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26 26
27 /* 27 /*
28 * Implements calculation of the Fermi density 28 * Implements calculation of the Fermi density effect as per the method
29 * described in: 29 * described in:
30 * 30 *
31 * R. M. Sternheimer, M. J. Berger, and S. M 31 * R. M. Sternheimer, M. J. Berger, and S. M. Seltzer. Density
32 * effect for the ionization loss of charged 32 * effect for the ionization loss of charged particles in various sub-
33 * stances. Atom. Data Nucl. Data Tabl., 30: 33 * stances. Atom. Data Nucl. Data Tabl., 30:261, 1984.
34 * 34 *
35 * Which (among other Sternheimer references) 35 * Which (among other Sternheimer references) builds on:
36 * 36 *
37 * R. M. Sternheimer. The density effect for 37 * R. M. Sternheimer. The density effect for ionization loss in
38 * materials. Phys. Rev., 88:851859, 1952. 38 * materials. Phys. Rev., 88:851859, 1952.
39 * 39 *
40 * The returned values of delta are directly f 40 * The returned values of delta are directly from the Sternheimer calculation,
41 * and not Sternheimer's popular three-part ap 41 * and not Sternheimer's popular three-part approximate parameterization
42 * introduced in the same paper. 42 * introduced in the same paper.
43 * 43 *
44 * Author: Matthew Strait <straitm@umn.edu> 20 44 * Author: Matthew Strait <straitm@umn.edu> 2019
45 */ 45 */
46 46
47 #include "G4DensityEffectCalculator.hh" 47 #include "G4DensityEffectCalculator.hh"
48 <<
49 #include "G4AtomicShells.hh" 48 #include "G4AtomicShells.hh"
50 #include "G4NistManager.hh" 49 #include "G4NistManager.hh"
51 #include "G4Pow.hh" 50 #include "G4Pow.hh"
52 51
53 static G4Pow* gpow = G4Pow::GetInstance(); << 52 static G4Pow * gpow = G4Pow::GetInstance();
54 53
55 const G4int maxWarnings = 20; 54 const G4int maxWarnings = 20;
56 55
57 G4DensityEffectCalculator::G4DensityEffectCalc 56 G4DensityEffectCalculator::G4DensityEffectCalculator(const G4Material* mat, G4int n)
58 : fMaterial(mat), nlev(n) << 57 : fMaterial(mat), fVerbose(0), fWarnings(0), nlev(n)
59 { 58 {
60 fVerbose = std::max(fVerbose, G4NistManager: 59 fVerbose = std::max(fVerbose, G4NistManager::Instance()->GetVerbose());
61 60
62 sternf = new G4double[nlev]; << 61 sternf = new G4double [nlev];
63 levE = new G4double[nlev]; << 62 levE = new G4double [nlev];
64 sternl = new G4double[nlev]; << 63 sternl = new G4double [nlev];
65 sternEbar = new G4double[nlev]; << 64 sternEbar = new G4double [nlev];
66 for (G4int i = 0; i < nlev; ++i) { << 65 for(G4int i=0; i<nlev; ++i) {
67 sternf[i] = 0.0; << 66 sternf[i] = 0.0;
68 levE[i] = 0.0; << 67 levE[i] = 0.0;
69 sternl[i] = 0.0; << 68 sternl[i] = 0.0;
70 sternEbar[i] = 0.0; 69 sternEbar[i] = 0.0;
71 } 70 }
72 71
73 fConductivity = sternx = 0.0; 72 fConductivity = sternx = 0.0;
74 G4bool conductor = (fMaterial->GetFreeElectr 73 G4bool conductor = (fMaterial->GetFreeElectronDensity() > 0.0);
75 74
76 G4int sh = 0; 75 G4int sh = 0;
77 G4double sum = 0.; 76 G4double sum = 0.;
78 const G4double tot = fMaterial->GetTotNbOfAt 77 const G4double tot = fMaterial->GetTotNbOfAtomsPerVolume();
79 for (size_t j = 0; j < fMaterial->GetNumberO << 78 for(size_t j = 0; j < fMaterial->GetNumberOfElements(); ++j) {
80 // The last subshell is considered to cont 79 // The last subshell is considered to contain the conduction
81 // electrons. Sternheimer 1984 says "the l 80 // electrons. Sternheimer 1984 says "the lowest chemical valance of
82 // the element" is used to set the number 81 // the element" is used to set the number of conduction electrons.
83 // I'm not sure if that means the highest 82 // I'm not sure if that means the highest subshell or the whole
84 // shell, but in any case, he also says th 83 // shell, but in any case, he also says that the choice is arbitrary
85 // and offers a possible alternative. This 84 // and offers a possible alternative. This is one of the sources of
86 // uncertainty in the model. 85 // uncertainty in the model.
87 const G4double frac = fMaterial->GetVecNbO << 86 const G4double frac = fMaterial->GetVecNbOfAtomsPerVolume()[j]/tot;
88 const G4int Z = fMaterial->GetElement((G4i << 87 const G4int Z = fMaterial->GetElement(j)->GetZasInt();
89 const G4int nshell = G4AtomicShells::GetNu 88 const G4int nshell = G4AtomicShells::GetNumberOfShells(Z);
90 for (G4int i = 0; i < nshell; ++i) { << 89 for(G4int i = 0; i < nshell; ++i) {
91 // For conductors, put *all* top shell e 90 // For conductors, put *all* top shell electrons into the conduction
92 // band, regardless of element. 91 // band, regardless of element.
93 const G4double xx = frac * G4AtomicShell << 92 const G4double xx = frac*G4AtomicShells::GetNumberOfElectrons(Z, i);
94 if (i < nshell - 1 || ! conductor) { << 93 if(i < nshell-1 || !conductor) {
95 sternf[sh] += xx; << 94 sternf[sh] += xx;
96 } << 95 } else {
97 else { <<
98 fConductivity += xx; 96 fConductivity += xx;
99 } 97 }
100 levE[sh] = G4AtomicShells::GetBindingEne << 98 levE[sh] = G4AtomicShells::GetBindingEnergy(Z, i)/CLHEP::eV;
101 ++sh; 99 ++sh;
102 } 100 }
103 } 101 }
104 for (G4int i = 0; i < nlev; ++i) { << 102 for(G4int i=0; i<nlev; ++i) {
105 sum += sternf[i]; 103 sum += sternf[i];
106 } 104 }
107 sum += fConductivity; << 105 sum = (sum > 0.0) ? 1./sum : 0.0;
108 << 106 for(G4int i=0; i<nlev; ++i) {
109 const G4double invsum = (sum > 0.0) ? 1. / s << 107 sternf[i] *= sum;
110 for (G4int i = 0; i < nlev; ++i) { << 108 }
111 sternf[i] *= invsum; << 109 plasmaE = fMaterial->GetIonisation()->GetPlasmaEnergy()/CLHEP::eV;
112 } << 110 meanexcite = fMaterial->GetIonisation()->GetMeanExcitationEnergy()/CLHEP::eV;
113 fConductivity *= invsum; <<
114 plasmaE = fMaterial->GetIonisation()->GetPla <<
115 meanexcite = fMaterial->GetIonisation()->Get <<
116 } 111 }
117 112
118 G4DensityEffectCalculator::~G4DensityEffectCal 113 G4DensityEffectCalculator::~G4DensityEffectCalculator()
119 { 114 {
120 delete[] sternf; << 115 delete [] sternf;
121 delete[] levE; << 116 delete [] levE;
122 delete[] sternl; << 117 delete [] sternl;
123 delete[] sternEbar; << 118 delete [] sternEbar;
124 } 119 }
125 120
126 G4double G4DensityEffectCalculator::ComputeDen 121 G4double G4DensityEffectCalculator::ComputeDensityCorrection(G4double x)
127 { 122 {
128 if (fVerbose > 1) { << 123 if(fVerbose > 1) {
129 G4cout << "G4DensityEffectCalculator::Comp << 124 G4cout << "G4DensityEffectCalculator::ComputeDensityCorrection for "
130 << ", x= " << x << G4endl; << 125 << fMaterial->GetName() << ", x= " << x << G4endl;
131 } 126 }
132 const G4double approx = fMaterial->GetIonisa 127 const G4double approx = fMaterial->GetIonisation()->GetDensityCorrection(x);
133 const G4double exact = FermiDeltaCalculation << 128 const G4double exact = FermiDeltaCalculation(x);
134 129
135 if (fVerbose > 1) { << 130 if(fVerbose > 1) {
136 G4cout << " Delta: computed= " << exact << 131 G4cout << " Delta: computed= " << exact
>> 132 << ", parametrized= " << approx << G4endl;
137 } 133 }
138 if (approx >= 0. && exact < 0.) { << 134 if(approx > 0. && exact < 0.) {
139 if (fVerbose > 0) { << 135 if(fVerbose > 0) {
140 ++fWarnings; 136 ++fWarnings;
141 if (fWarnings < maxWarnings) { << 137 if(fWarnings < maxWarnings) {
142 G4ExceptionDescription ed; << 138 G4ExceptionDescription ed;
143 ed << "Sternheimer fit failed for " << << 139 ed << "Sternheimer fit failed for " << fMaterial->GetName()
144 << ": Delta exact= " << exact << ", << 140 << ", x = " << x << ": Delta exact= "
145 G4Exception("G4DensityEffectCalculator << 141 << exact << ", approx= " << approx;
>> 142 G4Exception("G4DensityEffectCalculator::DensityCorrection", "mat008",
>> 143 JustWarning, ed);
146 } 144 }
147 } 145 }
148 return approx; 146 return approx;
149 } 147 }
150 // Fall back to approx if exact and approx a 148 // Fall back to approx if exact and approx are very different, under the
151 // assumption that this means the exact calc 149 // assumption that this means the exact calculation has gone haywire
152 // somehow, with the exception of the case w 150 // somehow, with the exception of the case where approx is negative. I
153 // have seen this clearly-wrong result occur 151 // have seen this clearly-wrong result occur for substances with extremely
154 // low density (1e-25 g/cc). 152 // low density (1e-25 g/cc).
155 if (approx >= 0. && std::abs(exact - approx) << 153 if(approx >= 0. && std::abs(exact - approx) > 1.) {
156 if (fVerbose > 0) { << 154 if(fVerbose > 0) {
157 ++fWarnings; 155 ++fWarnings;
158 if (fWarnings < maxWarnings) { << 156 if(fWarnings < maxWarnings) {
159 G4ExceptionDescription ed; << 157 G4ExceptionDescription ed;
160 ed << "Sternheimer exact= " << exact < << 158 ed << "Sternheimer exact= " << exact << " and approx= "
161 << " are too different for " << fMa << 159 << approx << " are too different for "
162 G4Exception("G4DensityEffectCalculator << 160 << fMaterial->GetName() << ", x = " << x;
>> 161 G4Exception("G4DensityEffectCalculator::DensityCorrection", "mat008",
>> 162 JustWarning, ed);
163 } 163 }
164 } 164 }
165 return approx; 165 return approx;
166 } 166 }
167 return exact; 167 return exact;
168 } 168 }
169 169
170 G4double G4DensityEffectCalculator::FermiDelta 170 G4double G4DensityEffectCalculator::FermiDeltaCalculation(G4double x)
171 { 171 {
172 // Above beta*gamma of 10^10, the exact trea 172 // Above beta*gamma of 10^10, the exact treatment is within machine
173 // precision of the limiting case, for ordin 173 // precision of the limiting case, for ordinary solids, at least. The
174 // convergence goes up as the density goes d 174 // convergence goes up as the density goes down, but even in a pretty
175 // hard vacuum it converges by 10^20. Also, 175 // hard vacuum it converges by 10^20. Also, it's hard to imagine how
176 // this energy is relevant (x = 20 -> 10^19 176 // this energy is relevant (x = 20 -> 10^19 GeV for muons). So this
177 // is mostly not here for physical reasons, 177 // is mostly not here for physical reasons, but rather to avoid ugly
178 // discontinuities in the return value. 178 // discontinuities in the return value.
179 if (x > 20.) { << 179 if(x > 20.) { return -1.; }
180 return -1.; <<
181 } <<
182 180
183 sternx = x; 181 sternx = x;
184 G4double sternrho = Newton(1.5, true); 182 G4double sternrho = Newton(1.5, true);
185 183
186 // Negative values, and values much larger t 184 // Negative values, and values much larger than unity are non-physical.
187 // Values between zero and one are also susp 185 // Values between zero and one are also suspect, but not as clearly wrong.
188 if (sternrho <= 0. || sternrho > 100.) { << 186 if(sternrho <= 0. || sternrho > 100.) {
189 if (fVerbose > 0) { << 187 if(fVerbose > 0) {
190 ++fWarnings; 188 ++fWarnings;
191 if (fWarnings < maxWarnings) { << 189 if(fWarnings < maxWarnings) {
192 G4ExceptionDescription ed; << 190 G4ExceptionDescription ed;
193 ed << "Sternheimer computation failed << 191 ed << "Sternheimer computation failed for " << fMaterial->GetName()
194 << ":\n" << 192 << ", x = " << x << ":\n"
195 << "Could not solve for Sternheimer << 193 << "Could not solve for Sternheimer rho. Probably you have a \n"
196 << "mean ionization energy which is << 194 << "mean ionization energy which is incompatible with your\n"
197 << "distribution of energy levels, << 195 << "distribution of energy levels, or an unusually dense material.\n"
198 << "Number of levels: " << nlev << << 196 << "Number of levels: " << nlev
199 << " Plasma energy(eV): " << plasma << 197 << " Mean ionization energy(eV): " << meanexcite
200 for (G4int i = 0; i < nlev; ++i) { << 198 << " Plasma energy(eV): " << plasmaE << "\n";
201 ed << "Level " << i << ": strength " << 199 for(G4int i = 0; i < nlev; ++i) {
202 } << 200 ed << "Level " << i << ": strength " << sternf[i]
203 G4Exception("G4DensityEffectCalculator << 201 << ": energy(eV)= " << levE[i] << "\n";
>> 202 }
>> 203 G4Exception("G4DensityEffectCalculator::SetupFermiDeltaCalc", "mat008",
>> 204 JustWarning, ed);
204 } 205 }
205 } 206 }
206 return -1.; 207 return -1.;
207 } 208 }
208 209
209 // Calculate the Sternheimer adjusted energy 210 // Calculate the Sternheimer adjusted energy levels and parameters l_i given
210 // the Sternheimer parameter rho. 211 // the Sternheimer parameter rho.
211 for (G4int i = 0; i < nlev; ++i) { << 212 sternrho /= plasmaE;
212 sternEbar[i] = levE[i] * (sternrho / plasm << 213 for(G4int i=0; i<nlev; ++i) {
213 sternl[i] = std::sqrt(gpow->powN(sternEbar << 214 sternEbar[i] = levE[i] * sternrho;
214 } << 215 sternl[i] = std::sqrt(gpow->powN(sternEbar[i], 2) + 2./3.*sternf[i]);
215 // The derivative of the function we are sol << 216 }
216 // negative for positive (physical) values, << 217
217 // zero is less than zero, it has no solutio << 218 // Make imphirical initial guess
218 // density effect in the Sternheimer "exact" << 219 const G4double sternL = Newton(sternrho, false);
219 // still an approximation). << 220 if(sternL > -1.) {
220 // << 221 return DeltaOnceSolved(sternL);
221 // For conductors, this test is not needed, <<
222 // the term fConductivity/(L*L), so the valu <<
223 // positive infinity. In the code we don't r <<
224 // rather set that term to zero, which means <<
225 // used, it would give the wrong result for <<
226 if (fConductivity == 0 && Ell(0) <= 0) { <<
227 return 0; <<
228 } <<
229 <<
230 // Attempt to find the root from 40 starting <<
231 // in log space. Trying a single starting p <<
232 // convergence in most cases. <<
233 for (G4int startLi = -10; startLi < 30; ++st <<
234 const G4double sternL = Newton(gpow->powN( <<
235 if (sternL != -1.) { <<
236 return DeltaOnceSolved(sternL); <<
237 } <<
238 } 222 }
239 return -1.; // Signal the caller to use the << 223
240 // because we have been unable << 224 return -1.; // Signal the caller to use the Sternheimer approximation,
>> 225 // because we have been unable to solve the exact form.
241 } 226 }
242 227
243 /* Newton's method for finding roots. Adapted 228 /* Newton's method for finding roots. Adapted from G4PolynominalSolver, but
244 * without the assumption that the input is a 229 * without the assumption that the input is a polynomial. Also, here we
245 * always expect the roots to be positive, so 230 * always expect the roots to be positive, so return -1 as an error value. */
246 G4double G4DensityEffectCalculator::Newton(G4d 231 G4double G4DensityEffectCalculator::Newton(G4double start, G4bool first)
247 { 232 {
248 const G4int maxIter = 100; 233 const G4int maxIter = 100;
249 G4int nbad = 0, ngood = 0; 234 G4int nbad = 0, ngood = 0;
250 235
251 G4double lambda(start), value(0.), dvalue(0. 236 G4double lambda(start), value(0.), dvalue(0.);
252 237
253 if (fVerbose > 2) { << 238 if(fVerbose > 2) {
254 G4cout << "G4DensityEffectCalculator::Newt << 239 G4cout << "G4DensityEffectCalculator::Newton: strat= " << start
>> 240 << " type: " << first << G4endl;
255 } 241 }
256 while (true) { << 242 while(true) {
257 if (first) { << 243 if(first) {
258 value = FRho(lambda); 244 value = FRho(lambda);
259 dvalue = DFRho(lambda); 245 dvalue = DFRho(lambda);
260 } << 246 } else {
261 else { <<
262 value = Ell(lambda); 247 value = Ell(lambda);
263 dvalue = DEll(lambda); 248 dvalue = DEll(lambda);
264 } 249 }
265 if (dvalue == 0.0) { << 250 if(dvalue == 0.0) { break; }
266 break; << 251 const G4double del = value/dvalue;
267 } <<
268 const G4double del = value / dvalue; <<
269 lambda -= del; 252 lambda -= del;
270 253
271 const G4double eps = std::abs(del / lambda << 254 const G4double eps = std::abs(del);
272 if (eps <= 1.e-12) { << 255 if(eps <= 1.e-12) {
273 ++ngood; 256 ++ngood;
274 if (ngood == 2) { << 257 if(ngood == 2) {
275 if (fVerbose > 2) { << 258 if(fVerbose > 2) {
276 G4cout << " Converged with result= << 259 G4cout << " Converged with result= " << lambda << G4endl;
277 } << 260 }
278 return lambda; << 261 return lambda;
279 } 262 }
280 } << 263 } else {
281 else { <<
282 ++nbad; 264 ++nbad;
283 } 265 }
284 if (nbad > maxIter || std::isnan(value) || << 266 if(nbad > maxIter || eps > 1.) { break; }
285 break; <<
286 } <<
287 } 267 }
288 if (fVerbose > 2) { << 268 if(fVerbose > 2) {
289 G4cout << " Failed to converge last value << 269 G4cout << " Failed to converge last value= " << value
290 << " lambda= " << lambda << G4endl; << 270 << " dvalue= " << dvalue << " lambda= " << lambda << G4endl;
291 } 271 }
292 return -1.; 272 return -1.;
293 } 273 }
294 274
295 /* Return the derivative of the equation used 275 /* Return the derivative of the equation used
296 * to solve for the Sternheimer parameter rho. 276 * to solve for the Sternheimer parameter rho. */
297 G4double G4DensityEffectCalculator::DFRho(G4do 277 G4double G4DensityEffectCalculator::DFRho(G4double rho)
298 { 278 {
299 G4double ans = 0.0; 279 G4double ans = 0.0;
300 for (G4int i = 0; i < nlev; ++i) { << 280 for(G4int i = 0; i < nlev; ++i) {
301 if (sternf[i] > 0.) { << 281 if(sternf[i] > 0.) {
302 ans += sternf[i] * gpow->powN(levE[i], 2 282 ans += sternf[i] * gpow->powN(levE[i], 2) * rho /
303 (gpow->powN(levE[i] * rho, 2) + 2 << 283 (gpow->powN(levE[i] * rho, 2)
>> 284 + 2./3. * sternf[i] * gpow->powN(plasmaE, 2));
304 } 285 }
305 } 286 }
306 return ans; 287 return ans;
307 } 288 }
308 289
309 /* Return the functional value for the equatio 290 /* Return the functional value for the equation used
310 * to solve for the Sternheimer parameter rho. 291 * to solve for the Sternheimer parameter rho. */
311 G4double G4DensityEffectCalculator::FRho(G4dou 292 G4double G4DensityEffectCalculator::FRho(G4double rho)
312 { 293 {
313 G4double ans = 0.0; 294 G4double ans = 0.0;
314 for (G4int i = 0; i < nlev; ++i) { << 295 for(G4int i = 0; i<nlev; ++i) {
315 if (sternf[i] > 0.) { << 296 if(sternf[i] > 0.) {
316 ans += sternf[i] * << 297 ans += sternf[i] * G4Log(gpow->powN(levE[i]*rho, 2) +
317 G4Log(gpow->powN(levE[i] * rho, 2 << 298 2./3. * sternf[i]*gpow->powN(plasmaE, 2));
318 } << 299 }
319 } 300 }
320 ans *= 0.5; // pulled out of loop for effic << 301 ans *= 0.5; // pulled out of loop for efficiency
321 302
322 if (fConductivity > 0.) { << 303 if(fConductivity > 0.) {
323 ans += fConductivity * G4Log(plasmaE * std 304 ans += fConductivity * G4Log(plasmaE * std::sqrt(fConductivity));
324 } 305 }
325 ans -= G4Log(meanexcite); 306 ans -= G4Log(meanexcite);
326 return ans; 307 return ans;
327 } 308 }
328 309
329 /* Return the derivative for the equation used 310 /* Return the derivative for the equation used to
330 * solve for the Sternheimer parameter l, call 311 * solve for the Sternheimer parameter l, called 'L' here. */
331 G4double G4DensityEffectCalculator::DEll(G4dou 312 G4double G4DensityEffectCalculator::DEll(G4double L)
332 { 313 {
333 G4double ans = 0.; 314 G4double ans = 0.;
334 for (G4int i = 0; i < nlev; ++i) { << 315 for(G4int i=0; i<nlev; ++i) {
335 if (sternf[i] > 0 && (sternEbar[i] > 0. || << 316 if(sternf[i] > 0 && (sternEbar[i] > 0. || L != 0.)) {
336 const G4double y = gpow->powN(sternEbar[ 317 const G4double y = gpow->powN(sternEbar[i], 2);
337 ans += sternf[i] / gpow->powN(y + L * L, << 318 ans += sternf[i]/gpow->powN(y + L*L, 2);
338 } 319 }
339 } 320 }
340 ans += fConductivity / gpow->powN(L * L, 2); << 321 ans *= (-2*L); // pulled out of the loop for efficiency
341 ans *= (-2 * L); // pulled out of the loop <<
342 return ans; 322 return ans;
343 } 323 }
344 324
345 /* Return the functional value for the equatio 325 /* Return the functional value for the equation used to
346 * solve for the Sternheimer parameter l, call 326 * solve for the Sternheimer parameter l, called 'L' here. */
347 G4double G4DensityEffectCalculator::Ell(G4doub 327 G4double G4DensityEffectCalculator::Ell(G4double L)
348 { 328 {
349 G4double ans = 0.; 329 G4double ans = 0.;
350 for (G4int i = 0; i < nlev; ++i) { << 330 for(G4int i=0; i<nlev; ++i) {
351 if (sternf[i] > 0. && (sternEbar[i] > 0. | << 331 if(sternf[i] > 0. && (sternEbar[i] > 0. || L != 0.)) {
352 ans += sternf[i] / (gpow->powN(sternEbar << 332 ans += sternf[i]/(gpow->powN(sternEbar[i], 2) + L*L);
353 } 333 }
354 } 334 }
355 if (fConductivity > 0. && L != 0.) { <<
356 ans += fConductivity / (L * L); <<
357 } <<
358 ans -= gpow->powZ(10, -2 * sternx); 335 ans -= gpow->powZ(10, -2 * sternx);
359 return ans; 336 return ans;
360 } 337 }
361 338
362 /** 339 /**
363 * Given the Sternheimer parameter l (called ' << 340 * Given the Sternheimer parameter l^2 (called 'sternL' here), and that
364 * the l_i and adjusted energies have been fou 341 * the l_i and adjusted energies have been found with SetupFermiDeltaCalc(),
365 * return the value of delta. Helper function 342 * return the value of delta. Helper function for DoFermiDeltaCalc().
366 */ 343 */
367 G4double G4DensityEffectCalculator::DeltaOnceS 344 G4double G4DensityEffectCalculator::DeltaOnceSolved(G4double sternL)
368 { 345 {
369 G4double ans = 0.; 346 G4double ans = 0.;
370 for (G4int i = 0; i < nlev; ++i) { << 347 for(G4int i=0; i<nlev; ++i) {
371 if (sternf[i] > 0.) { << 348 if(sternf[i] > 0.) {
372 ans += sternf[i] * << 349 ans += sternf[i] * G4Log((gpow->powN(sternl[i], 2)
373 G4Log((gpow->powN(sternl[i], 2) + << 350 + gpow->powN(sternL, 2))/gpow->powN(sternl[i], 2));
374 } 351 }
375 } 352 }
376 // sternl for the conduction electrons is sq << 353 ans -= gpow->powN(sternL, 2)/(1 + gpow->powZ(10, 2 * sternx));
377 // no factor of 2./3 as with the other level <<
378 if (fConductivity > 0) { <<
379 ans += fConductivity * G4Log((fConductivit <<
380 } <<
381 ans -= gpow->powN(sternL, 2) / (1 + gpow->po <<
382 return ans; 354 return ans;
383 } 355 }
384 356