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Public Member Functions | Protected Member Functions | Static Protected Member Functions | Protected Attributes | List of all members
JPHYSICS::JRadiation Class Reference

Auxiliary class for the calculation of the muon radiative cross sections. More...

#include <JRadiation.hh>

Inheritance diagram for JPHYSICS::JRadiation:
JPHYSICS::JRadiationFunction

Public Member Functions

virtual ~JRadiation ()
 Virtual desctructor.
 
 JRadiation (const double z, const double a, const int integrsteps, const double eminBrems, const double eminEErad, const double eminGNrad)
 Constructor.
 
double SigmaEErad (const double E, const double eps) const
 Pair production cross section.
 
virtual double TotalCrossSectionEErad (const double E) const
 Pair production cross section.
 
double TotalCrossSectionBrems (const double E) const
 Bremsstrahlung cross section.
 
virtual double SigmaGNrad (const double E, const double eps) const
 Photo-nuclear cross section.
 
virtual double TotalCrossSectionGNrad (const double E) const
 Photo-nuclear cross section.
 
double EfromBrems (const double E) const
 Bremsstrahlung shower energy.
 
double ThetaRMSfromBrems (const double E, const double v) const
 Get RMS of scattering angle for Bremsstrahlung.
 
double EfromEErad (const double E) const
 Pair production shower energy.
 
double ThetaRMSfromEErad (const double E, const double v) const
 Get RMS of scattering angle for pair production.
 
double EfromGNrad (const double E) const
 Photo-nuclear shower energy.
 
double ThetaRMSfromGNrad (const double E, const double v) const
 Get RMS of scattering angle for photo-nuclear shower.
 
virtual double CalculateACoeff (double E) const
 Ionization a parameter.
 

Protected Member Functions

double GofZEvrho (const double E, const double v, const double r) const
 
virtual double IntegralofG (const double E, const double eps) const
 

Static Protected Member Functions

static double sigmaGammaPparam (const double eps)
 
static double PhiofEofepsparam (const double E, const double eps)
 
static double le ()
 
static double r0 ()
 
static double Astar ()
 
static double B ()
 
static double BP ()
 

Protected Attributes

const double Z
 
const double A
 
const double Dn
 
const double DnP
 
const int steps
 
const double EminBrems
 
const double EminEErad
 
const double EminGNrad
 

Detailed Description

Auxiliary class for the calculation of the muon radiative cross sections.

Author
P. Kooijman

Bremsstrahlung and pair production cross sections are taken from Particle Data Group.

Gamma-nucleon cross section: Phys. Lett. B\ Vol. 697-3 (2011) 184-193.

Definition at line 36 of file JRadiation.hh.

Constructor & Destructor Documentation

◆ ~JRadiation()

virtual JPHYSICS::JRadiation::~JRadiation ( )
inlinevirtual

Virtual desctructor.

Definition at line 42 of file JRadiation.hh.

43 {}

◆ JRadiation()

JPHYSICS::JRadiation::JRadiation ( const double z,
const double a,
const int integrsteps,
const double eminBrems,
const double eminEErad,
const double eminGNrad )
inline

Constructor.

Parameters
znumber of protons
anumber of nucleons
integrstepsnumber of integration steps
eminBremsenergy threshold Bremsstrahlung [GeV]
eminEEradenergy threshold pair production [GeV]
eminGNradenergy threshold photo-production [GeV]

Definition at line 56 of file JRadiation.hh.

61 :
62 Z(z),
63 A(a),
64 Dn (1.54*pow(A,0.27)),
65 DnP (pow(Dn,(1-1/Z))),
66 steps(integrsteps),
67 EminBrems(eminBrems),
68 EminEErad(eminEErad),
69 EminGNrad(eminGNrad)
70 {}
JPHYSICS::JRadiation::EminBrems
const double EminBrems
Definition JRadiation.hh:496
JPHYSICS::JRadiation::EminEErad
const double EminEErad
Definition JRadiation.hh:497
JPHYSICS::JRadiation::EminGNrad
const double EminGNrad
Definition JRadiation.hh:498
JMATH::pow
T pow(const T &x, const double y)
Power .
Definition JMath.hh:97

Member Function Documentation

◆ SigmaEErad()

double JPHYSICS::JRadiation::SigmaEErad ( const double E,
const double eps ) const
inline

Pair production cross section.

Parameters
Emuon energy [GeV]
epsshower energy [GeV]
Returns
cross section [m^2/g]

Definition at line 80 of file JRadiation.hh.

82 {
83 //routine to calculate dsigma/de in cm^2/GeV for radiating a photon of energy eps
84
85 if(eps<4.*MASS_ELECTRON)return 0.;
86 if(eps>E-0.75*exp(1.0)*pow(Z,1./3.)) return 0.;
87 double zeta;
88 if(E<35.*MASS_MUON)
89 {
90 zeta = 0.;
91 }
92 else
93 {
94 zeta = (0.073*log((E/MASS_MUON)/(1.+1.95e-5*pow(Z,2./3.)*E/MASS_MUON))-0.26);
95 if(zeta<0.)
96 {
97 zeta=0.;
98 }
99 else
100 {
101 zeta = zeta/(0.058*log((E/MASS_MUON)/(1.+5.3e-5*pow(Z,1./3.)*E/MASS_MUON))-0.14);
102 }
103 }
104 double integ = IntegralofG(E,eps);
105 //cout<< eps<<" integ "<< integ<<endl;
106 return integ*(4/(3.*M_PI))*(Z*(Z+zeta)/A)*AVOGADRO*pow((ALPHA_ELECTRO_MAGNETIC*r0()),2.)*(1-eps/E)/eps;
107 }
JPHYSICS::JRadiation::IntegralofG
virtual double IntegralofG(const double E, const double eps) const
Definition JRadiation.hh:446
JPHYSICS::JRadiation::r0
static double r0()
Definition JRadiation.hh:486
JPHYSICS::ALPHA_ELECTRO_MAGNETIC
static const double ALPHA_ELECTRO_MAGNETIC
Electro-Magnetic coupling constant.
Definition JPhysics/JConstants.hh:32
JPHYSICS::MASS_ELECTRON
static const double MASS_ELECTRON
electron mass [GeV]
Definition JPhysics/JConstants.hh:68
JPHYSICS::AVOGADRO
static const double AVOGADRO
Avogadro's number.
Definition JPhysics/JConstants.hh:27

◆ TotalCrossSectionEErad()

virtual double JPHYSICS::JRadiation::TotalCrossSectionEErad ( const double E) const
inlinevirtual

Pair production cross section.

Parameters
Emuon energy [GeV]
Returns
cross section [m^2/g]

Reimplemented in JPHYSICS::JRadiationFunction.

Definition at line 116 of file JRadiation.hh.

117 {
118 //cout<<" entering TotcrsecEErad"<<endl;
119 // radiation goes approx as 1/E so sample in log E
120 // calculate the total cross section as S(dsigma/de)*de
121 // start at E and go backwards for precision
122 double sum(0.);
123 double dle = log(E/EminEErad)/steps;
124 //cout << "dle "<< dle<<endl;
125 for(int i=0;i<steps+1;i++)
126 {
127 double factor = 1.0;
128 if(i==0 || i==steps)factor=0.5;
129 //cout<<"i"<<i<<endl;
130 double eps = EminEErad*exp(i*dle);sum += factor*eps*SigmaEErad( E, eps);
131 //cout<<"eps "<<eps<<" sum "<<sum<<endl;
132 }
133 return sum*dle;
134 }
JPHYSICS::JRadiation::SigmaEErad
double SigmaEErad(const double E, const double eps) const
Pair production cross section.
Definition JRadiation.hh:80

◆ TotalCrossSectionBrems()

double JPHYSICS::JRadiation::TotalCrossSectionBrems ( const double E) const
inline

Bremsstrahlung cross section.

Parameters
Emuon energy [GeV]
Returns
cross section [m^2/g]

Definition at line 144 of file JRadiation.hh.

145 {
146 // double delta = (MASS_MUON*MASS_MUON*eps)/(2*E*(E-eps));
147 double delta = (MASS_MUON*MASS_MUON)/(2*E);
148 //double v = eps/E;
149 double Phin = log((B()*pow(Z,-1./3.)*(MASS_MUON+delta*(DnP*sqrt(exp(1.0))-2.)))/(DnP*(MASS_ELECTRON+delta*sqrt(exp(1.0))*B()*pow(Z,-1./3.))));
150 if(Phin<0.)Phin=0.;
151 double Phie = log((BP()*pow(Z,-2./3.)*MASS_MUON)/((1+delta*MASS_MUON/(MASS_ELECTRON*MASS_ELECTRON*sqrt(exp(1.0))))*(MASS_ELECTRON+delta*sqrt(exp(1.0))*BP()*pow(Z,-2./3.))));
152 if(Phie<0.)Phie=0.;
153 //if(eps>E/(1+MASS_MUON*MASS_MUON/(2.*MASS_ELECTRON*E)))Phie=0.;
154 double sig = (16./3.)*ALPHA_ELECTRO_MAGNETIC*AVOGADRO*pow((MASS_ELECTRON/MASS_MUON*r0()),2.0)*Z*(Z*Phin+Phie)/(A);
155 double epsint = log((E-MASS_MUON)/EminBrems)-(E-MASS_MUON-EminBrems)/E+0.375*(pow(E-MASS_MUON,2.)-pow(EminBrems,2.0))/pow(E,2.0);
156 return epsint*sig;//"cross section" in m^2/g multiplied by density and inverted gives mean free path
157 }
JPHYSICS::JRadiation::B
static double B()
Definition JRadiation.hh:488
JPHYSICS::JRadiation::BP
static double BP()
Definition JRadiation.hh:489
JPHYSICS::MASS_MUON
static const double MASS_MUON
muon mass [GeV]
Definition JPhysics/JConstants.hh:69

◆ SigmaGNrad()

virtual double JPHYSICS::JRadiation::SigmaGNrad ( const double E,
const double eps ) const
inlinevirtual

Photo-nuclear cross section.

Parameters
Emuon energy [GeV]
epsshower energy [GeV]
Returns
cross section [m^2/g]

Definition at line 167 of file JRadiation.hh.

168 {
169
170 //minimum radiated energy is 0.2 GeV, not very critical formulae become invalid for very much lower
171 //result is given in m^2/g GeV
172 if (eps<0.2) return 0.;
173 if (eps>E-MASS_PROTON) return 0.;
174 double Aeff;
175 if (A==1)
176 {Aeff = 1.;}
177 else
178 {Aeff = (0.22*A + 0.78 * pow(A,0.89));}
179 double sigmaGammaPofeps = (49.2 + 11.1 * log(eps) + 151.8/sqrt(eps))*pow(10,-34.);
180 double Psiofeps = ALPHA_ELECTRO_MAGNETIC/PI*Aeff*AVOGADRO/A*sigmaGammaPofeps/eps;
181 double Denom = 1+eps/LAMBDA*(1+LAMBDA/(2*MASS_PROTON)+eps/LAMBDA);
182 double epsoverE = eps/E;
183 double Numerator = E * E * (1 - epsoverE) / (MASS_MUON * MASS_MUON) * (1 + MASS_MUON * MASS_MUON * epsoverE * epsoverE / (LAMBDA * LAMBDA * (1 - epsoverE)));
184 double Factor = 1 - epsoverE + epsoverE * epsoverE / 2 * (1 + 2 * MASS_MUON * MASS_MUON / (LAMBDA * LAMBDA));
185 double PhiofEofeps = epsoverE - 1 + Factor * log (Numerator / Denom);
186 //cout<<"PhiofEofeps "<<PhiofEofeps<<" Psiofeps "<<Psiofeps<<endl;
187 return Psiofeps*PhiofEofeps;
188 }
JPHYSICS::MASS_PROTON
static const double MASS_PROTON
proton mass [GeV]
Definition JPhysics/JConstants.hh:82
LAMBDA
Auxiliary data structure to convert (lambda) function to printable object.
Definition JManip.hh:726

◆ TotalCrossSectionGNrad()

virtual double JPHYSICS::JRadiation::TotalCrossSectionGNrad ( const double E) const
inlinevirtual

Photo-nuclear cross section.

Parameters
Emuon energy [GeV]
Returns
cross section [m^2/g]

Reimplemented in JPHYSICS::JRadiationFunction.

Definition at line 197 of file JRadiation.hh.

198 {
199 double epsmin = 0.2;
200 double epsmax = E-MASS_PROTON/2;
201 double sum(0.);
202 double dle = log(epsmax/epsmin)/steps;
203 for(int i=0;i<steps+1;i++)
204 {
205 float factor = 1.0;
206 if(i==0 || i==steps)factor=0.5;
207 //cout<<"i"<<i<<endl;
208 double eps = epsmin*exp(i*dle);sum += factor*eps*SigmaGNrad( E, eps);
209 //cout<<"eps "<<eps<<" sum "<<sum<<endl;
210 }
211
212 return sum*dle;
213 }
JPHYSICS::JRadiation::SigmaGNrad
virtual double SigmaGNrad(const double E, const double eps) const
Photo-nuclear cross section.
Definition JRadiation.hh:167

◆ EfromBrems()

double JPHYSICS::JRadiation::EfromBrems ( const double E) const
inline

Bremsstrahlung shower energy.

Parameters
Emuon energy [GeV]
Returns
shower energy [GeV]

Definition at line 222 of file JRadiation.hh.

223 {
224 //double EminBrems(0.01);
225 //generate according to 1/k from minimum energy to E
226 double Er = 0.0;
227 for (int i = 1000; i != 0; --i) {
228 Er = EminBrems*exp(gRandom->Rndm()*log(E/EminBrems));
229 //check on the extra factor (1-v+3/4v^2)
230 if(gRandom->Rndm()<(1.-Er/E+0.75*pow(Er/E,2))) break;
231 }
232 return Er;
233 }

◆ ThetaRMSfromBrems()

double JPHYSICS::JRadiation::ThetaRMSfromBrems ( const double E,
const double v ) const
inline

Get RMS of scattering angle for Bremsstrahlung.

Parameters
Emuon energy [GeV]
venergy loss fraction
Returns
angle [rad]

Definition at line 243 of file JRadiation.hh.

244 {
245 using namespace std;
246
247 const double precision = 1.0e-3;
248
249 const double k1 = 0.092 * pow(E, -1.0/3.0);
250 const double k2 = 0.052 * pow(E, -1.0) * pow(Z, -1.0/4.0);
251 const double k3 = 0.220 * pow(E, -0.92);
252 const double k4 = 0.260 * pow(E, -0.91);
253
254 double rms = 0.0;
255
256 if (v <= 0.5) {
257
258 rms = max(min(k1*sqrt(v), k2), k3*v);
259
260 } else {
261
262 const double n = 0.81 * sqrt(E) / (sqrt(E) + 1.8);
263
264 double k5 = 0.0;
265
266 for (double vmin = 0.5, vmax = 1.0; ; ) {
267
268 const double v = 0.5 * (vmin + vmax);
269
270 const double y = k4 * pow(v, 1.0 + n) * pow(1.0 - v, -n);
271
272 if (abs(y - 0.2) <= precision) {
273
274 k5 = y * pow(1.0 - v, 1.0/2.0);
275
276 break;
277 }
278
279 if (y < 0.2)
280 vmin = v;
281 else
282 vmax = v;
283 }
284
285 rms = k4 * pow(v, 1.0 + n) * pow(1.0 - v, -n);
286
287 if (rms >= 0.2) {
288 rms = k5 * pow(1.0 - v, -1.0/2.0);
289 }
290 }
291
292 return rms;
293 }
JTOOLS::n
const int n
Definition JPolint.hh:791

◆ EfromEErad()

double JPHYSICS::JRadiation::EfromEErad ( const double E) const
inline

Pair production shower energy.

Parameters
Emuon energy [GeV]
Returns
shower energy [GeV]

Definition at line 302 of file JRadiation.hh.

303 {
304 //generate according to 1/k from minimum energy to E
305
306 const double eps =0.2;
307 const double IntGmax = IntegralofG(E,eps)*2.0;
308
309 double Er = 0.0;
310 for (int i = 1000; i != 0; --i)
311 {
312 Er = EminEErad*exp(gRandom->Rndm()*log(E/EminEErad));
313 //check on the extra factor, (1-v) and IntofG
314 double factor = (1.-Er/E)*IntegralofG(E,Er)/IntGmax;
315 if(gRandom->Rndm()<factor) break;
316 }
317 return Er;
318 }

◆ ThetaRMSfromEErad()

double JPHYSICS::JRadiation::ThetaRMSfromEErad ( const double E,
const double v ) const
inline

Get RMS of scattering angle for pair production.

Parameters
Emuon energy [GeV]
venergy loss fraction
Returns
angle [rad]

Definition at line 328 of file JRadiation.hh.

329 {
330 using namespace std;
331
332 const double a = 8.9e-4;
333 const double b = 1.5e-5;
334 const double c = 0.032;
335 const double d = 1.0;
336 const double e = 0.1;
337
338 const double n = -1.0;
339
340 const double u = v - 2.0*MASS_ELECTRON/E;
341
342 if (u > 0.0)
343 return (2.3 + log(E)) * (1.0/E) * pow(1.0 - v, n) * (u*u) * (1.0/(v*v)) *
344 min(a * pow(v, 1.0/4.0) * (1.0 + b*E) + c*v/(v+d), e);
345 else
346 return 0.0;
347 }
GAUSS_LAGUERRE::a
const double a
Definition JQuadrature.cc:42

◆ EfromGNrad()

double JPHYSICS::JRadiation::EfromGNrad ( const double E) const
inline

Photo-nuclear shower energy.

Parameters
Emuon energy [GeV]
Returns
shower energy [GeV]

Definition at line 356 of file JRadiation.hh.

357 {
358 //generate according to 1/k from minimum energy to E
359
360 double cmax = sigmaGammaPparam(EminGNrad);
361 if (cmax < sigmaGammaPparam(E))
362 cmax=sigmaGammaPparam(E);
363
364 double Pmax = PhiofEofepsparam(E,EminGNrad);
365
366 double Er = 0.0;
367 for (int i = 1000; i != 0; --i) {
368 Er = EminGNrad*exp(gRandom->Rndm()*log(E/EminGNrad));
369 const double factor = PhiofEofepsparam(E,Er)*sigmaGammaPparam(Er)/(cmax*Pmax);
370 if (gRandom->Rndm() < factor) return Er;
371 }
372
373 return Er;
374 }
JPHYSICS::JRadiation::sigmaGammaPparam
static double sigmaGammaPparam(const double eps)
Definition JRadiation.hh:469
JPHYSICS::JRadiation::PhiofEofepsparam
static double PhiofEofepsparam(const double E, const double eps)
Definition JRadiation.hh:474

◆ ThetaRMSfromGNrad()

double JPHYSICS::JRadiation::ThetaRMSfromGNrad ( const double E,
const double v ) const
inline

Get RMS of scattering angle for photo-nuclear shower.

Parameters
Emuon energy [GeV]
venergy loss fraction
Returns
angle [rad]

Definition at line 384 of file JRadiation.hh.

385 {
386 return 0.0;
387 }

◆ CalculateACoeff()

virtual double JPHYSICS::JRadiation::CalculateACoeff ( double E) const
inlinevirtual

Ionization a parameter.

Parameters
Emuon energy [GeV]
Returns
ionization coefficient [GeV*m^2/g]

Reimplemented in JPHYSICS::JRadiationFunction.

Definition at line 396 of file JRadiation.hh.

397 {
398 const double E2 = E*E;
399 const double beta = sqrt(E2 - MASS_MUON*MASS_MUON) / E;
400 const double beta2 = beta*beta;
401 const double gamma = E/MASS_MUON;
402 const double gamma2 = gamma*gamma;
403
404 const double p2 = E2 - MASS_MUON*MASS_MUON;
405 const double EMaxT = 2.*MASS_ELECTRON*p2 / (MASS_ELECTRON*MASS_ELECTRON + MASS_MUON*MASS_MUON + 2.*MASS_ELECTRON*E);
406 const double EMaxT2 = EMaxT*EMaxT;
407 const JSter& coeff = getSterCoefficient(Z);
408 const double I2 = coeff.I*coeff.I; // in GeV^2
409 const double X = log10(beta*gamma);
410
411 double delta = 0.0;
412
413 if (coeff.X0 < X && X < coeff.X1) {
414 delta = 4.6052*X + coeff.a*pow(coeff.X1-X,coeff.m) + coeff.C;
415 }
416
417 if (X > coeff.X1) {
418 delta = 4.6052*X + coeff.C;
419 }
420
421 double acoeff = (2*PI*AVOGADRO*ALPHA_ELECTRO_MAGNETIC*ALPHA_ELECTRO_MAGNETIC*le()*le())*Z/A*(MASS_ELECTRON/beta2)*(log(2.*MASS_ELECTRON*beta2*gamma2*EMaxT/I2)-2.*beta2+0.25*(EMaxT2/E2)-delta);
422
423 return acoeff;
424 }
JPHYSICS::JRadiation::le
static double le()
Definition JRadiation.hh:485
JPHYSICS::getSterCoefficient
static JSterCoefficient getSterCoefficient
Function object for Ster coefficients.
Definition JIonization.hh:82

◆ GofZEvrho()

double JPHYSICS::JRadiation::GofZEvrho ( const double E,
const double v,
const double r ) const
inlineprotected

Definition at line 427 of file JRadiation.hh.

430 {
431 const double ksi = MASS_MUON*MASS_MUON*v*v*(1-r*r)/(4*MASS_ELECTRON*MASS_ELECTRON*(1-v));//
432 const double b = v*v/(2*(1-v));//
433 const double Be = ((2+r*r)*(1+b)+ksi*(3+r*r))*log(1+1/ksi)+(1-r*r-b)/(1+ksi)-(3+r*r);
434 const double Bm = ((1+r*r)*(1+3*b/2)-(1+2*b)*(1-r*r)/ksi)*log(1+ksi)+ksi*(1-r*r-b)/(1+ksi)+(1+2*b)*(1-r*r);
435 const double Ye = (5-r*r+4*b*(1+r*r))/(2*(1+3*b)*log(3+1/ksi)-r*r-2*b*(2-r*r));
436 const double Ym = (4+r*r+3*b*(1+r*r))/((1+r*r)*(1.5+2*b)*log(3+ksi)+1-1.5*r*r);
437 const double Le = log((Astar()*pow(Z,-1./3.)*sqrt((1+ksi)*(1+Ye)))/
438 (1.+(2.*MASS_ELECTRON*sqrt(exp(1.))*Astar()*pow(Z,-1./3.)*(1+ksi)*(1+Ye))/(E*v*(1-r*r))));
439 const double Lm = log(((MASS_MUON/MASS_ELECTRON)*Astar()*pow(Z,-1./3.)*sqrt((1.+1./ksi)*(1.+Ym)))/
440 (1.+(2.*MASS_ELECTRON*sqrt(exp(1.))*Astar()*pow(Z,-1./3.)*(1+ksi)*(1+Ym))/(E*v*(1-r*r))));
441 double Phie = Be*Le; if(Phie<0.)Phie=0.;
442 double Phim = Bm*Lm; if(Phim<0.)Phim=0.;
443 return Phie+(MASS_ELECTRON*MASS_ELECTRON/(MASS_MUON*MASS_MUON))*Phim;
444 }
JPHYSICS::JRadiation::Astar
static double Astar()
Definition JRadiation.hh:487

◆ IntegralofG()

virtual double JPHYSICS::JRadiation::IntegralofG ( const double E,
const double eps ) const
inlineprotectedvirtual

Reimplemented in JPHYSICS::JRadiationFunction.

Definition at line 446 of file JRadiation.hh.

448 {
449 const double EP = E-eps;
450 const double v = eps/E;
451 const double tmin = log((4*MASS_ELECTRON/eps+12*pow(MASS_MUON,2)/(E*EP)*(1-4*MASS_ELECTRON/eps))
452 /(1+(1-6*pow(MASS_MUON,2)/(E*EP))*sqrt(1-4*MASS_ELECTRON/eps)));
453
454 if (tmin < 0.0) {
455 const double dt = -tmin/steps;
456 double sum(0.);
457 for (int i = 0;i<steps+1;i++)
458 {
459 double fac = 1.0;if(i==0 || i==steps)fac=0.5;
460 double t = tmin+i*dt;
461 double r = 1.-exp(t);
462 sum+=fac*GofZEvrho(E,v,r)*exp(t);
463 }
464 return sum*dt;
465 } else
466 return 0.0;
467 }
JPHYSICS::JRadiation::GofZEvrho
double GofZEvrho(const double E, const double v, const double r) const
Definition JRadiation.hh:427

◆ sigmaGammaPparam()

static double JPHYSICS::JRadiation::sigmaGammaPparam ( const double eps)
inlinestaticprotected

Definition at line 469 of file JRadiation.hh.

470 {
471 return (49.2 + 11.1 * log(eps) + 151.8/sqrt(eps));
472 }

◆ PhiofEofepsparam()

static double JPHYSICS::JRadiation::PhiofEofepsparam ( const double E,
const double eps )
inlinestaticprotected

Definition at line 474 of file JRadiation.hh.

475 {
476 const double Denom = 1+eps/LAMBDA*(1+LAMBDA/(2*MASS_PROTON)+eps/LAMBDA);
477 const double epsoverE = eps/E;
478 const double Numerator = E * E * (1 - epsoverE) / (MASS_MUON * MASS_MUON) * (1 + MASS_MUON * MASS_MUON * epsoverE * epsoverE /
479 (LAMBDA * LAMBDA * (1 - epsoverE)));
480 const double Factor = 1 - epsoverE + epsoverE * epsoverE / 2 * (1 + 2 * MASS_MUON * MASS_MUON / (LAMBDA * LAMBDA));
481 return (epsoverE - 1 + Factor * log (Numerator / Denom));
482 }

◆ le()

static double JPHYSICS::JRadiation::le ( )
inlinestaticprotected

Definition at line 485 of file JRadiation.hh.

485{ return 3.8616E-13;}

◆ r0()

static double JPHYSICS::JRadiation::r0 ( )
inlinestaticprotected

Definition at line 486 of file JRadiation.hh.

486{ return 2.817940e-15; }

◆ Astar()

static double JPHYSICS::JRadiation::Astar ( )
inlinestaticprotected

Definition at line 487 of file JRadiation.hh.

487{ return 183.0; }

◆ B()

static double JPHYSICS::JRadiation::B ( )
inlinestaticprotected

Definition at line 488 of file JRadiation.hh.

488{ return 183.0; }

◆ BP()

static double JPHYSICS::JRadiation::BP ( )
inlinestaticprotected

Definition at line 489 of file JRadiation.hh.

489{ return 1429.0; }

Member Data Documentation

◆ Z

const double JPHYSICS::JRadiation::Z
protected

Definition at line 491 of file JRadiation.hh.

◆ A

const double JPHYSICS::JRadiation::A
protected

Definition at line 492 of file JRadiation.hh.

◆ Dn

const double JPHYSICS::JRadiation::Dn
protected

Definition at line 493 of file JRadiation.hh.

◆ DnP

const double JPHYSICS::JRadiation::DnP
protected

Definition at line 494 of file JRadiation.hh.

◆ steps

const int JPHYSICS::JRadiation::steps
protected

Definition at line 495 of file JRadiation.hh.

◆ EminBrems

const double JPHYSICS::JRadiation::EminBrems
protected

Definition at line 496 of file JRadiation.hh.

◆ EminEErad

const double JPHYSICS::JRadiation::EminEErad
protected

Definition at line 497 of file JRadiation.hh.

◆ EminGNrad

const double JPHYSICS::JRadiation::EminGNrad
protected

Definition at line 498 of file JRadiation.hh.

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