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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. More...
 
 JRadiation (const double z, const double a, const int integrsteps, const double eminBrems, const double eminEErad, const double eminGNrad)
 Constructor. More...
 
double SigmaEErad (const double E, const double eps) const
 Pair production cross section. More...
 
virtual double TotalCrossSectionEErad (const double E) const
 Pair production cross section. More...
 
double TotalCrossSectionBrems (const double E) const
 Bremsstrahlung cross section. More...
 
virtual double SigmaGNrad (const double E, const double eps) const
 Photo-nuclear cross section. More...
 
virtual double TotalCrossSectionGNrad (const double E) const
 Photo-nuclear cross section. More...
 
double EfromBrems (const double E) const
 Bremsstrahlung shower energy. More...
 
double EfromEErad (const double E) const
 Pair production shower energy. More...
 
double EfromGNrad (const double E) const
 Photo-nuclear shower energy. More...
 

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 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

Definition at line 39 of file JRadiation.hh.

Constructor & Destructor Documentation

◆ ~JRadiation()

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

Virtual desctructor.

Definition at line 45 of file JRadiation.hh.

46  {}

◆ 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 59 of file JRadiation.hh.

64  :
65  Z(z),
66  A(a),
67  Dn (1.54*pow(A,0.27)),
68  DnP (pow(Dn,(1-1/Z))),
69  steps(integrsteps),
70  EminBrems(eminBrems),
71  EminEErad(eminEErad),
72  EminGNrad(eminGNrad)
73  {}

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 83 of file JRadiation.hh.

85  {
86  //routine to calculate dsigma/de in cm^2/GeV for radiating a photon of energy eps
87  if(eps<4.*MASS_ELECTRON)return 0.;
88  if(eps>E-0.75*exp(1.0)*pow(Z,1./3.)) return 0.;
89  double zeta;
90  if(E<35.*MASS_MUON)
91  {
92  zeta = 0.;
93  }
94  else
95  {
96  zeta = (0.073*log((E/MASS_MUON)/(1.+1.95e-5*pow(Z,2./3.)*E/MASS_MUON))-0.26);
97  if(zeta<0.)
98  {
99  zeta=0.;
100  }
101  else
102  {
103  zeta = zeta/(0.058*log((E/MASS_MUON)/(1.+5.3e-5*pow(Z,1./3.)*E/MASS_MUON))-0.14);
104  }
105  }
106  double integ = IntegralofG(E,eps);
107  //cout<< eps<<" integ "<< integ<<endl;
108  return integ*(4/(3.*M_PI))*(Z*(Z+zeta)/A)*AVOGADRO*pow((ALPHA_ELECTRO_MAGNETIC*r0()),2.)*(1-eps/E)/eps;
109  }

◆ 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 118 of file JRadiation.hh.

119  {
120  //cout<<" entering TotcrsecEErad"<<endl;
121  // radiation goes approx as 1/E so sample in log E
122  // calculate the total cross section as S(dsigma/de)*de
123  // start at E and go backwards for precision
124  double sum(0.);
125  double dle = log(E/EminEErad)/steps;
126  //cout << "dle "<< dle<<endl;
127  for(int i=0;i<steps+1;i++)
128  {
129  double factor = 1.0;
130  if(i==0 || i==steps)factor=0.5;
131  //cout<<"i"<<i<<endl;
132  double eps = EminEErad*exp(i*dle);sum += factor*eps*SigmaEErad( E, eps);
133  //cout<<"eps "<<eps<<" sum "<<sum<<endl;
134  }
135  return sum*dle;
136  }

◆ 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 145 of file JRadiation.hh.

146  {
147  // double delta = (MASS_MUON*MASS_MUON*eps)/(2*E*(E-eps));
148  double delta = (MASS_MUON*MASS_MUON)/(2*E);
149  //double v = eps/E;
150  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.))));
151  if(Phin<0.)Phin=0.;
152  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.))));
153  if(Phie<0.)Phie=0.;
154  //if(eps>E/(1+MASS_MUON*MASS_MUON/(2.*MASS_ELECTRON*E)))Phie=0.;
155  double sig = (16./3.)*ALPHA_ELECTRO_MAGNETIC*AVOGADRO*pow((MASS_ELECTRON/MASS_MUON*r0()),2.0)*Z*(Z*Phin+Phie)/(A);
156  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);
157  return epsint*sig;//"cross section" in m^2/g multiplied by density and inverted gives mean free path
158  }

◆ 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 168 of file JRadiation.hh.

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  }

◆ 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  }

◆ 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  }

◆ 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 242 of file JRadiation.hh.

243  {
244  //generate according to 1/k from minimum energy to E
245 
246  const double eps =0.2;
247  const double IntGmax = IntegralofG(E,eps)*2.0;
248 
249  double Er = 0.0;
250  for (int i = 1000; i != 0; --i)
251  {
252  Er = EminEErad*exp(gRandom->Rndm()*log(E/EminEErad));
253  //check on the extra factor, (1-v) and IntofG
254  double factor = (1.-Er/E)*IntegralofG(E,Er)/IntGmax;
255  if(gRandom->Rndm()<factor) break;
256  }
257  return Er;
258  }

◆ 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 266 of file JRadiation.hh.

267  {
268  //generate according to 1/k from minimum energy to E
269 
270  double cmax = sigmaGammaPparam(EminGNrad);
271  if (cmax < sigmaGammaPparam(E))
272  cmax=sigmaGammaPparam(E);
273 
274  double Pmax = PhiofEofepsparam(E,EminGNrad);
275 
276  double Er = 0.0;
277  for (int i = 1000; i != 0; --i) {
278  Er = EminGNrad*exp(gRandom->Rndm()*log(E/EminGNrad));
279  const double factor = PhiofEofepsparam(E,Er)*sigmaGammaPparam(Er)/(cmax*Pmax);
280  if (gRandom->Rndm() < factor) return Er;
281  }
282 
283  return Er;
284  }

◆ GofZEvrho()

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

Definition at line 288 of file JRadiation.hh.

291  {
292  const double ksi = MASS_MUON*MASS_MUON*v*v*(1-r*r)/(4*MASS_ELECTRON*MASS_ELECTRON*(1-v));//
293  const double b = v*v/(2*(1-v));//
294  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);
295  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);
296  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));
297  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);
298  const double Le = log((Astar()*pow(Z,-1./3.)*sqrt((1+ksi)*(1+Ye)))/
299  (1.+(2.*MASS_ELECTRON*sqrt(exp(1.))*Astar()*pow(Z,-1./3.)*(1+ksi)*(1+Ye))/(E*v*(1-r*r))));
300  const double Lm = log(((MASS_MUON/MASS_ELECTRON)*Astar()*pow(Z,-1./3.)*sqrt((1.+1./ksi)*(1.+Ym)))/
301  (1.+(2.*MASS_ELECTRON*sqrt(exp(1.))*Astar()*pow(Z,-1./3.)*(1+ksi)*(1+Ym))/(E*v*(1-r*r))));
302  double Phie = Be*Le; if(Phie<0.)Phie=0.;
303  double Phim = Bm*Lm; if(Phim<0.)Phim=0.;
304  return Phie+(MASS_ELECTRON*MASS_ELECTRON/(MASS_MUON*MASS_MUON))*Phim;
305  }

◆ IntegralofG()

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

Reimplemented in JPHYSICS::JRadiationFunction.

Definition at line 307 of file JRadiation.hh.

309  {
310  const double EP = E-eps;
311  const double v = eps/E;
312  const double tmin = log((4*MASS_ELECTRON/eps+12*pow(MASS_MUON,2)/(E*EP)*(1-4*MASS_ELECTRON/eps))
313  /(1+(1-6*pow(MASS_MUON,2)/(E*EP))*sqrt(1-4*MASS_ELECTRON/eps)));
314 
315  if (tmin < 0.0) {
316  const double dt = -tmin/steps;
317  double sum(0.);
318  for (int i = 0;i<steps+1;i++)
319  {
320  double fac = 1.0;if(i==0 || i==steps)fac=0.5;
321  double t = tmin+i*dt;
322  double r = 1.-exp(t);
323  sum+=fac*GofZEvrho(E,v,r)*exp(t);
324  }
325  return sum*dt;
326  } else
327  return 0.0;
328  }

◆ sigmaGammaPparam()

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

Definition at line 330 of file JRadiation.hh.

331  {
332  return (49.2 + 11.1 * log(eps) + 151.8/sqrt(eps));
333  }

◆ PhiofEofepsparam()

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

Definition at line 335 of file JRadiation.hh.

336  {
337  const double Denom = 1+eps/LAMBDA*(1+LAMBDA/(2*MASS_PROTON)+eps/LAMBDA);
338  const double epsoverE = eps/E;
339  const double Numerator = E * E * (1 - epsoverE) / (MASS_MUON * MASS_MUON) * (1 + MASS_MUON * MASS_MUON * epsoverE * epsoverE /
340  (LAMBDA * LAMBDA * (1 - epsoverE)));
341  const double Factor = 1 - epsoverE + epsoverE * epsoverE / 2 * (1 + 2 * MASS_MUON * MASS_MUON / (LAMBDA * LAMBDA));
342  return (epsoverE - 1 + Factor * log (Numerator / Denom));
343  }

◆ r0()

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

Definition at line 346 of file JRadiation.hh.

346 { return 2.817940e-15; }

◆ Astar()

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

Definition at line 347 of file JRadiation.hh.

347 { return 183.0; }

◆ B()

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

Definition at line 348 of file JRadiation.hh.

348 { return 183.0; }

◆ BP()

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

Definition at line 349 of file JRadiation.hh.

349 { return 1429.0; }

Member Data Documentation

◆ Z

const double JPHYSICS::JRadiation::Z
protected

Definition at line 351 of file JRadiation.hh.

◆ A

const double JPHYSICS::JRadiation::A
protected

Definition at line 352 of file JRadiation.hh.

◆ Dn

const double JPHYSICS::JRadiation::Dn
protected

Definition at line 353 of file JRadiation.hh.

◆ DnP

const double JPHYSICS::JRadiation::DnP
protected

Definition at line 354 of file JRadiation.hh.

◆ steps

const int JPHYSICS::JRadiation::steps
protected

Definition at line 355 of file JRadiation.hh.

◆ EminBrems

const double JPHYSICS::JRadiation::EminBrems
protected

Definition at line 356 of file JRadiation.hh.

◆ EminEErad

const double JPHYSICS::JRadiation::EminEErad
protected

Definition at line 357 of file JRadiation.hh.

◆ EminGNrad

const double JPHYSICS::JRadiation::EminGNrad
protected

Definition at line 358 of file JRadiation.hh.

The documentation for this class was generated from the following file:
JPHYSICS::JRadiation::r0
static double r0()
Definition: JRadiation.hh:346
JPHYSICS::JRadiation::steps
const int steps
Definition: JRadiation.hh:355
JPHYSICS::JRadiation::EminGNrad
const double EminGNrad
Definition: JRadiation.hh:358
JPHYSICS::JRadiation::PhiofEofepsparam
static double PhiofEofepsparam(const double E, const double eps)
Definition: JRadiation.hh:335
JTOOLS::MASS_MUON
static const double MASS_MUON
muon mass [GeV]
Definition: JConstants.hh:59
JPHYSICS::JRadiation::IntegralofG
virtual double IntegralofG(const double E, const double eps) const
Definition: JRadiation.hh:307
JTOOLS::ALPHA_ELECTRO_MAGNETIC
static const double ALPHA_ELECTRO_MAGNETIC
Electro-Magnetic coupling constant.
Definition: JConstants.hh:28
JTOOLS::MASS_PROTON
static const double MASS_PROTON
proton mass [GeV]
Definition: JConstants.hh:67
JPHYSICS::JRadiation::A
const double A
Definition: JRadiation.hh:352
JPHYSICS::JRadiation::BP
static double BP()
Definition: JRadiation.hh:349
JPHYSICS::JRadiation::Z
const double Z
Definition: JRadiation.hh:351
JTOOLS::AVOGADRO
static const double AVOGADRO
Avogadro's number [gr^-1].
Definition: JConstants.hh:24
JPHYSICS::JRadiation::EminBrems
const double EminBrems
Definition: JRadiation.hh:356
JPHYSICS::JRadiation::Dn
const double Dn
Definition: JRadiation.hh:353
JTOOLS::v
data_type v[N+1][M+1]
Definition: JPolint.hh:707
JTOOLS::MASS_ELECTRON
static const double MASS_ELECTRON
electron mass [GeV]
Definition: JConstants.hh:58
JPHYSICS::JRadiation::GofZEvrho
double GofZEvrho(const double E, const double v, const double r) const
Definition: JRadiation.hh:288
JTOOLS::PI
static const double PI
Constants.
Definition: JConstants.hh:20
JPHYSICS::JRadiation::B
static double B()
Definition: JRadiation.hh:348
JTOOLS::r
data_type r[M+1]
Definition: JPolint.hh:709
JPHYSICS::JRadiation::sigmaGammaPparam
static double sigmaGammaPparam(const double eps)
Definition: JRadiation.hh:330
JPHYSICS::JRadiation::SigmaGNrad
virtual double SigmaGNrad(const double E, const double eps) const
Photo-nuclear cross section.
Definition: JRadiation.hh:168
JPHYSICS::JRadiation::DnP
const double DnP
Definition: JRadiation.hh:354
JPHYSICS::JRadiation::Astar
static double Astar()
Definition: JRadiation.hh:347
JPHYSICS::JRadiation::SigmaEErad
double SigmaEErad(const double E, const double eps) const
Pair production cross section.
Definition: JRadiation.hh:83
JPHYSICS::JRadiation::EminEErad
const double EminEErad
Definition: JRadiation.hh:357
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