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26
27 #include <iostream>
28 #include "G4ecpssrBaseLixsModel.hh"
29 #include "globals.hh"
30 #include "G4PhysicalConstants.hh"
31 #include "G4SystemOfUnits.hh"
32 #include "G4AtomicTransitionManager.hh"
33 #include "G4NistManager.hh"
34 #include "G4Proton.hh"
35 #include "G4Alpha.hh"
36 #include "G4LinLogInterpolation.hh"
37 #include "G4Exp.hh"
38
39 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
40
41 G4ecpssrBaseLixsModel::G4ecpssrBaseLixsModel()
42 {
43 verboseLevel=0;
44
45 // Storing FLi data needed for 0.2 to 3.0 velocities region
46 const char* path = G4FindDataDir("G4LEDATA");
47
48 if (!path) {
49 G4Exception("G4ecpssrLCrossSection::G4ecpssrBaseLixsModel()","em0006", FatalException ,"G4LEDATA environment variable not set");
50 return;
51 }
52 std::ostringstream fileName1;
53 std::ostringstream fileName2;
54
55 fileName1 << path << "/pixe/uf/FL1.dat";
56 fileName2 << path << "/pixe/uf/FL2.dat";
57
58 // Reading of FL1.dat
59 std::ifstream FL1(fileName1.str().c_str());
60 if (!FL1) G4Exception("G4ecpssrLCrossSection::G4ecpssrBaseLixsModel()","em0003",FatalException, "error opening FL1 data file");
61
62 dummyVec1.push_back(0.);
63
64 while(!FL1.eof())
65 {
66 double x1;
67 double y1;
68
69 FL1>>x1>>y1;
70
71 // Mandatory vector initialization
72 if (x1 != dummyVec1.back())
73 {
74 dummyVec1.push_back(x1);
75 aVecMap1[x1].push_back(-1.);
76 }
77
78 FL1>>FL1Data[x1][y1];
79
80 if (y1 != aVecMap1[x1].back()) aVecMap1[x1].push_back(y1);
81 }
82
83 // Reading of FL2.dat
84
85 std::ifstream FL2(fileName2.str().c_str());
86 if (!FL2) G4Exception("G4ecpssrLCrossSection::G4ecpssrBaseLixsModel()","em0003", FatalException," error opening FL2 data file");
87
88 dummyVec2.push_back(0.);
89
90 while(!FL2.eof())
91 {
92 double x2;
93 double y2;
94
95 FL2>>x2>>y2;
96
97 // Mandatory vector initialization
98 if (x2 != dummyVec2.back())
99 {
100 dummyVec2.push_back(x2);
101 aVecMap2[x2].push_back(-1.);
102 }
103
104 FL2>>FL2Data[x2][y2];
105
106 if (y2 != aVecMap2[x2].back()) aVecMap2[x2].push_back(y2);
107 }
108 }
109
110 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
111
112 G4ecpssrBaseLixsModel::~G4ecpssrBaseLixsModel()
113 {}
114
115 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
116
117 G4double G4ecpssrBaseLixsModel::ExpIntFunction(G4int n,G4double x)
118
119 {
120 // this function allows fast evaluation of the n order exponential integral function En(x)
121 G4int i;
122 G4int ii;
123 G4int nm1;
124 G4double a;
125 G4double b;
126 G4double c;
127 G4double d;
128 G4double del;
129 G4double fact;
130 G4double h;
131 G4double psi;
132 G4double ans = 0;
133 static const G4double euler= 0.5772156649;
134 static const G4int maxit= 100;
135 static const G4double fpmin = 1.0e-30;
136 static const G4double eps = 1.0e-7;
137 nm1=n-1;
138 if (n<0 || x<0.0 || (x==0.0 && (n==0 || n==1)))
139 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::ExpIntFunction: bad arguments in ExpIntFunction"
140 << G4endl;
141 else {
142 if (n==0) ans=G4Exp(-x)/x;
143 else {
144 if (x==0.0) ans=1.0/nm1;
145 else {
146 if (x > 1.0) {
147 b=x+n;
148 c=1.0/fpmin;
149 d=1.0/b;
150 h=d;
151 for (i=1;i<=maxit;i++) {
152 a=-i*(nm1+i);
153 b +=2.0;
154 d=1.0/(a*d+b);
155 c=b+a/c;
156 del=c*d;
157 h *=del;
158 if (std::fabs(del-1.0) < eps) {
159 ans=h*G4Exp(-x);
160 return ans;
161 }
162 }
163 } else {
164 ans = (nm1!=0 ? 1.0/nm1 : -std::log(x)-euler);
165 fact=1.0;
166 for (i=1;i<=maxit;i++) {
167 fact *=-x/i;
168 if (i !=nm1) del = -fact/(i-nm1);
169 else {
170 psi = -euler;
171 for (ii=1;ii<=nm1;ii++) psi +=1.0/ii;
172 del=fact*(-std::log(x)+psi);
173 }
174 ans += del;
175 if (std::fabs(del) < std::fabs(ans)*eps) return ans;
176 }
177 }
178 }
179 }
180 }
181 return ans;
182 }
183
184 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
185
186 G4double G4ecpssrBaseLixsModel::CalculateL1CrossSection(G4int zTarget,G4double massIncident, G4double energyIncident)
187 {
188
189 if (zTarget <=4) return 0.;
190
191 //this L1-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
192 //and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
193
194 G4NistManager* massManager = G4NistManager::Instance();
195
196 G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
197
198 G4double zIncident = 0;
199 G4Proton* aProtone = G4Proton::Proton();
200 G4Alpha* aAlpha = G4Alpha::Alpha();
201
202 if (massIncident == aProtone->GetPDGMass() )
203 {
204 zIncident = (aProtone->GetPDGCharge())/eplus;
205 }
206 else
207 {
208 if (massIncident == aAlpha->GetPDGMass())
209 {
210 zIncident = (aAlpha->GetPDGCharge())/eplus;
211 }
212 else
213 {
214 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateL1CrossSection : Proton or Alpha incident particles only. " << G4endl;
215 G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
216 return 0;
217 }
218 }
219
220 G4double l1BindingEnergy = transitionManager->Shell(zTarget,1)->BindingEnergy(); //Observed binding energy of L1-subshell
221 G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
222 G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2; //Mass of the system (projectile, target)
223 static const G4double zlshell= 4.15;
224 // *** see Benka, ADANDT 22, p 223
225 G4double screenedzTarget = zTarget-zlshell; //Effective nuclear charge as seen by electrons in L1-sub shell
226 static const G4double rydbergMeV= 13.6056923e-6;
227
228 static const G4double nl= 2.;
229 // *** see Benka, ADANDT 22, p 220, f3
230 G4double tetal1 = (l1BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV); //Screening parameter
231 // *** see Benka, ADANDT 22, p 220, f3
232
233 if (verboseLevel>0) G4cout << " tetal1=" << tetal1<< G4endl;
234
235 G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
236 // *** also called etaS
237 // *** see Benka, ADANDT 22, p 220, f3
238
239 static const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ; //Bohr radius of hydrogen
240
241 G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
242 // *** see Benka, ADANDT 22, p 220, f2, for protons
243 // *** see Basbas, Phys Rev A7, p 1000
244
245 G4double velocityl1 = CalculateVelocity(1, zTarget, massIncident, energyIncident); // Scaled velocity
246
247 if (verboseLevel>0) G4cout << " velocityl1=" << velocityl1<< G4endl;
248
249 static const G4double l1AnalyticalApproximation= 1.5;
250 G4double x1 =(nl*l1AnalyticalApproximation)/velocityl1;
251 // *** 1.5 is cK = cL1 (it is 1.25 for L2 & L3)
252 // *** see Brandt, Phys Rev A20, p 469, f16 in expression of h
253
254 if (verboseLevel>0) G4cout << " x1=" << x1<< G4endl;
255
256 G4double electrIonizationEnergyl1=0.;
257 // *** see Basbas, Phys Rev A17, p1665, f27
258 // *** see Brandt, Phys Rev A20, p469
259 // *** see Liu, Comp Phys Comm 97, p325, f A5
260
261 if ( x1<=0.035) electrIonizationEnergyl1= 0.75*pi*(std::log(1./(x1*x1))-1.);
262 else
263 {
264 if ( x1<=3.)
265 electrIonizationEnergyl1 =G4Exp(-2.*x1)/(0.031+(0.213*std::pow(x1,0.5))+(0.005*x1)-(0.069*std::pow(x1,3./2.))+(0.324*x1*x1));
266 else
267 {if ( x1<=11.) electrIonizationEnergyl1 =2.*G4Exp(-2.*x1)/std::pow(x1,1.6);}
268 }
269
270 G4double hFunctionl1 =(electrIonizationEnergyl1*2.*nl)/(tetal1*std::pow(velocityl1,3)); //takes into account the polarization effect
271 // *** see Brandt, Phys Rev A20, p 469, f16
272
273 if (verboseLevel>0) G4cout << " hFunctionl1=" << hFunctionl1<< G4endl;
274
275 G4double gFunctionl1 = (1.+(9.*velocityl1)+(31.*velocityl1*velocityl1)+(49.*std::pow(velocityl1,3.))+(162.*std::pow(velocityl1,4.))+(63.*std::pow(velocityl1,5.))+(18.*std::pow(velocityl1,6.))+(1.97*std::pow(velocityl1,7.)))/std::pow(1.+velocityl1,9.);//takes into account the reduced binding effect
276 // *** see Brandt, Phys Rev A20, p 469, f19
277
278 if (verboseLevel>0) G4cout << " gFunctionl1=" << gFunctionl1<< G4endl;
279
280 G4double sigmaPSS_l1 = 1.+(((2.*zIncident)/(screenedzTarget*tetal1))*(gFunctionl1-hFunctionl1)); //Binding-polarization factor
281 // *** also called dzeta
282 // *** also called epsilon
283 // *** see Basbas, Phys Rev A17, p1667, f45
284
285 if (verboseLevel>0) G4cout << "sigmaPSS_l1 =" << sigmaPSS_l1<< G4endl;
286
287 const G4double cNaturalUnit= 137.;
288
289 G4double yl1Formula=0.4*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(nl*velocityl1/sigmaPSS_l1);
290 // *** also called yS
291 // *** see Brandt, Phys Rev A20, p467, f6
292 // *** see Brandt, Phys Rev A23, p1728
293
294 G4double l1relativityCorrection = std::pow((1.+(1.1*yl1Formula*yl1Formula)),0.5)+yl1Formula; // Relativistic correction parameter
295 // *** also called mRS
296 // *** see Brandt, Phys Rev A20, p467, f6
297
298 //G4double reducedVelocity_l1 = velocityl1*std::pow(l1relativityCorrection,0.5); //Reduced velocity parameter
299
300 G4double L1etaOverTheta2;
301
302 G4double universalFunction_l1 = 0.;
303
304 G4double sigmaPSSR_l1;
305
306 // low velocity formula
307 // *****************
308 if ( velocityl1 <20. )
309 {
310
311 L1etaOverTheta2 =(reducedEnergy* l1relativityCorrection)/((tetal1*sigmaPSS_l1)*(tetal1*sigmaPSS_l1));
312 // *** 1) RELATIVISTIC CORRECTION ADDED
313 // *** 2) sigma_PSS_l1 ADDED
314 // *** reducedEnergy is etaS, l1relativityCorrection is mRS
315 // *** see Phys Rev A20, p468, top
316
317 if ( ((tetal1*sigmaPSS_l1) >=0.2) && ((tetal1*sigmaPSS_l1) <=2.6670) && (L1etaOverTheta2>=0.1e-3) && (L1etaOverTheta2<=0.866e2) )
318 universalFunction_l1 = FunctionFL1((tetal1*sigmaPSS_l1),L1etaOverTheta2);
319
320 if (verboseLevel>0) G4cout << "at low velocity range, universalFunction_l1 =" << universalFunction_l1 << G4endl;
321
322 sigmaPSSR_l1 = (sigma0/(tetal1*sigmaPSS_l1))*universalFunction_l1;// Plane-wave Born -Aproximation L1-subshell ionisation Cross Section
323 // *** see Benka, ADANDT 22, p220, f1
324
325 if (verboseLevel>0) G4cout << " at low velocity range, sigma PWBA L1 CS = " << sigmaPSSR_l1<< G4endl;
326 }
327 else
328 {
329 L1etaOverTheta2 = reducedEnergy/(tetal1*tetal1);
330 // Medium & high velocity
331 // *** 1) NO RELATIVISTIC CORRECTION
332 // *** 2) NO sigma_PSS_l1
333 // *** see Benka, ADANDT 22, p223
334
335 if ( (tetal1 >=0.2) && (tetal1 <=2.6670) && (L1etaOverTheta2>=0.1e-3) && (L1etaOverTheta2<=0.866e2) )
336 universalFunction_l1 = FunctionFL1(tetal1,L1etaOverTheta2);
337
338 if (verboseLevel>0) G4cout << "at medium and high velocity range, universalFunction_l1 =" << universalFunction_l1 << G4endl;
339
340 sigmaPSSR_l1 = (sigma0/tetal1)*universalFunction_l1;// Plane-wave Born -Aproximation L1-subshell ionisation Cross Section
341 // *** see Benka, ADANDT 22, p220, f1
342
343 if (verboseLevel>0) G4cout << " sigma PWBA L1 CS at medium and high velocity range = " << sigmaPSSR_l1<< G4endl;
344 }
345
346 G4double pssDeltal1 = (4./(systemMass *sigmaPSS_l1*tetal1))*(sigmaPSS_l1/velocityl1)*(sigmaPSS_l1/velocityl1);
347 // *** also called dzeta*delta
348 // *** see Brandt, Phys Rev A23, p1727, f B2
349
350 if (verboseLevel>0) G4cout << " pssDeltal1=" << pssDeltal1<< G4endl;
351
352 if (pssDeltal1>1) return 0.;
353
354 G4double energyLossl1 = std::pow(1-pssDeltal1,0.5);
355 // *** also called z
356 // *** see Brandt, Phys Rev A23, p1727, after f B2
357
358 if (verboseLevel>0) G4cout << " energyLossl1=" << energyLossl1<< G4endl;
359
360 G4double coulombDeflectionl1 =
361 (8.*pi*zIncident/systemMass)*std::pow(tetal1*sigmaPSS_l1,-2.)*std::pow(velocityl1/sigmaPSS_l1,-3.)*(zTarget/screenedzTarget);
362 // *** see Brandt, Phys Rev A20, v2s and f2 and B2
363 // *** with factor n2 compared to Brandt, Phys Rev A23, p1727, f B3
364
365 G4double cParameterl1 =2.* coulombDeflectionl1/(energyLossl1*(energyLossl1+1.));
366 // *** see Brandt, Phys Rev A23, p1727, f B4
367
368 G4double coulombDeflectionFunction_l1 = 9.*ExpIntFunction(10,cParameterl1); //Coulomb-deflection effect correction
369
370 if (verboseLevel>0) G4cout << " coulombDeflectionFunction_l1 =" << coulombDeflectionFunction_l1 << G4endl;
371
372 G4double crossSection_L1 = coulombDeflectionFunction_l1 * sigmaPSSR_l1;
373
374 //ECPSSR L1 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
375 //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
376
377 if (verboseLevel>0) G4cout << " crossSection_L1 =" << crossSection_L1 << G4endl;
378
379 if (crossSection_L1 >= 0)
380 {
381 return crossSection_L1 * barn;
382 }
383
384 else {return 0;}
385 }
386
387 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
388
389 G4double G4ecpssrBaseLixsModel::CalculateL2CrossSection(G4int zTarget,G4double massIncident, G4double energyIncident)
390
391 {
392 if (zTarget <=13 ) return 0.;
393
394 // this L2-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
395 // and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
396
397 G4NistManager* massManager = G4NistManager::Instance();
398
399 G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
400
401 G4double zIncident = 0;
402
403 G4Proton* aProtone = G4Proton::Proton();
404 G4Alpha* aAlpha = G4Alpha::Alpha();
405
406 if (massIncident == aProtone->GetPDGMass() )
407 zIncident = (aProtone->GetPDGCharge())/eplus;
408
409 else
410 {
411 if (massIncident == aAlpha->GetPDGMass())
412 zIncident = (aAlpha->GetPDGCharge())/eplus;
413
414 else
415 {
416 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateL2CrossSection : Proton or Alpha incident particles only. " << G4endl;
417 G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
418 return 0;
419 }
420 }
421
422 G4double l2BindingEnergy = transitionManager->Shell(zTarget,2)->BindingEnergy(); //Observed binding energy of L2-subshell
423
424 G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
425
426 G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2; //Mass of the system (projectile, target)
427
428 const G4double zlshell= 4.15;
429
430 G4double screenedzTarget = zTarget-zlshell; //Effective nuclear charge as seen by electrons in L2-subshell
431
432 const G4double rydbergMeV= 13.6056923e-6;
433
434 const G4double nl= 2.;
435
436 G4double tetal2 = (l2BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV); //Screening parameter
437
438 if (verboseLevel>0) G4cout << " tetal2=" << tetal2<< G4endl;
439
440 G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
441
442 const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ; //Bohr radius of hydrogen
443
444 G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
445
446 G4double velocityl2 = CalculateVelocity(2, zTarget, massIncident, energyIncident); // Scaled velocity
447
448 if (verboseLevel>0) G4cout << " velocityl2=" << velocityl2<< G4endl;
449
450 const G4double l23AnalyticalApproximation= 1.25;
451
452 G4double x2 = (nl*l23AnalyticalApproximation)/velocityl2;
453
454 if (verboseLevel>0) G4cout << " x2=" << x2<< G4endl;
455
456 G4double electrIonizationEnergyl2=0.;
457
458 if ( x2<=0.035) electrIonizationEnergyl2= 0.75*pi*(std::log(1./(x2*x2))-1.);
459 else
460 {
461 if ( x2<=3.)
462 electrIonizationEnergyl2 =G4Exp(-2.*x2)/(0.031+(0.213*std::pow(x2,0.5))+(0.005*x2)-(0.069*std::pow(x2,3./2.))+(0.324*x2*x2));
463 else
464 {if ( x2<=11.) electrIonizationEnergyl2 =2.*G4Exp(-2.*x2)/std::pow(x2,1.6); }
465 }
466
467 G4double hFunctionl2 =(electrIonizationEnergyl2*2.*nl)/(tetal2*std::pow(velocityl2,3)); //takes into account the polarization effect
468
469 if (verboseLevel>0) G4cout << " hFunctionl2=" << hFunctionl2<< G4endl;
470
471 G4double gFunctionl2 = (1.+(10.*velocityl2)+(45.*velocityl2*velocityl2)+(102.*std::pow(velocityl2,3.))+(331.*std::pow(velocityl2,4.))+(6.7*std::pow(velocityl2,5.))+(58.*std::pow(velocityl2,6.))+(7.8*std::pow(velocityl2,7.))+ (0.888*std::pow(velocityl2,8.)) )/std::pow(1.+velocityl2,10.);
472 //takes into account the reduced binding effect
473
474 if (verboseLevel>0) G4cout << " gFunctionl2=" << gFunctionl2<< G4endl;
475
476 G4double sigmaPSS_l2 = 1.+(((2.*zIncident)/(screenedzTarget*tetal2))*(gFunctionl2-hFunctionl2)); //Binding-polarization factor
477
478 if (verboseLevel>0) G4cout << " sigmaPSS_l2=" << sigmaPSS_l2<< G4endl;
479
480 const G4double cNaturalUnit= 137.;
481
482 G4double yl2Formula=0.15*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocityl2/sigmaPSS_l2);
483
484 G4double l2relativityCorrection = std::pow((1.+(1.1*yl2Formula*yl2Formula)),0.5)+yl2Formula; // Relativistic correction parameter
485
486 G4double L2etaOverTheta2;
487
488 G4double universalFunction_l2 = 0.;
489
490 G4double sigmaPSSR_l2 ;
491
492 if ( velocityl2 < 20. )
493 {
494
495 L2etaOverTheta2 = (reducedEnergy*l2relativityCorrection)/((sigmaPSS_l2*tetal2)*(sigmaPSS_l2*tetal2));
496
497 if ( (tetal2*sigmaPSS_l2>=0.2) && (tetal2*sigmaPSS_l2<=2.6670) && (L2etaOverTheta2>=0.1e-3) && (L2etaOverTheta2<=0.866e2) )
498 universalFunction_l2 = FunctionFL2((tetal2*sigmaPSS_l2),L2etaOverTheta2);
499
500 sigmaPSSR_l2 = (sigma0/(tetal2*sigmaPSS_l2))*universalFunction_l2;
501
502 if (verboseLevel>0) G4cout << " sigma PWBA L2 CS at low velocity range = " << sigmaPSSR_l2<< G4endl;
503 }
504 else
505 {
506
507 L2etaOverTheta2 = reducedEnergy /(tetal2*tetal2);
508
509 if ( (tetal2>=0.2) && (tetal2<=2.6670) && (L2etaOverTheta2>=0.1e-3) && (L2etaOverTheta2<=0.866e2) )
510 universalFunction_l2 = FunctionFL2((tetal2),L2etaOverTheta2);
511
512 sigmaPSSR_l2 = (sigma0/tetal2)*universalFunction_l2;
513
514 if (verboseLevel>0) G4cout << " sigma PWBA L2 CS at medium and high velocity range = " << sigmaPSSR_l2<< G4endl;
515
516 }
517
518 G4double pssDeltal2 = (4./(systemMass*sigmaPSS_l2*tetal2))*(sigmaPSS_l2/velocityl2)*(sigmaPSS_l2/velocityl2);
519
520 if (pssDeltal2>1) return 0.;
521
522 G4double energyLossl2 = std::pow(1-pssDeltal2,0.5);
523
524 if (verboseLevel>0) G4cout << " energyLossl2=" << energyLossl2<< G4endl;
525
526 G4double coulombDeflectionl2
527 =(8.*pi*zIncident/systemMass)*std::pow(tetal2*sigmaPSS_l2,-2.)*std::pow(velocityl2/sigmaPSS_l2,-3.)*(zTarget/screenedzTarget);
528
529 G4double cParameterl2 = 2.*coulombDeflectionl2/(energyLossl2*(energyLossl2+1.));
530
531 G4double coulombDeflectionFunction_l2 = 11.*ExpIntFunction(12,cParameterl2); //Coulomb-deflection effect correction
532 // *** see Brandt, Phys Rev A10, p477, f25
533
534 if (verboseLevel>0) G4cout << " coulombDeflectionFunction_l2 =" << coulombDeflectionFunction_l2 << G4endl;
535
536 G4double crossSection_L2 = coulombDeflectionFunction_l2 * sigmaPSSR_l2;
537 //ECPSSR L2 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
538 //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
539
540 if (verboseLevel>0) G4cout << " crossSection_L2 =" << crossSection_L2 << G4endl;
541
542 if (crossSection_L2 >= 0)
543 {
544 return crossSection_L2 * barn;
545 }
546 else {return 0;}
547 }
548
549 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
550
551
552 G4double G4ecpssrBaseLixsModel::CalculateL3CrossSection(G4int zTarget,G4double massIncident, G4double energyIncident)
553
554 {
555 if (zTarget <=13) return 0.;
556
557 //this L3-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
558 //and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
559
560 G4NistManager* massManager = G4NistManager::Instance();
561
562 G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
563
564 G4double zIncident = 0;
565
566 G4Proton* aProtone = G4Proton::Proton();
567 G4Alpha* aAlpha = G4Alpha::Alpha();
568
569 if (massIncident == aProtone->GetPDGMass() )
570
571 zIncident = (aProtone->GetPDGCharge())/eplus;
572
573 else
574 {
575 if (massIncident == aAlpha->GetPDGMass())
576
577 zIncident = (aAlpha->GetPDGCharge())/eplus;
578
579 else
580 {
581 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateL3CrossSection : Proton or Alpha incident particles only. " << G4endl;
582 G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
583 return 0;
584 }
585 }
586
587 G4double l3BindingEnergy = transitionManager->Shell(zTarget,3)->BindingEnergy();
588
589 G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
590
591 G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2;//Mass of the system (projectile, target)
592
593 const G4double zlshell= 4.15;
594
595 G4double screenedzTarget = zTarget-zlshell;//Effective nuclear charge as seen by electrons in L3-subshell
596
597 const G4double rydbergMeV= 13.6056923e-6;
598
599 const G4double nl= 2.;
600
601 G4double tetal3 = (l3BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV);//Screening parameter
602
603 if (verboseLevel>0) G4cout << " tetal3=" << tetal3<< G4endl;
604
605 G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
606
607 const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ;//Bohr radius of hydrogen
608
609 G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
610
611 G4double velocityl3 = CalculateVelocity(3, zTarget, massIncident, energyIncident);// Scaled velocity
612
613 if (verboseLevel>0) G4cout << " velocityl3=" << velocityl3<< G4endl;
614
615 const G4double l23AnalyticalApproximation= 1.25;
616
617 G4double x3 = (nl*l23AnalyticalApproximation)/velocityl3;
618
619 if (verboseLevel>0) G4cout << " x3=" << x3<< G4endl;
620
621 G4double electrIonizationEnergyl3=0.;
622
623 if ( x3<=0.035) electrIonizationEnergyl3= 0.75*pi*(std::log(1./(x3*x3))-1.);
624 else
625 {
626 if ( x3<=3.) electrIonizationEnergyl3 =G4Exp(-2.*x3)/(0.031+(0.213*std::pow(x3,0.5))+(0.005*x3)-(0.069*std::pow(x3,3./2.))+(0.324*x3*x3));
627 else
628 {
629 if ( x3<=11.) electrIonizationEnergyl3 =2.*G4Exp(-2.*x3)/std::pow(x3,1.6);}
630 }
631
632 G4double hFunctionl3 =(electrIonizationEnergyl3*2.*nl)/(tetal3*std::pow(velocityl3,3));//takes into account the polarization effect
633
634 if (verboseLevel>0) G4cout << " hFunctionl3=" << hFunctionl3<< G4endl;
635
636 G4double gFunctionl3 = (1.+(10.*velocityl3)+(45.*velocityl3*velocityl3)+(102.*std::pow(velocityl3,3.))+(331.*std::pow(velocityl3,4.))+(6.7*std::pow(velocityl3,5.))+(58.*std::pow(velocityl3,6.))+(7.8*std::pow(velocityl3,7.))+ (0.888*std::pow(velocityl3,8.)) )/std::pow(1.+velocityl3,10.);
637 //takes into account the reduced binding effect
638
639 if (verboseLevel>0) G4cout << " gFunctionl3=" << gFunctionl3<< G4endl;
640
641 G4double sigmaPSS_l3 = 1.+(((2.*zIncident)/(screenedzTarget*tetal3))*(gFunctionl3-hFunctionl3));//Binding-polarization factor
642
643 if (verboseLevel>0) G4cout << "sigmaPSS_l3 =" << sigmaPSS_l3<< G4endl;
644
645 const G4double cNaturalUnit= 137.;
646
647 G4double yl3Formula=0.15*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocityl3/sigmaPSS_l3);
648
649 G4double l3relativityCorrection = std::pow((1.+(1.1*yl3Formula*yl3Formula)),0.5)+yl3Formula; // Relativistic correction parameter
650
651 G4double L3etaOverTheta2;
652
653 G4double universalFunction_l3 = 0.;
654
655 G4double sigmaPSSR_l3;
656
657 if ( velocityl3 < 20. )
658 {
659
660 L3etaOverTheta2 = (reducedEnergy* l3relativityCorrection)/((sigmaPSS_l3*tetal3)*(sigmaPSS_l3*tetal3));
661
662 if ( (tetal3*sigmaPSS_l3>=0.2) && (tetal3*sigmaPSS_l3<=2.6670) && (L3etaOverTheta2>=0.1e-3) && (L3etaOverTheta2<=0.866e2) )
663
664 universalFunction_l3 = 2.*FunctionFL2((tetal3*sigmaPSS_l3), L3etaOverTheta2 );
665
666 sigmaPSSR_l3 = (sigma0/(tetal3*sigmaPSS_l3))*universalFunction_l3;
667
668 if (verboseLevel>0) G4cout << " sigma PWBA L3 CS at low velocity range = " << sigmaPSSR_l3<< G4endl;
669
670 }
671
672 else
673
674 {
675
676 L3etaOverTheta2 = reducedEnergy/(tetal3*tetal3);
677
678 if ( (tetal3>=0.2) && (tetal3<=2.6670) && (L3etaOverTheta2>=0.1e-3) && (L3etaOverTheta2<=0.866e2) )
679
680 universalFunction_l3 = 2.*FunctionFL2(tetal3, L3etaOverTheta2 );
681
682 sigmaPSSR_l3 = (sigma0/tetal3)*universalFunction_l3;
683
684 if (verboseLevel>0) G4cout << " sigma PWBA L3 CS at medium and high velocity range = " << sigmaPSSR_l3<< G4endl;
685 }
686
687 G4double pssDeltal3 = (4./(systemMass*sigmaPSS_l3*tetal3))*(sigmaPSS_l3/velocityl3)*(sigmaPSS_l3/velocityl3);
688
689 if (verboseLevel>0) G4cout << " pssDeltal3=" << pssDeltal3<< G4endl;
690
691 if (pssDeltal3>1) return 0.;
692
693 G4double energyLossl3 = std::pow(1-pssDeltal3,0.5);
694
695 if (verboseLevel>0) G4cout << " energyLossl3=" << energyLossl3<< G4endl;
696
697 G4double coulombDeflectionl3 =
698 (8.*pi*zIncident/systemMass)*std::pow(tetal3*sigmaPSS_l3,-2.)*std::pow(velocityl3/sigmaPSS_l3,-3.)*(zTarget/screenedzTarget);
699
700 G4double cParameterl3 = 2.*coulombDeflectionl3/(energyLossl3*(energyLossl3+1.));
701
702 G4double coulombDeflectionFunction_l3 = 11.*ExpIntFunction(12,cParameterl3);//Coulomb-deflection effect correction
703 // *** see Brandt, Phys Rev A10, p477, f25
704
705 if (verboseLevel>0) G4cout << " coulombDeflectionFunction_l3 =" << coulombDeflectionFunction_l3 << G4endl;
706
707 G4double crossSection_L3 = coulombDeflectionFunction_l3 * sigmaPSSR_l3;
708 //ECPSSR L3 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
709 //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
710
711 if (verboseLevel>0) G4cout << " crossSection_L3 =" << crossSection_L3 << G4endl;
712
713 if (crossSection_L3 >= 0)
714 {
715 return crossSection_L3 * barn;
716 }
717 else {return 0;}
718 }
719
720 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
721
722 G4double G4ecpssrBaseLixsModel::CalculateVelocity(G4int subShell, G4int zTarget, G4double massIncident, G4double energyIncident)
723
724 {
725
726 G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
727
728 G4double liBindingEnergy = transitionManager->Shell(zTarget,subShell)->BindingEnergy();
729
730 G4Proton* aProtone = G4Proton::Proton();
731 G4Alpha* aAlpha = G4Alpha::Alpha();
732
733 if (!((massIncident == aProtone->GetPDGMass()) || (massIncident == aAlpha->GetPDGMass())))
734 {
735 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateVelocity : Proton or Alpha incident particles only. " << G4endl;
736 G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
737 return 0;
738 }
739
740 constexpr G4double zlshell= 4.15;
741
742 G4double screenedzTarget = zTarget- zlshell;
743
744 constexpr G4double rydbergMeV= 13.6056923e-6;
745
746 constexpr G4double nl= 2.;
747
748 G4double tetali = (liBindingEnergy*nl*nl)/(screenedzTarget*screenedzTarget*rydbergMeV);
749
750 G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
751
752 G4double velocity = 2.*nl*std::pow(reducedEnergy,0.5)/tetali;
753 // *** see Brandt, Phys Rev A10, p10, f4
754
755 return velocity;
756 }
757
758 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
759
760 G4double G4ecpssrBaseLixsModel::FunctionFL1(G4double k, G4double theta)
761 {
762 G4double sigma = 0.;
763 G4double valueT1 = 0;
764 G4double valueT2 = 0;
765 G4double valueE21 = 0;
766 G4double valueE22 = 0;
767 G4double valueE12 = 0;
768 G4double valueE11 = 0;
769 G4double xs11 = 0;
770 G4double xs12 = 0;
771 G4double xs21 = 0;
772 G4double xs22 = 0;
773
774 // PROTECTION TO ALLOW INTERPOLATION AT MINIMUM AND MAXIMUM Eta/Theta2 values
775
776 if (
777 theta==8.66e-4 ||
778 theta==8.66e-3 ||
779 theta==8.66e-2 ||
780 theta==8.66e-1 ||
781 theta==8.66e+00 ||
782 theta==8.66e+01
783 ) theta=theta-1e-12;
784
785 if (
786 theta==1.e-4 ||
787 theta==1.e-3 ||
788 theta==1.e-2 ||
789 theta==1.e-1 ||
790 theta==1.e+00 ||
791 theta==1.e+01
792 ) theta=theta+1e-12;
793
794 // END PROTECTION
795
796 auto t2 = std::upper_bound(dummyVec1.begin(),dummyVec1.end(), k);
797 auto t1 = t2-1;
798
799 auto e12 = std::upper_bound(aVecMap1[(*t1)].begin(),aVecMap1[(*t1)].end(), theta);
800 auto e11 = e12-1;
801
802 auto e22 = std::upper_bound(aVecMap1[(*t2)].begin(),aVecMap1[(*t2)].end(), theta);
803 auto e21 = e22-1;
804
805 valueT1 =*t1;
806 valueT2 =*t2;
807 valueE21 =*e21;
808 valueE22 =*e22;
809 valueE12 =*e12;
810 valueE11 =*e11;
811
812 xs11 = FL1Data[valueT1][valueE11];
813 xs12 = FL1Data[valueT1][valueE12];
814 xs21 = FL1Data[valueT2][valueE21];
815 xs22 = FL1Data[valueT2][valueE22];
816
817 if (verboseLevel>0)
818 G4cout
819 << valueT1 << " "
820 << valueT2 << " "
821 << valueE11 << " "
822 << valueE12 << " "
823 << valueE21 << " "
824 << valueE22 << " "
825 << xs11 << " "
826 << xs12 << " "
827 << xs21 << " "
828 << xs22 << " "
829 << G4endl;
830
831 G4double xsProduct = xs11 * xs12 * xs21 * xs22;
832
833 if (xs11==0 || xs12==0 ||xs21==0 ||xs22==0) return (0.);
834
835 if (xsProduct != 0.)
836 {
837 sigma = QuadInterpolator( valueE11, valueE12,
838 valueE21, valueE22,
839 xs11, xs12,
840 xs21, xs22,
841 valueT1, valueT2,
842 k, theta );
843 }
844
845 return sigma;
846 }
847
848 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
849
850 G4double G4ecpssrBaseLixsModel::FunctionFL2(G4double k, G4double theta)
851 {
852
853 G4double sigma = 0.;
854 G4double valueT1 = 0;
855 G4double valueT2 = 0;
856 G4double valueE21 = 0;
857 G4double valueE22 = 0;
858 G4double valueE12 = 0;
859 G4double valueE11 = 0;
860 G4double xs11 = 0;
861 G4double xs12 = 0;
862 G4double xs21 = 0;
863 G4double xs22 = 0;
864
865 // PROTECTION TO ALLOW INTERPOLATION AT MINIMUM AND MAXIMUM Eta/Theta2 values
866
867 if (
868 theta==8.66e-4 ||
869 theta==8.66e-3 ||
870 theta==8.66e-2 ||
871 theta==8.66e-1 ||
872 theta==8.66e+00 ||
873 theta==8.66e+01
874 ) theta=theta-1e-12;
875
876 if (
877 theta==1.e-4 ||
878 theta==1.e-3 ||
879 theta==1.e-2 ||
880 theta==1.e-1 ||
881 theta==1.e+00 ||
882 theta==1.e+01
883 ) theta=theta+1e-12;
884
885 // END PROTECTION
886
887 auto t2 = std::upper_bound(dummyVec2.begin(),dummyVec2.end(), k);
888 auto t1 = t2-1;
889 auto e12 = std::upper_bound(aVecMap2[(*t1)].begin(),aVecMap2[(*t1)].end(), theta);
890 auto e11 = e12-1;
891 auto e22 = std::upper_bound(aVecMap2[(*t2)].begin(),aVecMap2[(*t2)].end(), theta);
892 auto e21 = e22-1;
893
894 valueT1 =*t1;
895 valueT2 =*t2;
896 valueE21 =*e21;
897 valueE22 =*e22;
898 valueE12 =*e12;
899 valueE11 =*e11;
900
901 xs11 = FL2Data[valueT1][valueE11];
902 xs12 = FL2Data[valueT1][valueE12];
903 xs21 = FL2Data[valueT2][valueE21];
904 xs22 = FL2Data[valueT2][valueE22];
905
906 if (verboseLevel>0)
907 G4cout
908 << valueT1 << " "
909 << valueT2 << " "
910 << valueE11 << " "
911 << valueE12 << " "
912 << valueE21 << " "
913 << valueE22 << " "
914 << xs11 << " "
915 << xs12 << " "
916 << xs21 << " "
917 << xs22 << " "
918 << G4endl;
919
920 G4double xsProduct = xs11 * xs12 * xs21 * xs22;
921
922 if (xs11==0 || xs12==0 ||xs21==0 ||xs22==0) return (0.);
923
924 if (xsProduct != 0.)
925 {
926 sigma = QuadInterpolator( valueE11, valueE12,
927 valueE21, valueE22,
928 xs11, xs12,
929 xs21, xs22,
930 valueT1, valueT2,
931 k, theta );
932 }
933
934 return sigma;
935 }
936
937 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
938
939 G4double G4ecpssrBaseLixsModel::LinLinInterpolate(G4double e1,
940 G4double e2,
941 G4double e,
942 G4double xs1,
943 G4double xs2)
944 {
945 G4double value = xs1 + (xs2 - xs1)*(e - e1)/ (e2 - e1);
946 return value;
947 }
948
949 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
950
951 G4double G4ecpssrBaseLixsModel::LinLogInterpolate(G4double e1,
952 G4double e2,
953 G4double e,
954 G4double xs1,
955 G4double xs2)
956 {
957 G4double d1 = std::log(xs1);
958 G4double d2 = std::log(xs2);
959 G4double value = G4Exp(d1 + (d2 - d1)*(e - e1)/ (e2 - e1));
960 return value;
961 }
962
963 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
964
965 G4double G4ecpssrBaseLixsModel::LogLogInterpolate(G4double e1,
966 G4double e2,
967 G4double e,
968 G4double xs1,
969 G4double xs2)
970 {
971 G4double a = (std::log10(xs2)-std::log10(xs1)) / (std::log10(e2)-std::log10(e1));
972 G4double b = std::log10(xs2) - a*std::log10(e2);
973 G4double sigma = a*std::log10(e) + b;
974 G4double value = (std::pow(10.,sigma));
975 return value;
976 }
977
978 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
979
980 G4double G4ecpssrBaseLixsModel::QuadInterpolator(G4double e11, G4double e12,
981 G4double e21, G4double e22,
982 G4double xs11, G4double xs12,
983 G4double xs21, G4double xs22,
984 G4double t1, G4double t2,
985 G4double t, G4double e)
986 {
987 // Log-Log
988 G4double interpolatedvalue1 = LogLogInterpolate(e11, e12, e, xs11, xs12);
989 G4double interpolatedvalue2 = LogLogInterpolate(e21, e22, e, xs21, xs22);
990 G4double value = LogLogInterpolate(t1, t2, t, interpolatedvalue1, interpolatedvalue2);
991 return value;
992
993 }
994