). { // Calculate the differential cross section d^2s/dpdv (in 10^22 cm^2) for e+e- pair production // by muons based on the Kokoulin,Petrukhin parameterization // Input : v, the fraction of the energy transfered to the e+e- pair // p, the asymmetry parameter of the e+e- pair p = (E(+) - E(-)) / (E(+) + E(-)) // E, muon energy in MeV // assert(v>=0); assert(p>=0); assert(E>=0); double a4 = MuELoss::a_4; double pi = MuELoss::pi; double ZLe2 = pow(fMaterial.Z()*MuELoss::Le,2.); double me_mm_2 = MuELoss::Me_Mm_2; double fie = FIe(v,p,E); double fim = FIm(v,p,E); return a4 * (2./(3.*pi)) * ZLe2 * ( (1.-v)/v ) * ( fie + fim * me_mm_2 ); }

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

Implements ProcessModel. Definition at line 53 of file KokoulinPetrukhinModel.cxx. References bpair(). { // Calculates the muon -dE/dx in ( MeV cm^2 / gr ) due to e+e- pair production // Input : E, muon energy in MeV return bpair(E) * E; }

double KokoulinPetrukhinModel::FIe (  double  v, double  p, double  E )  const [private]

Definition at line 135 of file KokoulinPetrukhinModel.cxx. References Le(). Referenced by d2s_dvdp(). { // Approximate the FIe factor (dimensionless) from pair production cross section // Input : v, the fraction of the energy transfered to the e+e- pair // p, the asymmetry parameter of the e+e- pair p = (E(+) - E(-)) / (E(+) + E(-)) // E, muon energy in MeV // double b = v*v / (2*(1-v)); double p2 = p*p; double xi = (1.-p2) * pow( 0.5 *v *MuELoss::Mm_Me , 2.) / (1-v); double A = ( (2.+p2) * (1.+b) + xi*(3.+p2) ) * log(1.+1./xi); double B = (1.-p2-b) / (1.+xi); double C = 3. + p2; return (A+B-C)*Le(v,p,E); }

double KokoulinPetrukhinModel::FIm (  double  v, double  p, double  E )  const [private]

Definition at line 152 of file KokoulinPetrukhinModel.cxx. References Lm(). Referenced by d2s_dvdp(). { // Approximates the factor FIm factor (dimensionless) from pair production cross section // Input : v, the fraction of the energy transfered to the e+e- pair // p, the asymmetry parameter of the e+e- pair p = (E(+) - E(-)) / (E(+) + E(-)) // E, muon energy in MeV // double b = v*v / (2*(1-v)); double p2 = p*p; double xi = (1.-p2) * pow( 0.5 *v *MuELoss::Mm_Me , 2.) / (1-v); double A = ( (1.+p2)*(1.+3.*b/2.) - (1.+2.*b)*(1.-p2)/xi ) * log(1.+xi); double B = xi * (1. - p2 - b) / (1.+xi); double C = (1.+2.*b) * (1.-p2); return (A+B+C)*Lm(v,p,E); }

double KokoulinPetrukhinModel::Le (  double  v, double  p, double  E )  const [private]

Definition at line 169 of file KokoulinPetrukhinModel.cxx. References C, Ye(), and Material::Z(). Referenced by FIe(). { // Approximates the Le factor (dimensionless) appearing in the factor FIe at pair production xsec // Input : v, the fraction of the energy transfered to the e+e- pair // p, the asymmetry parameter of the e+e- pair p = (E(+) - E(-)) / (E(+) + E(-)) // E, muon energy in MeV // double p2 = p*p; double xi = (1.-p2) * pow( 0.5 *v *MuELoss::Mm_Me , 2.) / (1-v); double Y = Ye(v,p); double Z_13 = pow(fMaterial.Z(),-1./3.); double Z13 = pow(fMaterial.Z(), 1./3.); double MeR = MuELoss::Me * MuELoss::R; double x_Y = (1+xi)*(1+Y); double A = MuELoss::R * Z_13 * sqrt( x_Y ); double B = 1. + (2. * MeR * MuELoss::sqrt_e * Z_13 * x_Y) / ( E*v*(1-p2) ); double C = 1.5 * MuELoss::Me_Mm * Z13; double D = 1 + C*C*x_Y; return log(A/B) - 0.5 * log(D); }

double KokoulinPetrukhinModel::Lm (  double  v, double  p, double  E )  const [private]

Definition at line 192 of file KokoulinPetrukhinModel.cxx. References Ym(), and Material::Z(). Referenced by FIm(). { // Approximates the Lm factor (dimensioness) appearing in the factor FIm at pair production xsec // Input : v, the fraction of the energy transfered to the e+e- pair // p, the asymmetry parameter of the e+e- pair p = (E(+) - E(-)) / (E(+) + E(-)) // E, muon energy in MeV double p2 = p*p; double xi = (1.-p2) * pow( 0.5 *v *MuELoss::Mm_Me , 2.) / (1-v); double Y = Ym(v,p); double Z_13 = pow(fMaterial.Z(),-1/3.); double Z_23 = pow(fMaterial.Z(),-2/3.); double MeR = MuELoss::Me * MuELoss::R; double A = (2./3.) * MuELoss::Mm_Me * MuELoss::R * Z_23; double B = 1. + ( 2. * MeR * MuELoss::sqrt_e * Z_13 * (1+xi) * (1+Y) ) / ( E*v*(1-p2) ); return log(A/B); }

double KokoulinPetrukhinModel::P_max (  double  v, double  E )  const [private]

Definition at line 251 of file KokoulinPetrukhinModel.cxx. Referenced by bpair(). { return (1. - 6.*MuELoss::Mm_2 / (E*E*(1.-v)) ) * sqrt(1.-4.*MuELoss::Me/(E*v)); }

double KokoulinPetrukhinModel::V_max (  double  E  )  const [private]

Definition at line 244 of file KokoulinPetrukhinModel.cxx. References Material::Z(). Referenced by bpair(). { // Maximum value of parameter v = E(+)+(E-)/E return 1.- 3.* MuELoss::sqrt_e * MuELoss::Mm * pow(fMaterial.Z(), 1./3.) / (4.*E); }

double KokoulinPetrukhinModel::V_min (  double  E  )  const [private]

Definition at line 237 of file KokoulinPetrukhinModel.cxx. Referenced by bpair(). { // Minimum value of parameter v = E(+)+(E-)/E return 4.*MuELoss::Me/E; }

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

Implements ProcessModel. Definition at line 43 of file KokoulinPetrukhinModel.cxx. References ValidityRange::Emax, ValidityRange::Emin, ValidityRange_t, and Material::Z(). { ValidityRange_t validity_range; validity_range.Emin = 0.75*sqrt(MuELoss::e)*(MuELoss::Mm)*pow(fMaterial.Z(), 1./3.); validity_range.Emax = 10000000.; // MeV return validity_range; }

double KokoulinPetrukhinModel::Ye (  double  v, double  p )  const [private]

Definition at line 211 of file KokoulinPetrukhinModel.cxx. Referenced by Le(). { // Approximates the Ye factor (dimensionless) in the factor Le at pair production xsec // Input : v, the fraction of the energy transfered to the e+e- pair // p, the asymmetry parameter of the e+e- pair p = (E(+) - E(-)) / (E(+) + E(-)) // double b = v*v / (2*(1-v)); double p2 = p*p; double xi = (1.-p2) * pow( 0.5 *v *MuELoss::Mm_Me , 2.) / (1-v); return ( 5. - p2 + 4*b*(1+p2) ) / ( 2.*(1.+3.*b)*log(3.+1./xi) - p2 - 2.*b*(2.-p2) ); }

double KokoulinPetrukhinModel::Ym (  double  v, double  p )  const [private]

Definition at line 224 of file KokoulinPetrukhinModel.cxx. Referenced by Lm(). { // Approximates the Ym factor (dimensionless) in the factor Lm at pair production xsec // Input : v, the fraction of the energy transfered to the e+e- pair // p, the asymmetry parameter of the e+e- pair p = (E(+) - E(-)) / (E(+) + E(-)) // double b = v*v / (2*(1-v)); double p2 = p*p; double xi = (1.-p2) * pow( 0.5 *v *MuELoss::Mm_Me , 2.) / (1-v); return ( 4. + p2 + 3.*b*(1.+p2) ) / ( (1.+p2)*(1.5+2.*b)*log(3.+xi) + 1. - 1.5*p2 ); }

---

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

• KokoulinPetrukhinModel.h
• KokoulinPetrukhinModel.cxx

---