Geant4 9.6.0
Toolkit for the simulation of the passage of particles through matter
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G4ecpssrBaseLixsModel.cc
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26
27#include <cmath>
28#include <iostream>
29
30#include "G4ecpssrBaseLixsModel.hh"
31
32#include "globals.hh"
33#include "G4PhysicalConstants.hh"
34#include "G4SystemOfUnits.hh"
35#include "G4AtomicTransitionManager.hh"
36#include "G4NistManager.hh"
37#include "G4Proton.hh"
38#include "G4Alpha.hh"
39#include "G4LinLogInterpolation.hh"
40
41//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
42
43G4ecpssrBaseLixsModel::G4ecpssrBaseLixsModel()
44{
45 verboseLevel=0;
46
47 // Storing FLi data needed for 0.2 to 3.0 velocities region
48
49 char *path = getenv("G4LEDATA");
50
51 if (!path) {
52 G4Exception("G4ecpssrLCrossSection::G4ecpssrBaseLixsModel()","em0006", FatalException ,"G4LEDATA environment variable not set");
53 return;
54 }
55 std::ostringstream fileName1;
56 std::ostringstream fileName2;
57
58 fileName1 << path << "/pixe/uf/FL1.dat";
59 fileName2 << path << "/pixe/uf/FL2.dat";
60
61 // Reading of FL1.dat
62
63 std::ifstream FL1(fileName1.str().c_str());
64 if (!FL1) G4Exception("G4ecpssrLCrossSection::G4ecpssrBaseLixsModel()","em0003",FatalException, "error opening FL1 data file");
65
66 dummyVec1.push_back(0.);
67
68 while(!FL1.eof())
69 {
70 double x1;
71 double y1;
72
73 FL1>>x1>>y1;
74
75 // Mandatory vector initialization
76 if (x1 != dummyVec1.back())
77 {
78 dummyVec1.push_back(x1);
79 aVecMap1[x1].push_back(-1.);
80 }
81
82 FL1>>FL1Data[x1][y1];
83
84 if (y1 != aVecMap1[x1].back()) aVecMap1[x1].push_back(y1);
85 }
86
87 // Reading of FL2.dat
88
89 std::ifstream FL2(fileName2.str().c_str());
90 if (!FL2) G4Exception("G4ecpssrLCrossSection::G4ecpssrBaseLixsModel()","em0003", FatalException," error opening FL2 data file");
91
92 dummyVec2.push_back(0.);
93
94 while(!FL2.eof())
95 {
96 double x2;
97 double y2;
98
99 FL2>>x2>>y2;
100
101 // Mandatory vector initialization
102 if (x2 != dummyVec2.back())
103 {
104 dummyVec2.push_back(x2);
105 aVecMap2[x2].push_back(-1.);
106 }
107
108 FL2>>FL2Data[x2][y2];
109
110 if (y2 != aVecMap2[x2].back()) aVecMap2[x2].push_back(y2);
111 }
112
113}
114
115//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
116
117G4ecpssrBaseLixsModel::~G4ecpssrBaseLixsModel()
118{}
119
120//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
121
122G4double G4ecpssrBaseLixsModel::ExpIntFunction(G4int n,G4double x)
123
124{
125// this function allows fast evaluation of the n order exponential integral function En(x)
126
127 G4int i;
128 G4int ii;
129 G4int nm1;
130 G4double a;
131 G4double b;
132 G4double c;
133 G4double d;
134 G4double del;
135 G4double fact;
136 G4double h;
137 G4double psi;
138 G4double ans = 0;
139 const G4double euler= 0.5772156649;
140 const G4int maxit= 100;
141 const G4double fpmin = 1.0e-30;
142 const G4double eps = 1.0e-7;
143 nm1=n-1;
144 if (n<0 || x<0.0 || (x==0.0 && (n==0 || n==1)))
145 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::ExpIntFunction: bad arguments in ExpIntFunction"
146 << G4endl;
147 else {
148 if (n==0) ans=std::exp(-x)/x;
149 else {
150 if (x==0.0) ans=1.0/nm1;
151 else {
152 if (x > 1.0) {
153 b=x+n;
154 c=1.0/fpmin;
155 d=1.0/b;
156 h=d;
157 for (i=1;i<=maxit;i++) {
158 a=-i*(nm1+i);
159 b +=2.0;
160 d=1.0/(a*d+b);
161 c=b+a/c;
162 del=c*d;
163 h *=del;
164 if (std::fabs(del-1.0) < eps) {
165 ans=h*std::exp(-x);
166 return ans;
167 }
168 }
169 } else {
170 ans = (nm1!=0 ? 1.0/nm1 : -std::log(x)-euler);
171 fact=1.0;
172 for (i=1;i<=maxit;i++) {
173 fact *=-x/i;
174 if (i !=nm1) del = -fact/(i-nm1);
175 else {
176 psi = -euler;
177 for (ii=1;ii<=nm1;ii++) psi +=1.0/ii;
178 del=fact*(-std::log(x)+psi);
179 }
180 ans += del;
181 if (std::fabs(del) < std::fabs(ans)*eps) return ans;
182 }
183 }
184 }
185 }
186 }
187return ans;
188}
189
190//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
191
192G4double G4ecpssrBaseLixsModel::CalculateL1CrossSection(G4int zTarget,G4double massIncident, G4double energyIncident)
193{
194
195 if (zTarget <=4) return 0.;
196
197 //this L1-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
198 //and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
199
200 G4NistManager* massManager = G4NistManager::Instance();
201
202 G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
203
204 G4double zIncident = 0;
205 G4Proton* aProtone = G4Proton::Proton();
206 G4Alpha* aAlpha = G4Alpha::Alpha();
207
208 if (massIncident == aProtone->GetPDGMass() )
209
210 zIncident = (aProtone->GetPDGCharge())/eplus;
211
212 else
213 {
214 if (massIncident == aAlpha->GetPDGMass())
215
216 zIncident = (aAlpha->GetPDGCharge())/eplus;
217
218 else
219 {
220 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateL1CrossSection : Proton or Alpha incident particles only. " << G4endl;
221 G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
222 return 0;
223 }
224 }
225
226 G4double l1BindingEnergy = transitionManager->Shell(zTarget,1)->BindingEnergy(); //Observed binding energy of L1-subshell
227
228 G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
229
230 G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2; //Mass of the system (projectile, target)
231
232 const G4double zlshell= 4.15;
233 // *** see Benka, ADANDT 22, p 223
234
235 G4double screenedzTarget = zTarget-zlshell; //Effective nuclear charge as seen by electrons in L1-sub shell
236
237 const G4double rydbergMeV= 13.6056923e-6;
238
239 const G4double nl= 2.;
240 // *** see Benka, ADANDT 22, p 220, f3
241
242 G4double tetal1 = (l1BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV); //Screening parameter
243 // *** see Benka, ADANDT 22, p 220, f3
244
245 if (verboseLevel>0) G4cout << " tetal1=" << tetal1<< G4endl;
246
247 G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
248 // *** also called etaS
249 // *** see Benka, ADANDT 22, p 220, f3
250
251 const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ; //Bohr radius of hydrogen
252
253 G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
254 // *** see Benka, ADANDT 22, p 220, f2, for protons
255 // *** see Basbas, Phys Rev A7, p 1000
256
257 G4double velocityl1 = CalculateVelocity(1, zTarget, massIncident, energyIncident); // Scaled velocity
258
259 if (verboseLevel>0) G4cout << " velocityl1=" << velocityl1<< G4endl;
260
261 const G4double l1AnalyticalApproximation= 1.5;
262 G4double x1 =(nl*l1AnalyticalApproximation)/velocityl1;
263 // *** 1.5 is cK = cL1 (it is 1.25 for L2 & L3)
264 // *** see Brandt, Phys Rev A20, p 469, f16 in expression of h
265
266 if (verboseLevel>0) G4cout << " x1=" << x1<< G4endl;
267
268 G4double electrIonizationEnergyl1=0.;
269 // *** see Basbas, Phys Rev A17, p1665, f27
270 // *** see Brandt, Phys Rev A20, p469
271 // *** see Liu, Comp Phys Comm 97, p325, f A5
272
273 if ( x1<=0.035) electrIonizationEnergyl1= 0.75*pi*(std::log(1./(x1*x1))-1.);
274 else
275 {
276 if ( x1<=3.)
277 electrIonizationEnergyl1 =std::exp(-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));
278 else
279 {if ( x1<=11.) electrIonizationEnergyl1 =2.*std::exp(-2.*x1)/std::pow(x1,1.6);}
280 }
281
282 G4double hFunctionl1 =(electrIonizationEnergyl1*2.*nl)/(tetal1*std::pow(velocityl1,3)); //takes into account the polarization effect
283 // *** see Brandt, Phys Rev A20, p 469, f16
284
285 if (verboseLevel>0) G4cout << " hFunctionl1=" << hFunctionl1<< G4endl;
286
287 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
288 // *** see Brandt, Phys Rev A20, p 469, f19
289
290 if (verboseLevel>0) G4cout << " gFunctionl1=" << gFunctionl1<< G4endl;
291
292 G4double sigmaPSS_l1 = 1.+(((2.*zIncident)/(screenedzTarget*tetal1))*(gFunctionl1-hFunctionl1)); //Binding-polarization factor
293 // *** also called dzeta
294 // *** also called epsilon
295 // *** see Basbas, Phys Rev A17, p1667, f45
296
297 if (verboseLevel>0) G4cout << "sigmaPSS_l1 =" << sigmaPSS_l1<< G4endl;
298
299 const G4double cNaturalUnit= 137.;
300
301 G4double yl1Formula=0.4*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(nl*velocityl1/sigmaPSS_l1);
302 // *** also called yS
303 // *** see Brandt, Phys Rev A20, p467, f6
304 // *** see Brandt, Phys Rev A23, p1728
305
306 G4double l1relativityCorrection = std::pow((1.+(1.1*yl1Formula*yl1Formula)),0.5)+yl1Formula; // Relativistic correction parameter
307 // *** also called mRS
308 // *** see Brandt, Phys Rev A20, p467, f6
309
310 //G4double reducedVelocity_l1 = velocityl1*std::pow(l1relativityCorrection,0.5); //Reduced velocity parameter
311
312 G4double L1etaOverTheta2;
313
314 G4double universalFunction_l1 = 0.;
315
316 G4double sigmaPSSR_l1;
317
318 // low velocity formula
319 // *****************
320 if ( velocityl1 <20. )
321 {
322
323 L1etaOverTheta2 =(reducedEnergy* l1relativityCorrection)/((tetal1*sigmaPSS_l1)*(tetal1*sigmaPSS_l1));
324 // *** 1) RELATIVISTIC CORRECTION ADDED
325 // *** 2) sigma_PSS_l1 ADDED
326 // *** reducedEnergy is etaS, l1relativityCorrection is mRS
327 // *** see Phys Rev A20, p468, top
328
329 if ( ((tetal1*sigmaPSS_l1) >=0.2) && ((tetal1*sigmaPSS_l1) <=2.6670) && (L1etaOverTheta2>=0.1e-3) && (L1etaOverTheta2<=0.866e2) )
330
331 universalFunction_l1 = FunctionFL1((tetal1*sigmaPSS_l1),L1etaOverTheta2);
332
333 if (verboseLevel>0) G4cout << "at low velocity range, universalFunction_l1 =" << universalFunction_l1 << G4endl;
334
335 sigmaPSSR_l1 = (sigma0/(tetal1*sigmaPSS_l1))*universalFunction_l1;// Plane-wave Born -Aproximation L1-subshell ionisation Cross Section
336 // *** see Benka, ADANDT 22, p220, f1
337
338 if (verboseLevel>0) G4cout << " at low velocity range, sigma PWBA L1 CS = " << sigmaPSSR_l1<< G4endl;
339
340 }
341
342 else
343
344 {
345
346 L1etaOverTheta2 = reducedEnergy/(tetal1*tetal1);
347 // Medium & high velocity
348 // *** 1) NO RELATIVISTIC CORRECTION
349 // *** 2) NO sigma_PSS_l1
350 // *** see Benka, ADANDT 22, p223
351
352 if ( (tetal1 >=0.2) && (tetal1 <=2.6670) && (L1etaOverTheta2>=0.1e-3) && (L1etaOverTheta2<=0.866e2) )
353
354 universalFunction_l1 = FunctionFL1(tetal1,L1etaOverTheta2);
355
356 if (verboseLevel>0) G4cout << "at medium and high velocity range, universalFunction_l1 =" << universalFunction_l1 << G4endl;
357
358 sigmaPSSR_l1 = (sigma0/tetal1)*universalFunction_l1;// Plane-wave Born -Aproximation L1-subshell ionisation Cross Section
359 // *** see Benka, ADANDT 22, p220, f1
360
361 if (verboseLevel>0) G4cout << " sigma PWBA L1 CS at medium and high velocity range = " << sigmaPSSR_l1<< G4endl;
362 }
363
364 G4double pssDeltal1 = (4./(systemMass *sigmaPSS_l1*tetal1))*(sigmaPSS_l1/velocityl1)*(sigmaPSS_l1/velocityl1);
365 // *** also called dzeta*delta
366 // *** see Brandt, Phys Rev A23, p1727, f B2
367
368 if (verboseLevel>0) G4cout << " pssDeltal1=" << pssDeltal1<< G4endl;
369
370 if (pssDeltal1>1) return 0.;
371
372 G4double energyLossl1 = std::pow(1-pssDeltal1,0.5);
373 // *** also called z
374 // *** see Brandt, Phys Rev A23, p1727, after f B2
375
376 if (verboseLevel>0) G4cout << " energyLossl1=" << energyLossl1<< G4endl;
377
378 G4double coulombDeflectionl1 =
379 (8.*pi*zIncident/systemMass)*std::pow(tetal1*sigmaPSS_l1,-2.)*std::pow(velocityl1/sigmaPSS_l1,-3.)*(zTarget/screenedzTarget);
380 // *** see Brandt, Phys Rev A20, v2s and f2 and B2
381 // *** with factor n2 compared to Brandt, Phys Rev A23, p1727, f B3
382
383 G4double cParameterl1 =2.* coulombDeflectionl1/(energyLossl1*(energyLossl1+1.));
384 // *** see Brandt, Phys Rev A23, p1727, f B4
385
386 G4double coulombDeflectionFunction_l1 = 9.*ExpIntFunction(10,cParameterl1); //Coulomb-deflection effect correction
387
388 if (verboseLevel>0) G4cout << " coulombDeflectionFunction_l1 =" << coulombDeflectionFunction_l1 << G4endl;
389
390 G4double crossSection_L1 = coulombDeflectionFunction_l1 * sigmaPSSR_l1;
391
392 //ECPSSR L1 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
393 //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
394
395 if (verboseLevel>0) G4cout << " crossSection_L1 =" << crossSection_L1 << G4endl;
396
397 if (crossSection_L1 >= 0)
398 {
399 return crossSection_L1 * barn;
400 }
401
402 else {return 0;}
403}
404
405//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
406
407G4double G4ecpssrBaseLixsModel::CalculateL2CrossSection(G4int zTarget,G4double massIncident, G4double energyIncident)
408
409{
410 if (zTarget <=13 ) return 0.;
411
412 // this L2-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
413 // and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
414
415 G4NistManager* massManager = G4NistManager::Instance();
416
417 G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
418
419 G4double zIncident = 0;
420
421 G4Proton* aProtone = G4Proton::Proton();
422 G4Alpha* aAlpha = G4Alpha::Alpha();
423
424 if (massIncident == aProtone->GetPDGMass() )
425
426 zIncident = (aProtone->GetPDGCharge())/eplus;
427
428 else
429 {
430 if (massIncident == aAlpha->GetPDGMass())
431
432 zIncident = (aAlpha->GetPDGCharge())/eplus;
433
434 else
435 {
436 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateL2CrossSection : Proton or Alpha incident particles only. " << G4endl;
437 G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
438 return 0;
439 }
440 }
441
442 G4double l2BindingEnergy = transitionManager->Shell(zTarget,2)->BindingEnergy(); //Observed binding energy of L2-subshell
443
444 G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
445
446 G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2; //Mass of the system (projectile, target)
447
448 const G4double zlshell= 4.15;
449
450 G4double screenedzTarget = zTarget-zlshell; //Effective nuclear charge as seen by electrons in L2-subshell
451
452 const G4double rydbergMeV= 13.6056923e-6;
453
454 const G4double nl= 2.;
455
456 G4double tetal2 = (l2BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV); //Screening parameter
457
458 if (verboseLevel>0) G4cout << " tetal2=" << tetal2<< G4endl;
459
460 G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
461
462 const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ; //Bohr radius of hydrogen
463
464 G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
465
466 G4double velocityl2 = CalculateVelocity(2, zTarget, massIncident, energyIncident); // Scaled velocity
467
468 if (verboseLevel>0) G4cout << " velocityl2=" << velocityl2<< G4endl;
469
470 const G4double l23AnalyticalApproximation= 1.25;
471
472 G4double x2 = (nl*l23AnalyticalApproximation)/velocityl2;
473
474 if (verboseLevel>0) G4cout << " x2=" << x2<< G4endl;
475
476 G4double electrIonizationEnergyl2=0.;
477
478 if ( x2<=0.035) electrIonizationEnergyl2= 0.75*pi*(std::log(1./(x2*x2))-1.);
479 else
480 {
481 if ( x2<=3.)
482 electrIonizationEnergyl2 =std::exp(-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));
483 else
484 {if ( x2<=11.) electrIonizationEnergyl2 =2.*std::exp(-2.*x2)/std::pow(x2,1.6); }
485 }
486
487 G4double hFunctionl2 =(electrIonizationEnergyl2*2.*nl)/(tetal2*std::pow(velocityl2,3)); //takes into account the polarization effect
488
489 if (verboseLevel>0) G4cout << " hFunctionl2=" << hFunctionl2<< G4endl;
490
491 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.);
492 //takes into account the reduced binding effect
493
494 if (verboseLevel>0) G4cout << " gFunctionl2=" << gFunctionl2<< G4endl;
495
496 G4double sigmaPSS_l2 = 1.+(((2.*zIncident)/(screenedzTarget*tetal2))*(gFunctionl2-hFunctionl2)); //Binding-polarization factor
497
498 if (verboseLevel>0) G4cout << " sigmaPSS_l2=" << sigmaPSS_l2<< G4endl;
499
500 const G4double cNaturalUnit= 137.;
501
502 G4double yl2Formula=0.15*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocityl2/sigmaPSS_l2);
503
504 G4double l2relativityCorrection = std::pow((1.+(1.1*yl2Formula*yl2Formula)),0.5)+yl2Formula; // Relativistic correction parameter
505
506 G4double L2etaOverTheta2;
507
508 G4double universalFunction_l2 = 0.;
509
510 G4double sigmaPSSR_l2 ;
511
512 if ( velocityl2 < 20. )
513 {
514
515 L2etaOverTheta2 = (reducedEnergy*l2relativityCorrection)/((sigmaPSS_l2*tetal2)*(sigmaPSS_l2*tetal2));
516
517 if ( (tetal2*sigmaPSS_l2>=0.2) && (tetal2*sigmaPSS_l2<=2.6670) && (L2etaOverTheta2>=0.1e-3) && (L2etaOverTheta2<=0.866e2) )
518
519 universalFunction_l2 = FunctionFL2((tetal2*sigmaPSS_l2),L2etaOverTheta2);
520
521 sigmaPSSR_l2 = (sigma0/(tetal2*sigmaPSS_l2))*universalFunction_l2;
522
523 if (verboseLevel>0) G4cout << " sigma PWBA L2 CS at low velocity range = " << sigmaPSSR_l2<< G4endl;
524 }
525 else
526 {
527
528 L2etaOverTheta2 = reducedEnergy /(tetal2*tetal2);
529
530 if ( (tetal2>=0.2) && (tetal2<=2.6670) && (L2etaOverTheta2>=0.1e-3) && (L2etaOverTheta2<=0.866e2) )
531
532 universalFunction_l2 = FunctionFL2((tetal2),L2etaOverTheta2);
533
534 sigmaPSSR_l2 = (sigma0/tetal2)*universalFunction_l2;
535
536 if (verboseLevel>0) G4cout << " sigma PWBA L2 CS at medium and high velocity range = " << sigmaPSSR_l2<< G4endl;
537
538 }
539
540 G4double pssDeltal2 = (4./(systemMass*sigmaPSS_l2*tetal2))*(sigmaPSS_l2/velocityl2)*(sigmaPSS_l2/velocityl2);
541
542 if (pssDeltal2>1) return 0.;
543
544 G4double energyLossl2 = std::pow(1-pssDeltal2,0.5);
545
546 if (verboseLevel>0) G4cout << " energyLossl2=" << energyLossl2<< G4endl;
547
548 G4double coulombDeflectionl2
549 =(8.*pi*zIncident/systemMass)*std::pow(tetal2*sigmaPSS_l2,-2.)*std::pow(velocityl2/sigmaPSS_l2,-3.)*(zTarget/screenedzTarget);
550
551 G4double cParameterl2 = 2.*coulombDeflectionl2/(energyLossl2*(energyLossl2+1.));
552
553 G4double coulombDeflectionFunction_l2 = 11.*ExpIntFunction(12,cParameterl2); //Coulomb-deflection effect correction
554 // *** see Brandt, Phys Rev A10, p477, f25
555
556 if (verboseLevel>0) G4cout << " coulombDeflectionFunction_l2 =" << coulombDeflectionFunction_l2 << G4endl;
557
558 G4double crossSection_L2 = coulombDeflectionFunction_l2 * sigmaPSSR_l2;
559 //ECPSSR L2 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
560 //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
561
562 if (verboseLevel>0) G4cout << " crossSection_L2 =" << crossSection_L2 << G4endl;
563
564 if (crossSection_L2 >= 0)
565 {
566 return crossSection_L2 * barn;
567 }
568 else {return 0;}
569}
570
571//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
572
573
574G4double G4ecpssrBaseLixsModel::CalculateL3CrossSection(G4int zTarget,G4double massIncident, G4double energyIncident)
575
576{
577 if (zTarget <=13) return 0.;
578
579 //this L3-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
580 //and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
581
582 G4NistManager* massManager = G4NistManager::Instance();
583
584 G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
585
586 G4double zIncident = 0;
587
588 G4Proton* aProtone = G4Proton::Proton();
589 G4Alpha* aAlpha = G4Alpha::Alpha();
590
591 if (massIncident == aProtone->GetPDGMass() )
592
593 zIncident = (aProtone->GetPDGCharge())/eplus;
594
595 else
596 {
597 if (massIncident == aAlpha->GetPDGMass())
598
599 zIncident = (aAlpha->GetPDGCharge())/eplus;
600
601 else
602 {
603 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateL3CrossSection : Proton or Alpha incident particles only. " << G4endl;
604 G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
605 return 0;
606 }
607 }
608
609 G4double l3BindingEnergy = transitionManager->Shell(zTarget,3)->BindingEnergy();
610
611 G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
612
613 G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2;//Mass of the system (projectile, target)
614
615 const G4double zlshell= 4.15;
616
617 G4double screenedzTarget = zTarget-zlshell;//Effective nuclear charge as seen by electrons in L3-subshell
618
619 const G4double rydbergMeV= 13.6056923e-6;
620
621 const G4double nl= 2.;
622
623 G4double tetal3 = (l3BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV);//Screening parameter
624
625 if (verboseLevel>0) G4cout << " tetal3=" << tetal3<< G4endl;
626
627 G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
628
629 const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ;//Bohr radius of hydrogen
630
631 G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
632
633 G4double velocityl3 = CalculateVelocity(3, zTarget, massIncident, energyIncident);// Scaled velocity
634
635 if (verboseLevel>0) G4cout << " velocityl3=" << velocityl3<< G4endl;
636
637 const G4double l23AnalyticalApproximation= 1.25;
638
639 G4double x3 = (nl*l23AnalyticalApproximation)/velocityl3;
640
641 if (verboseLevel>0) G4cout << " x3=" << x3<< G4endl;
642
643 G4double electrIonizationEnergyl3=0.;
644
645 if ( x3<=0.035) electrIonizationEnergyl3= 0.75*pi*(std::log(1./(x3*x3))-1.);
646 else
647 {
648 if ( x3<=3.) electrIonizationEnergyl3 =std::exp(-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));
649 else
650 {
651 if ( x3<=11.) electrIonizationEnergyl3 =2.*std::exp(-2.*x3)/std::pow(x3,1.6);}
652 }
653
654 G4double hFunctionl3 =(electrIonizationEnergyl3*2.*nl)/(tetal3*std::pow(velocityl3,3));//takes into account the polarization effect
655
656 if (verboseLevel>0) G4cout << " hFunctionl3=" << hFunctionl3<< G4endl;
657
658 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.);
659 //takes into account the reduced binding effect
660
661 if (verboseLevel>0) G4cout << " gFunctionl3=" << gFunctionl3<< G4endl;
662
663 G4double sigmaPSS_l3 = 1.+(((2.*zIncident)/(screenedzTarget*tetal3))*(gFunctionl3-hFunctionl3));//Binding-polarization factor
664
665 if (verboseLevel>0) G4cout << "sigmaPSS_l3 =" << sigmaPSS_l3<< G4endl;
666
667 const G4double cNaturalUnit= 137.;
668
669 G4double yl3Formula=0.15*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocityl3/sigmaPSS_l3);
670
671 G4double l3relativityCorrection = std::pow((1.+(1.1*yl3Formula*yl3Formula)),0.5)+yl3Formula; // Relativistic correction parameter
672
673 G4double L3etaOverTheta2;
674
675 G4double universalFunction_l3 = 0.;
676
677 G4double sigmaPSSR_l3;
678
679 if ( velocityl3 < 20. )
680 {
681
682 L3etaOverTheta2 = (reducedEnergy* l3relativityCorrection)/((sigmaPSS_l3*tetal3)*(sigmaPSS_l3*tetal3));
683
684 if ( (tetal3*sigmaPSS_l3>=0.2) && (tetal3*sigmaPSS_l3<=2.6670) && (L3etaOverTheta2>=0.1e-3) && (L3etaOverTheta2<=0.866e2) )
685
686 universalFunction_l3 = 2.*FunctionFL2((tetal3*sigmaPSS_l3), L3etaOverTheta2 );
687
688 sigmaPSSR_l3 = (sigma0/(tetal3*sigmaPSS_l3))*universalFunction_l3;
689
690 if (verboseLevel>0) G4cout << " sigma PWBA L3 CS at low velocity range = " << sigmaPSSR_l3<< G4endl;
691
692 }
693
694 else
695
696 {
697
698 L3etaOverTheta2 = reducedEnergy/(tetal3*tetal3);
699
700 if ( (tetal3>=0.2) && (tetal3<=2.6670) && (L3etaOverTheta2>=0.1e-3) && (L3etaOverTheta2<=0.866e2) )
701
702 universalFunction_l3 = 2.*FunctionFL2(tetal3, L3etaOverTheta2 );
703
704 sigmaPSSR_l3 = (sigma0/tetal3)*universalFunction_l3;
705
706 if (verboseLevel>0) G4cout << " sigma PWBA L3 CS at medium and high velocity range = " << sigmaPSSR_l3<< G4endl;
707 }
708
709 G4double pssDeltal3 = (4./(systemMass*sigmaPSS_l3*tetal3))*(sigmaPSS_l3/velocityl3)*(sigmaPSS_l3/velocityl3);
710
711 if (verboseLevel>0) G4cout << " pssDeltal3=" << pssDeltal3<< G4endl;
712
713 if (pssDeltal3>1) return 0.;
714
715 G4double energyLossl3 = std::pow(1-pssDeltal3,0.5);
716
717 if (verboseLevel>0) G4cout << " energyLossl3=" << energyLossl3<< G4endl;
718
719 G4double coulombDeflectionl3 =
720 (8.*pi*zIncident/systemMass)*std::pow(tetal3*sigmaPSS_l3,-2.)*std::pow(velocityl3/sigmaPSS_l3,-3.)*(zTarget/screenedzTarget);
721
722 G4double cParameterl3 = 2.*coulombDeflectionl3/(energyLossl3*(energyLossl3+1.));
723
724 G4double coulombDeflectionFunction_l3 = 11.*ExpIntFunction(12,cParameterl3);//Coulomb-deflection effect correction
725 // *** see Brandt, Phys Rev A10, p477, f25
726
727 if (verboseLevel>0) G4cout << " coulombDeflectionFunction_l3 =" << coulombDeflectionFunction_l3 << G4endl;
728
729 G4double crossSection_L3 = coulombDeflectionFunction_l3 * sigmaPSSR_l3;
730 //ECPSSR L3 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
731 //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
732
733 if (verboseLevel>0) G4cout << " crossSection_L3 =" << crossSection_L3 << G4endl;
734
735 if (crossSection_L3 >= 0)
736 {
737 return crossSection_L3 * barn;
738 }
739 else {return 0;}
740}
741
742//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
743
744G4double G4ecpssrBaseLixsModel::CalculateVelocity(G4int subShell, G4int zTarget, G4double massIncident, G4double energyIncident)
745
746{
747
748 G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
749
750 G4double liBindingEnergy = transitionManager->Shell(zTarget,subShell)->BindingEnergy();
751
752 G4Proton* aProtone = G4Proton::Proton();
753 G4Alpha* aAlpha = G4Alpha::Alpha();
754
755 if (!((massIncident == aProtone->GetPDGMass()) || (massIncident == aAlpha->GetPDGMass())))
756 {
757 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateVelocity : Proton or Alpha incident particles only. " << G4endl;
758 G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
759 return 0;
760 }
761
762 const G4double zlshell= 4.15;
763
764 G4double screenedzTarget = zTarget- zlshell;
765
766 const G4double rydbergMeV= 13.6056923e-6;
767
768 const G4double nl= 2.;
769
770 G4double tetali = (liBindingEnergy*nl*nl)/(screenedzTarget*screenedzTarget*rydbergMeV);
771
772 G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
773
774 G4double velocity = 2.*nl*std::pow(reducedEnergy,0.5)/tetali;
775 // *** see Brandt, Phys Rev A10, p10, f4
776
777 return velocity;
778}
779
780//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
781
782G4double G4ecpssrBaseLixsModel::FunctionFL1(G4double k, G4double theta)
783{
784
785 G4double sigma = 0.;
786 G4double valueT1 = 0;
787 G4double valueT2 = 0;
788 G4double valueE21 = 0;
789 G4double valueE22 = 0;
790 G4double valueE12 = 0;
791 G4double valueE11 = 0;
792 G4double xs11 = 0;
793 G4double xs12 = 0;
794 G4double xs21 = 0;
795 G4double xs22 = 0;
796
797 // PROTECTION TO ALLOW INTERPOLATION AT MINIMUM AND MAXIMUM Eta/Theta2 values
798
799 if (
800 theta==8.66e-4 ||
801 theta==8.66e-3 ||
802 theta==8.66e-2 ||
803 theta==8.66e-1 ||
804 theta==8.66e+00 ||
805 theta==8.66e+01
806 ) theta=theta-1e-12;
807
808 if (
809 theta==1.e-4 ||
810 theta==1.e-3 ||
811 theta==1.e-2 ||
812 theta==1.e-1 ||
813 theta==1.e+00 ||
814 theta==1.e+01
815 ) theta=theta+1e-12;
816
817 // END PROTECTION
818
819 std::vector<double>::iterator t2 = std::upper_bound(dummyVec1.begin(),dummyVec1.end(), k);
820 std::vector<double>::iterator t1 = t2-1;
821
822 std::vector<double>::iterator e12 = std::upper_bound(aVecMap1[(*t1)].begin(),aVecMap1[(*t1)].end(), theta);
823 std::vector<double>::iterator e11 = e12-1;
824
825 std::vector<double>::iterator e22 = std::upper_bound(aVecMap1[(*t2)].begin(),aVecMap1[(*t2)].end(), theta);
826 std::vector<double>::iterator e21 = e22-1;
827
828 valueT1 =*t1;
829 valueT2 =*t2;
830 valueE21 =*e21;
831 valueE22 =*e22;
832 valueE12 =*e12;
833 valueE11 =*e11;
834
835 xs11 = FL1Data[valueT1][valueE11];
836 xs12 = FL1Data[valueT1][valueE12];
837 xs21 = FL1Data[valueT2][valueE21];
838 xs22 = FL1Data[valueT2][valueE22];
839
840 if (verboseLevel>0)
841 G4cout
842 << valueT1 << " "
843 << valueT2 << " "
844 << valueE11 << " "
845 << valueE12 << " "
846 << valueE21 << " "
847 << valueE22 << " "
848 << xs11 << " "
849 << xs12 << " "
850 << xs21 << " "
851 << xs22 << " "
852 << G4endl;
853
854 G4double xsProduct = xs11 * xs12 * xs21 * xs22;
855
856 if (xs11==0 || xs12==0 ||xs21==0 ||xs22==0) return (0.);
857
858 if (xsProduct != 0.)
859 {
860 sigma = QuadInterpolator( valueE11, valueE12,
861 valueE21, valueE22,
862 xs11, xs12,
863 xs21, xs22,
864 valueT1, valueT2,
865 k, theta );
866 }
867
868 return sigma;
869}
870
871//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
872
873G4double G4ecpssrBaseLixsModel::FunctionFL2(G4double k, G4double theta)
874{
875
876 G4double sigma = 0.;
877 G4double valueT1 = 0;
878 G4double valueT2 = 0;
879 G4double valueE21 = 0;
880 G4double valueE22 = 0;
881 G4double valueE12 = 0;
882 G4double valueE11 = 0;
883 G4double xs11 = 0;
884 G4double xs12 = 0;
885 G4double xs21 = 0;
886 G4double xs22 = 0;
887
888 // PROTECTION TO ALLOW INTERPOLATION AT MINIMUM AND MAXIMUM Eta/Theta2 values
889
890 if (
891 theta==8.66e-4 ||
892 theta==8.66e-3 ||
893 theta==8.66e-2 ||
894 theta==8.66e-1 ||
895 theta==8.66e+00 ||
896 theta==8.66e+01
897 ) theta=theta-1e-12;
898
899 if (
900 theta==1.e-4 ||
901 theta==1.e-3 ||
902 theta==1.e-2 ||
903 theta==1.e-1 ||
904 theta==1.e+00 ||
905 theta==1.e+01
906 ) theta=theta+1e-12;
907
908 // END PROTECTION
909
910 std::vector<double>::iterator t2 = std::upper_bound(dummyVec2.begin(),dummyVec2.end(), k);
911 std::vector<double>::iterator t1 = t2-1;
912
913 std::vector<double>::iterator e12 = std::upper_bound(aVecMap2[(*t1)].begin(),aVecMap2[(*t1)].end(), theta);
914 std::vector<double>::iterator e11 = e12-1;
915
916 std::vector<double>::iterator e22 = std::upper_bound(aVecMap2[(*t2)].begin(),aVecMap2[(*t2)].end(), theta);
917 std::vector<double>::iterator e21 = e22-1;
918
919 valueT1 =*t1;
920 valueT2 =*t2;
921 valueE21 =*e21;
922 valueE22 =*e22;
923 valueE12 =*e12;
924 valueE11 =*e11;
925
926 xs11 = FL2Data[valueT1][valueE11];
927 xs12 = FL2Data[valueT1][valueE12];
928 xs21 = FL2Data[valueT2][valueE21];
929 xs22 = FL2Data[valueT2][valueE22];
930
931 if (verboseLevel>0)
932 G4cout
933 << valueT1 << " "
934 << valueT2 << " "
935 << valueE11 << " "
936 << valueE12 << " "
937 << valueE21 << " "
938 << valueE22 << " "
939 << xs11 << " "
940 << xs12 << " "
941 << xs21 << " "
942 << xs22 << " "
943 << G4endl;
944
945 G4double xsProduct = xs11 * xs12 * xs21 * xs22;
946
947 if (xs11==0 || xs12==0 ||xs21==0 ||xs22==0) return (0.);
948
949 if (xsProduct != 0.)
950 {
951 sigma = QuadInterpolator( valueE11, valueE12,
952 valueE21, valueE22,
953 xs11, xs12,
954 xs21, xs22,
955 valueT1, valueT2,
956 k, theta );
957 }
958
959 return sigma;
960}
961
962//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
963
964G4double G4ecpssrBaseLixsModel::LinLinInterpolate(G4double e1,
965 G4double e2,
966 G4double e,
967 G4double xs1,
968 G4double xs2)
969{
970 G4double value = xs1 + (xs2 - xs1)*(e - e1)/ (e2 - e1);
971 return value;
972}
973
974//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
975
976G4double G4ecpssrBaseLixsModel::LinLogInterpolate(G4double e1,
977 G4double e2,
978 G4double e,
979 G4double xs1,
980 G4double xs2)
981{
982 G4double d1 = std::log(xs1);
983 G4double d2 = std::log(xs2);
984 G4double value = std::exp(d1 + (d2 - d1)*(e - e1)/ (e2 - e1));
985 return value;
986}
987
988//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
989
990G4double G4ecpssrBaseLixsModel::LogLogInterpolate(G4double e1,
991 G4double e2,
992 G4double e,
993 G4double xs1,
994 G4double xs2)
995{
996 G4double a = (std::log10(xs2)-std::log10(xs1)) / (std::log10(e2)-std::log10(e1));
997 G4double b = std::log10(xs2) - a*std::log10(e2);
998 G4double sigma = a*std::log10(e) + b;
999 G4double value = (std::pow(10.,sigma));
1000 return value;
1001}
1002
1003//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
1004
1005G4double G4ecpssrBaseLixsModel::QuadInterpolator(G4double e11, G4double e12,
1006 G4double e21, G4double e22,
1007 G4double xs11, G4double xs12,
1008 G4double xs21, G4double xs22,
1009 G4double t1, G4double t2,
1010 G4double t, G4double e)
1011{
1012// Log-Log
1013 G4double interpolatedvalue1 = LogLogInterpolate(e11, e12, e, xs11, xs12);
1014 G4double interpolatedvalue2 = LogLogInterpolate(e21, e22, e, xs21, xs22);
1015 G4double value = LogLogInterpolate(t1, t2, t, interpolatedvalue1, interpolatedvalue2);
1016
1017/*
1018// Lin-Log
1019 G4double interpolatedvalue1 = LinLogInterpolate(e11, e12, e, xs11, xs12);
1020 G4double interpolatedvalue2 = LinLogInterpolate(e21, e22, e, xs21, xs22);
1021 G4double value = LinLogInterpolate(t1, t2, t, interpolatedvalue1, interpolatedvalue2);
1022*/
1023
1024/*
1025// Lin-Lin
1026 G4double interpolatedvalue1 = LinLinInterpolate(e11, e12, e, xs11, xs12);
1027 G4double interpolatedvalue2 = LinLinInterpolate(e21, e22, e, xs21, xs22);
1028 G4double value = LinLinInterpolate(t1, t2, t, interpolatedvalue1, interpolatedvalue2);
1029*/
1030 return value;
1031
1032}
1033
FatalException
@ FatalException
Definition: G4ExceptionSeverity.hh:60
G4double
double G4double
Definition: G4Types.hh:64
G4int
int G4int
Definition: G4Types.hh:66
G4endl
#define G4endl
Definition: G4ios.hh:52
G4cout
G4DLLIMPORT std::ostream G4cout
G4Alpha::Alpha
static G4Alpha * Alpha()
Definition: G4Alpha.cc:89
G4AtomicShell::BindingEnergy
G4double BindingEnergy() const
Definition: G4AtomicShell.hh:79
G4AtomicTransitionManager::Shell
G4AtomicShell * Shell(G4int Z, size_t shellIndex) const
Definition: G4AtomicTransitionManager.cc:174
G4AtomicTransitionManager::Instance
static G4AtomicTransitionManager * Instance()
Definition: G4AtomicTransitionManager.cc:163
G4NistManager::Instance
static G4NistManager * Instance()
Definition: G4NistManager.cc:68
G4NistManager::GetAtomicMassAmu
G4double GetAtomicMassAmu(const G4String &symb) const
Definition: G4NistManager.hh:343
G4ParticleDefinition::GetPDGCharge
G4double GetPDGCharge() const
Definition: G4ParticleDefinition.hh:119
G4Proton::Proton
static G4Proton * Proton()
Definition: G4Proton.cc:93
G4ecpssrBaseLixsModel::CalculateL1CrossSection
G4double CalculateL1CrossSection(G4int zTarget, G4double massIncident, G4double energyIncident)
Definition: G4ecpssrBaseLixsModel.cc:192
G4ecpssrBaseLixsModel::CalculateL2CrossSection
G4double CalculateL2CrossSection(G4int zTarget, G4double massIncident, G4double energyIncident)
Definition: G4ecpssrBaseLixsModel.cc:407
G4ecpssrBaseLixsModel::ExpIntFunction
G4double ExpIntFunction(G4int n, G4double x)
Definition: G4ecpssrBaseLixsModel.cc:122
G4ecpssrBaseLixsModel::CalculateVelocity
G4double CalculateVelocity(G4int subShell, G4int zTarget, G4double massIncident, G4double energyIncident)
Definition: G4ecpssrBaseLixsModel.cc:744
G4ecpssrBaseLixsModel::CalculateL3CrossSection
G4double CalculateL3CrossSection(G4int zTarget, G4double massIncident, G4double energyIncident)
Definition: G4ecpssrBaseLixsModel.cc:574
G4Exception
void G4Exception(const char *originOfException, const char *exceptionCode, G4ExceptionSeverity severity, const char *comments)
Definition: G4Exception.cc:41