179 static const G4double epsmin = 1.e-4 , epsmax = 1.e10;
181 static const G4double Zdat[15] = { 4., 6., 13., 20., 26., 29., 32., 38.,47.,
182 50., 56., 64., 74., 79., 82. };
185 static const G4double celectron[15][22] =
186 {{1.125,1.072,1.051,1.047,1.047,1.050,1.052,1.054,
187 1.054,1.057,1.062,1.069,1.075,1.090,1.105,1.111,
188 1.112,1.108,1.100,1.093,1.089,1.087 },
189 {1.408,1.246,1.143,1.096,1.077,1.059,1.053,1.051,
190 1.052,1.053,1.058,1.065,1.072,1.087,1.101,1.108,
191 1.109,1.105,1.097,1.090,1.086,1.082 },
192 {2.833,2.268,1.861,1.612,1.486,1.309,1.204,1.156,
193 1.136,1.114,1.106,1.106,1.109,1.119,1.129,1.132,
194 1.131,1.124,1.113,1.104,1.099,1.098 },
195 {3.879,3.016,2.380,2.007,1.818,1.535,1.340,1.236,
196 1.190,1.133,1.107,1.099,1.098,1.103,1.110,1.113,
197 1.112,1.105,1.096,1.089,1.085,1.098 },
198 {6.937,4.330,2.886,2.256,1.987,1.628,1.395,1.265,
199 1.203,1.122,1.080,1.065,1.061,1.063,1.070,1.073,
200 1.073,1.070,1.064,1.059,1.056,1.056 },
201 {9.616,5.708,3.424,2.551,2.204,1.762,1.485,1.330,
202 1.256,1.155,1.099,1.077,1.070,1.068,1.072,1.074,
203 1.074,1.070,1.063,1.059,1.056,1.052 },
204 {11.72,6.364,3.811,2.806,2.401,1.884,1.564,1.386,
205 1.300,1.180,1.112,1.082,1.073,1.066,1.068,1.069,
206 1.068,1.064,1.059,1.054,1.051,1.050 },
207 {18.08,8.601,4.569,3.183,2.662,2.025,1.646,1.439,
208 1.339,1.195,1.108,1.068,1.053,1.040,1.039,1.039,
209 1.039,1.037,1.034,1.031,1.030,1.036 },
210 {18.22,10.48,5.333,3.713,3.115,2.367,1.898,1.631,
211 1.498,1.301,1.171,1.105,1.077,1.048,1.036,1.033,
212 1.031,1.028,1.024,1.022,1.021,1.024 },
213 {14.14,10.65,5.710,3.929,3.266,2.453,1.951,1.669,
214 1.528,1.319,1.178,1.106,1.075,1.040,1.027,1.022,
215 1.020,1.017,1.015,1.013,1.013,1.020 },
216 {14.11,11.73,6.312,4.240,3.478,2.566,2.022,1.720,
217 1.569,1.342,1.186,1.102,1.065,1.022,1.003,0.997,
218 0.995,0.993,0.993,0.993,0.993,1.011 },
219 {22.76,20.01,8.835,5.287,4.144,2.901,2.219,1.855,
220 1.677,1.410,1.224,1.121,1.073,1.014,0.986,0.976,
221 0.974,0.972,0.973,0.974,0.975,0.987 },
222 {50.77,40.85,14.13,7.184,5.284,3.435,2.520,2.059,
223 1.837,1.512,1.283,1.153,1.091,1.010,0.969,0.954,
224 0.950,0.947,0.949,0.952,0.954,0.963 },
225 {65.87,59.06,15.87,7.570,5.567,3.650,2.682,2.182,
226 1.939,1.579,1.325,1.178,1.108,1.014,0.965,0.947,
227 0.941,0.938,0.940,0.944,0.946,0.954 },
228 {55.60,47.34,15.92,7.810,5.755,3.767,2.760,2.239,
229 1.985,1.609,1.343,1.188,1.113,1.013,0.960,0.939,
230 0.933,0.930,0.933,0.936,0.939,0.949 }};
232 static const G4double cpositron[15][22] = {
233 {2.589,2.044,1.658,1.446,1.347,1.217,1.144,1.110,
234 1.097,1.083,1.080,1.086,1.092,1.108,1.123,1.131,
235 1.131,1.126,1.117,1.108,1.103,1.100 },
236 {3.904,2.794,2.079,1.710,1.543,1.325,1.202,1.145,
237 1.122,1.096,1.089,1.092,1.098,1.114,1.130,1.137,
238 1.138,1.132,1.122,1.113,1.108,1.102 },
239 {7.970,6.080,4.442,3.398,2.872,2.127,1.672,1.451,
240 1.357,1.246,1.194,1.179,1.178,1.188,1.201,1.205,
241 1.203,1.190,1.173,1.159,1.151,1.145 },
242 {9.714,7.607,5.747,4.493,3.815,2.777,2.079,1.715,
243 1.553,1.353,1.253,1.219,1.211,1.214,1.225,1.228,
244 1.225,1.210,1.191,1.175,1.166,1.174 },
245 {17.97,12.95,8.628,6.065,4.849,3.222,2.275,1.820,
246 1.624,1.382,1.259,1.214,1.202,1.202,1.214,1.219,
247 1.217,1.203,1.184,1.169,1.160,1.151 },
248 {24.83,17.06,10.84,7.355,5.767,3.707,2.546,1.996,
249 1.759,1.465,1.311,1.252,1.234,1.228,1.238,1.241,
250 1.237,1.222,1.201,1.184,1.174,1.159 },
251 {23.26,17.15,11.52,8.049,6.375,4.114,2.792,2.155,
252 1.880,1.535,1.353,1.281,1.258,1.247,1.254,1.256,
253 1.252,1.234,1.212,1.194,1.183,1.170 },
254 {22.33,18.01,12.86,9.212,7.336,4.702,3.117,2.348,
255 2.015,1.602,1.385,1.297,1.268,1.251,1.256,1.258,
256 1.254,1.237,1.214,1.195,1.185,1.179 },
257 {33.91,24.13,15.71,10.80,8.507,5.467,3.692,2.808,
258 2.407,1.873,1.564,1.425,1.374,1.330,1.324,1.320,
259 1.312,1.288,1.258,1.235,1.221,1.205 },
260 {32.14,24.11,16.30,11.40,9.015,5.782,3.868,2.917,
261 2.490,1.925,1.596,1.447,1.391,1.342,1.332,1.327,
262 1.320,1.294,1.264,1.240,1.226,1.214 },
263 {29.51,24.07,17.19,12.28,9.766,6.238,4.112,3.066,
264 2.602,1.995,1.641,1.477,1.414,1.356,1.342,1.336,
265 1.328,1.302,1.270,1.245,1.231,1.233 },
266 {38.19,30.85,21.76,15.35,12.07,7.521,4.812,3.498,
267 2.926,2.188,1.763,1.563,1.484,1.405,1.382,1.371,
268 1.361,1.330,1.294,1.267,1.251,1.239 },
269 {49.71,39.80,27.96,19.63,15.36,9.407,5.863,4.155,
270 3.417,2.478,1.944,1.692,1.589,1.480,1.441,1.423,
271 1.409,1.372,1.330,1.298,1.280,1.258 },
272 {59.25,45.08,30.36,20.83,16.15,9.834,6.166,4.407,
273 3.641,2.648,2.064,1.779,1.661,1.531,1.482,1.459,
274 1.442,1.400,1.354,1.319,1.299,1.272 },
275 {56.38,44.29,30.50,21.18,16.51,10.11,6.354,4.542,
276 3.752,2.724,2.116,1.817,1.692,1.554,1.499,1.474,
277 1.456,1.412,1.364,1.328,1.307,1.282 }};
281 static const G4double hecorr[15] = {
282 120.70, 117.50, 105.00, 92.92, 79.23, 74.510, 68.29,
283 57.39, 41.97, 36.14, 24.53, 10.21, -7.855, -16.84,
295 G4double eKineticEnergy = kinEnergy;
297 if(mass > CLHEP::electron_mass_c2)
300 G4double c = mass*TAU*(TAU+2.)/(CLHEP::electron_mass_c2*(TAU+1.)) ;
302 G4double tau = 0.5*(w+std::sqrt(w*w+4.*c)) ;
303 eKineticEnergy = CLHEP::electron_mass_c2*tau ;
306 G4double eTotalEnergy = eKineticEnergy + CLHEP::electron_mass_c2 ;
307 G4double beta2 = eKineticEnergy*(eTotalEnergy+CLHEP::electron_mass_c2)
308 /(eTotalEnergy*eTotalEnergy);
309 G4double bg2 = eKineticEnergy*(eTotalEnergy+CLHEP::electron_mass_c2)
310 /(CLHEP::electron_mass_c2*CLHEP::electron_mass_c2);
312 static const G4double epsfactor = 2.*CLHEP::electron_mass_c2*
313 CLHEP::electron_mass_c2*CLHEP::Bohr_radius*CLHEP::Bohr_radius
314 /(CLHEP::hbarc*CLHEP::hbarc);
317 if (eps<epsmin) sigma = 2.*eps*eps;
318 else if(eps<epsmax) sigma =
G4Log(1.+2.*eps)-2.*eps/(1.+2.*eps);
319 else sigma =
G4Log(2.*eps)-1.+1./eps;
321 sigma *= chargeSquare*atomicNumber*atomicNumber/(beta2*bg2);
329 while ((iZ>=0)&&(Zdat[iZ]>=atomicNumber)) { --iZ; }
331 iZ = std::min(std::max(iZ, 0), 13);
335 G4double ratZ = (atomicNumber-ZZ1)*(atomicNumber+ZZ1)/
336 ((ZZ2-ZZ1)*(ZZ2+ZZ1));
338 static const G4double Tlim = 10.*CLHEP::MeV;
340 CLHEP::twopi*CLHEP::classic_electr_radius*CLHEP::classic_electr_radius;
341 static const G4double beta2lim = Tlim*(Tlim+2.*CLHEP::electron_mass_c2)/
342 ((Tlim+CLHEP::electron_mass_c2)*(Tlim+CLHEP::electron_mass_c2));
343 static const G4double bg2lim = Tlim*(Tlim+2.*CLHEP::electron_mass_c2)/
344 (CLHEP::electron_mass_c2*CLHEP::electron_mass_c2);
347 0.2672*CLHEP::barn, 0.5922*CLHEP::barn, 2.653*CLHEP::barn, 6.235*CLHEP::barn,
348 11.69*CLHEP::barn , 13.24*CLHEP::barn , 16.12*CLHEP::barn, 23.00*CLHEP::barn,
349 35.13*CLHEP::barn , 39.95*CLHEP::barn , 50.85*CLHEP::barn, 67.19*CLHEP::barn,
350 91.15*CLHEP::barn , 104.4*CLHEP::barn , 113.1*CLHEP::barn};
353 100*CLHEP::eV, 200*CLHEP::eV, 400*CLHEP::eV, 700*CLHEP::eV,
354 1*CLHEP::keV, 2*CLHEP::keV, 4*CLHEP::keV, 7*CLHEP::keV,
355 10*CLHEP::keV, 20*CLHEP::keV, 40*CLHEP::keV, 70*CLHEP::keV,
356 100*CLHEP::keV, 200*CLHEP::keV, 400*CLHEP::keV, 700*CLHEP::keV,
357 1*CLHEP::MeV, 2*CLHEP::MeV, 4*CLHEP::MeV, 7*CLHEP::MeV,
358 10*CLHEP::MeV, 20*CLHEP::MeV};
360 if(eKineticEnergy <= Tlim)
365 while ((iT>=0)&&(Tdat[iT]>=eKineticEnergy)) iT -= 1;
367 iT = std::min(std::max(iT, 0), 20);
371 G4double E = T + CLHEP::electron_mass_c2;
372 G4double b2small = T*(E+CLHEP::electron_mass_c2)/(E*E);
375 E = T + CLHEP::electron_mass_c2;
376 G4double b2big = T*(E+CLHEP::electron_mass_c2)/(E*E);
377 G4double ratb2 = (beta2-b2small)/(b2big-b2small);
381 c1 = celectron[iZ][iT];
382 c2 = celectron[iZ+1][iT];
383 cc1 = c1+ratZ*(c2-c1);
385 c1 = celectron[iZ][iT+1];
386 c2 = celectron[iZ+1][iT+1];
390 c1 = cpositron[iZ][iT];
391 c2 = cpositron[iZ+1][iT];
392 cc1 = c1+ratZ*(c2-c1);
394 c1 = cpositron[iZ][iT+1];
395 c2 = cpositron[iZ+1][iT+1];
398 sigma *= sigmafactor/(cc1+ratb2*(cc2-cc1));
402 c1 = bg2lim*sig0[iZ]*(1.+hecorr[iZ]*(beta2-beta2lim))/bg2;
403 c2 = bg2lim*sig0[iZ+1]*(1.+hecorr[iZ+1]*(beta2-beta2lim))/bg2;
404 if((atomicNumber >= ZZ1) && (atomicNumber <= ZZ2))
405 sigma = c1+ratZ*(c2-c1) ;
406 else if(atomicNumber < ZZ1)
407 sigma = atomicNumber*atomicNumber*c1/(ZZ1*ZZ1);
408 else if(atomicNumber > ZZ2)
409 sigma = atomicNumber*atomicNumber*c2/(ZZ2*ZZ2);
412 sigma *= (1.+0.30/(1.+std::sqrt(1000.*eKineticEnergy)));