Geant4 10.7.0
Toolkit for the simulation of the passage of particles through matter
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G4ecpssrBaseLixsModel.cc
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26
27#include <iostream>
28
29#include "G4ecpssrBaseLixsModel.hh"
30
31#include "globals.hh"
32#include "G4PhysicalConstants.hh"
33#include "G4SystemOfUnits.hh"
34#include "G4AtomicTransitionManager.hh"
35#include "G4NistManager.hh"
36#include "G4Proton.hh"
37#include "G4Alpha.hh"
38#include "G4LinLogInterpolation.hh"
39#include "G4Exp.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 = std::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//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
115
116G4ecpssrBaseLixsModel::~G4ecpssrBaseLixsModel()
117{}
118
119//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
120
121G4double G4ecpssrBaseLixsModel::ExpIntFunction(G4int n,G4double x)
122
123{
124// this function allows fast evaluation of the n order exponential integral function En(x)
125
126 G4int i;
127 G4int ii;
128 G4int nm1;
129 G4double a;
130 G4double b;
131 G4double c;
132 G4double d;
133 G4double del;
134 G4double fact;
135 G4double h;
136 G4double psi;
137 G4double ans = 0;
138 static const G4double euler= 0.5772156649;
139 static const G4int maxit= 100;
140 static const G4double fpmin = 1.0e-30;
141 static const G4double eps = 1.0e-7;
142 nm1=n-1;
143 if (n<0 || x<0.0 || (x==0.0 && (n==0 || n==1)))
144 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::ExpIntFunction: bad arguments in ExpIntFunction"
145 << G4endl;
146 else {
147 if (n==0) ans=G4Exp(-x)/x;
148 else {
149 if (x==0.0) ans=1.0/nm1;
150 else {
151 if (x > 1.0) {
152 b=x+n;
153 c=1.0/fpmin;
154 d=1.0/b;
155 h=d;
156 for (i=1;i<=maxit;i++) {
157 a=-i*(nm1+i);
158 b +=2.0;
159 d=1.0/(a*d+b);
160 c=b+a/c;
161 del=c*d;
162 h *=del;
163 if (std::fabs(del-1.0) < eps) {
164 ans=h*G4Exp(-x);
165 return ans;
166 }
167 }
168 } else {
169 ans = (nm1!=0 ? 1.0/nm1 : -std::log(x)-euler);
170 fact=1.0;
171 for (i=1;i<=maxit;i++) {
172 fact *=-x/i;
173 if (i !=nm1) del = -fact/(i-nm1);
174 else {
175 psi = -euler;
176 for (ii=1;ii<=nm1;ii++) psi +=1.0/ii;
177 del=fact*(-std::log(x)+psi);
178 }
179 ans += del;
180 if (std::fabs(del) < std::fabs(ans)*eps) return ans;
181 }
182 }
183 }
184 }
185 }
186 return ans;
187}
188
189//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
190
191G4double G4ecpssrBaseLixsModel::CalculateL1CrossSection(G4int zTarget,G4double massIncident, G4double energyIncident)
192{
193
194 if (zTarget <=4) return 0.;
195
196 //this L1-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
197 //and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
198
199 G4NistManager* massManager = G4NistManager::Instance();
200
201 G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
202
203 G4double zIncident = 0;
204 G4Proton* aProtone = G4Proton::Proton();
205 G4Alpha* aAlpha = G4Alpha::Alpha();
206
207 if (massIncident == aProtone->GetPDGMass() )
208 {
209 zIncident = (aProtone->GetPDGCharge())/eplus;
210 }
211 else
212 {
213 if (massIncident == aAlpha->GetPDGMass())
214 {
215 zIncident = (aAlpha->GetPDGCharge())/eplus;
216 }
217 else
218 {
219 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateL1CrossSection : Proton or Alpha incident particles only. " << G4endl;
220 G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
221 return 0;
222 }
223 }
224
225 G4double l1BindingEnergy = transitionManager->Shell(zTarget,1)->BindingEnergy(); //Observed binding energy of L1-subshell
226 G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
227 G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2; //Mass of the system (projectile, target)
228 static const G4double zlshell= 4.15;
229 // *** see Benka, ADANDT 22, p 223
230 G4double screenedzTarget = zTarget-zlshell; //Effective nuclear charge as seen by electrons in L1-sub shell
231 static const G4double rydbergMeV= 13.6056923e-6;
232
233 static const G4double nl= 2.;
234 // *** see Benka, ADANDT 22, p 220, f3
235 G4double tetal1 = (l1BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV); //Screening parameter
236 // *** see Benka, ADANDT 22, p 220, f3
237
238 if (verboseLevel>0) G4cout << " tetal1=" << tetal1<< G4endl;
239
240 G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
241 // *** also called etaS
242 // *** see Benka, ADANDT 22, p 220, f3
243
244 static const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ; //Bohr radius of hydrogen
245
246 G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
247 // *** see Benka, ADANDT 22, p 220, f2, for protons
248 // *** see Basbas, Phys Rev A7, p 1000
249
250 G4double velocityl1 = CalculateVelocity(1, zTarget, massIncident, energyIncident); // Scaled velocity
251
252 if (verboseLevel>0) G4cout << " velocityl1=" << velocityl1<< G4endl;
253
254 static const G4double l1AnalyticalApproximation= 1.5;
255 G4double x1 =(nl*l1AnalyticalApproximation)/velocityl1;
256 // *** 1.5 is cK = cL1 (it is 1.25 for L2 & L3)
257 // *** see Brandt, Phys Rev A20, p 469, f16 in expression of h
258
259 if (verboseLevel>0) G4cout << " x1=" << x1<< G4endl;
260
261 G4double electrIonizationEnergyl1=0.;
262 // *** see Basbas, Phys Rev A17, p1665, f27
263 // *** see Brandt, Phys Rev A20, p469
264 // *** see Liu, Comp Phys Comm 97, p325, f A5
265
266 if ( x1<=0.035) electrIonizationEnergyl1= 0.75*pi*(std::log(1./(x1*x1))-1.);
267 else
268 {
269 if ( x1<=3.)
270 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));
271 else
272 {if ( x1<=11.) electrIonizationEnergyl1 =2.*G4Exp(-2.*x1)/std::pow(x1,1.6);}
273 }
274
275 G4double hFunctionl1 =(electrIonizationEnergyl1*2.*nl)/(tetal1*std::pow(velocityl1,3)); //takes into account the polarization effect
276 // *** see Brandt, Phys Rev A20, p 469, f16
277
278 if (verboseLevel>0) G4cout << " hFunctionl1=" << hFunctionl1<< G4endl;
279
280 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
281 // *** see Brandt, Phys Rev A20, p 469, f19
282
283 if (verboseLevel>0) G4cout << " gFunctionl1=" << gFunctionl1<< G4endl;
284
285 G4double sigmaPSS_l1 = 1.+(((2.*zIncident)/(screenedzTarget*tetal1))*(gFunctionl1-hFunctionl1)); //Binding-polarization factor
286 // *** also called dzeta
287 // *** also called epsilon
288 // *** see Basbas, Phys Rev A17, p1667, f45
289
290 if (verboseLevel>0) G4cout << "sigmaPSS_l1 =" << sigmaPSS_l1<< G4endl;
291
292 const G4double cNaturalUnit= 137.;
293
294 G4double yl1Formula=0.4*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(nl*velocityl1/sigmaPSS_l1);
295 // *** also called yS
296 // *** see Brandt, Phys Rev A20, p467, f6
297 // *** see Brandt, Phys Rev A23, p1728
298
299 G4double l1relativityCorrection = std::pow((1.+(1.1*yl1Formula*yl1Formula)),0.5)+yl1Formula; // Relativistic correction parameter
300 // *** also called mRS
301 // *** see Brandt, Phys Rev A20, p467, f6
302
303 //G4double reducedVelocity_l1 = velocityl1*std::pow(l1relativityCorrection,0.5); //Reduced velocity parameter
304
305 G4double L1etaOverTheta2;
306
307 G4double universalFunction_l1 = 0.;
308
309 G4double sigmaPSSR_l1;
310
311 // low velocity formula
312 // *****************
313 if ( velocityl1 <20. )
314 {
315
316 L1etaOverTheta2 =(reducedEnergy* l1relativityCorrection)/((tetal1*sigmaPSS_l1)*(tetal1*sigmaPSS_l1));
317 // *** 1) RELATIVISTIC CORRECTION ADDED
318 // *** 2) sigma_PSS_l1 ADDED
319 // *** reducedEnergy is etaS, l1relativityCorrection is mRS
320 // *** see Phys Rev A20, p468, top
321
322 if ( ((tetal1*sigmaPSS_l1) >=0.2) && ((tetal1*sigmaPSS_l1) <=2.6670) && (L1etaOverTheta2>=0.1e-3) && (L1etaOverTheta2<=0.866e2) )
323 universalFunction_l1 = FunctionFL1((tetal1*sigmaPSS_l1),L1etaOverTheta2);
324
325 if (verboseLevel>0) G4cout << "at low velocity range, universalFunction_l1 =" << universalFunction_l1 << G4endl;
326
327 sigmaPSSR_l1 = (sigma0/(tetal1*sigmaPSS_l1))*universalFunction_l1;// Plane-wave Born -Aproximation L1-subshell ionisation Cross Section
328 // *** see Benka, ADANDT 22, p220, f1
329
330 if (verboseLevel>0) G4cout << " at low velocity range, sigma PWBA L1 CS = " << sigmaPSSR_l1<< G4endl;
331 }
332 else
333 {
334 L1etaOverTheta2 = reducedEnergy/(tetal1*tetal1);
335 // Medium & high velocity
336 // *** 1) NO RELATIVISTIC CORRECTION
337 // *** 2) NO sigma_PSS_l1
338 // *** see Benka, ADANDT 22, p223
339
340 if ( (tetal1 >=0.2) && (tetal1 <=2.6670) && (L1etaOverTheta2>=0.1e-3) && (L1etaOverTheta2<=0.866e2) )
341 universalFunction_l1 = FunctionFL1(tetal1,L1etaOverTheta2);
342
343 if (verboseLevel>0) G4cout << "at medium and high velocity range, universalFunction_l1 =" << universalFunction_l1 << G4endl;
344
345 sigmaPSSR_l1 = (sigma0/tetal1)*universalFunction_l1;// Plane-wave Born -Aproximation L1-subshell ionisation Cross Section
346 // *** see Benka, ADANDT 22, p220, f1
347
348 if (verboseLevel>0) G4cout << " sigma PWBA L1 CS at medium and high velocity range = " << sigmaPSSR_l1<< G4endl;
349 }
350
351 G4double pssDeltal1 = (4./(systemMass *sigmaPSS_l1*tetal1))*(sigmaPSS_l1/velocityl1)*(sigmaPSS_l1/velocityl1);
352 // *** also called dzeta*delta
353 // *** see Brandt, Phys Rev A23, p1727, f B2
354
355 if (verboseLevel>0) G4cout << " pssDeltal1=" << pssDeltal1<< G4endl;
356
357 if (pssDeltal1>1) return 0.;
358
359 G4double energyLossl1 = std::pow(1-pssDeltal1,0.5);
360 // *** also called z
361 // *** see Brandt, Phys Rev A23, p1727, after f B2
362
363 if (verboseLevel>0) G4cout << " energyLossl1=" << energyLossl1<< G4endl;
364
365 G4double coulombDeflectionl1 =
366 (8.*pi*zIncident/systemMass)*std::pow(tetal1*sigmaPSS_l1,-2.)*std::pow(velocityl1/sigmaPSS_l1,-3.)*(zTarget/screenedzTarget);
367 // *** see Brandt, Phys Rev A20, v2s and f2 and B2
368 // *** with factor n2 compared to Brandt, Phys Rev A23, p1727, f B3
369
370 G4double cParameterl1 =2.* coulombDeflectionl1/(energyLossl1*(energyLossl1+1.));
371 // *** see Brandt, Phys Rev A23, p1727, f B4
372
373 G4double coulombDeflectionFunction_l1 = 9.*ExpIntFunction(10,cParameterl1); //Coulomb-deflection effect correction
374
375 if (verboseLevel>0) G4cout << " coulombDeflectionFunction_l1 =" << coulombDeflectionFunction_l1 << G4endl;
376
377 G4double crossSection_L1 = coulombDeflectionFunction_l1 * sigmaPSSR_l1;
378
379 //ECPSSR L1 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
380 //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
381
382 if (verboseLevel>0) G4cout << " crossSection_L1 =" << crossSection_L1 << G4endl;
383
384 if (crossSection_L1 >= 0)
385 {
386 return crossSection_L1 * barn;
387 }
388
389 else {return 0;}
390}
391
392//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
393
394G4double G4ecpssrBaseLixsModel::CalculateL2CrossSection(G4int zTarget,G4double massIncident, G4double energyIncident)
395
396{
397 if (zTarget <=13 ) return 0.;
398
399 // this L2-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
400 // and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
401
402 G4NistManager* massManager = G4NistManager::Instance();
403
404 G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
405
406 G4double zIncident = 0;
407
408 G4Proton* aProtone = G4Proton::Proton();
409 G4Alpha* aAlpha = G4Alpha::Alpha();
410
411 if (massIncident == aProtone->GetPDGMass() )
412 zIncident = (aProtone->GetPDGCharge())/eplus;
413
414 else
415 {
416 if (massIncident == aAlpha->GetPDGMass())
417 zIncident = (aAlpha->GetPDGCharge())/eplus;
418
419 else
420 {
421 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateL2CrossSection : Proton or Alpha incident particles only. " << G4endl;
422 G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
423 return 0;
424 }
425 }
426
427 G4double l2BindingEnergy = transitionManager->Shell(zTarget,2)->BindingEnergy(); //Observed binding energy of L2-subshell
428
429 G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
430
431 G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2; //Mass of the system (projectile, target)
432
433 const G4double zlshell= 4.15;
434
435 G4double screenedzTarget = zTarget-zlshell; //Effective nuclear charge as seen by electrons in L2-subshell
436
437 const G4double rydbergMeV= 13.6056923e-6;
438
439 const G4double nl= 2.;
440
441 G4double tetal2 = (l2BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV); //Screening parameter
442
443 if (verboseLevel>0) G4cout << " tetal2=" << tetal2<< G4endl;
444
445 G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
446
447 const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ; //Bohr radius of hydrogen
448
449 G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
450
451 G4double velocityl2 = CalculateVelocity(2, zTarget, massIncident, energyIncident); // Scaled velocity
452
453 if (verboseLevel>0) G4cout << " velocityl2=" << velocityl2<< G4endl;
454
455 const G4double l23AnalyticalApproximation= 1.25;
456
457 G4double x2 = (nl*l23AnalyticalApproximation)/velocityl2;
458
459 if (verboseLevel>0) G4cout << " x2=" << x2<< G4endl;
460
461 G4double electrIonizationEnergyl2=0.;
462
463 if ( x2<=0.035) electrIonizationEnergyl2= 0.75*pi*(std::log(1./(x2*x2))-1.);
464 else
465 {
466 if ( x2<=3.)
467 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));
468 else
469 {if ( x2<=11.) electrIonizationEnergyl2 =2.*G4Exp(-2.*x2)/std::pow(x2,1.6); }
470 }
471
472 G4double hFunctionl2 =(electrIonizationEnergyl2*2.*nl)/(tetal2*std::pow(velocityl2,3)); //takes into account the polarization effect
473
474 if (verboseLevel>0) G4cout << " hFunctionl2=" << hFunctionl2<< G4endl;
475
476 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.);
477 //takes into account the reduced binding effect
478
479 if (verboseLevel>0) G4cout << " gFunctionl2=" << gFunctionl2<< G4endl;
480
481 G4double sigmaPSS_l2 = 1.+(((2.*zIncident)/(screenedzTarget*tetal2))*(gFunctionl2-hFunctionl2)); //Binding-polarization factor
482
483 if (verboseLevel>0) G4cout << " sigmaPSS_l2=" << sigmaPSS_l2<< G4endl;
484
485 const G4double cNaturalUnit= 137.;
486
487 G4double yl2Formula=0.15*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocityl2/sigmaPSS_l2);
488
489 G4double l2relativityCorrection = std::pow((1.+(1.1*yl2Formula*yl2Formula)),0.5)+yl2Formula; // Relativistic correction parameter
490
491 G4double L2etaOverTheta2;
492
493 G4double universalFunction_l2 = 0.;
494
495 G4double sigmaPSSR_l2 ;
496
497 if ( velocityl2 < 20. )
498 {
499
500 L2etaOverTheta2 = (reducedEnergy*l2relativityCorrection)/((sigmaPSS_l2*tetal2)*(sigmaPSS_l2*tetal2));
501
502 if ( (tetal2*sigmaPSS_l2>=0.2) && (tetal2*sigmaPSS_l2<=2.6670) && (L2etaOverTheta2>=0.1e-3) && (L2etaOverTheta2<=0.866e2) )
503 universalFunction_l2 = FunctionFL2((tetal2*sigmaPSS_l2),L2etaOverTheta2);
504
505 sigmaPSSR_l2 = (sigma0/(tetal2*sigmaPSS_l2))*universalFunction_l2;
506
507 if (verboseLevel>0) G4cout << " sigma PWBA L2 CS at low velocity range = " << sigmaPSSR_l2<< G4endl;
508 }
509 else
510 {
511
512 L2etaOverTheta2 = reducedEnergy /(tetal2*tetal2);
513
514 if ( (tetal2>=0.2) && (tetal2<=2.6670) && (L2etaOverTheta2>=0.1e-3) && (L2etaOverTheta2<=0.866e2) )
515 universalFunction_l2 = FunctionFL2((tetal2),L2etaOverTheta2);
516
517 sigmaPSSR_l2 = (sigma0/tetal2)*universalFunction_l2;
518
519 if (verboseLevel>0) G4cout << " sigma PWBA L2 CS at medium and high velocity range = " << sigmaPSSR_l2<< G4endl;
520
521 }
522
523 G4double pssDeltal2 = (4./(systemMass*sigmaPSS_l2*tetal2))*(sigmaPSS_l2/velocityl2)*(sigmaPSS_l2/velocityl2);
524
525 if (pssDeltal2>1) return 0.;
526
527 G4double energyLossl2 = std::pow(1-pssDeltal2,0.5);
528
529 if (verboseLevel>0) G4cout << " energyLossl2=" << energyLossl2<< G4endl;
530
531 G4double coulombDeflectionl2
532 =(8.*pi*zIncident/systemMass)*std::pow(tetal2*sigmaPSS_l2,-2.)*std::pow(velocityl2/sigmaPSS_l2,-3.)*(zTarget/screenedzTarget);
533
534 G4double cParameterl2 = 2.*coulombDeflectionl2/(energyLossl2*(energyLossl2+1.));
535
536 G4double coulombDeflectionFunction_l2 = 11.*ExpIntFunction(12,cParameterl2); //Coulomb-deflection effect correction
537 // *** see Brandt, Phys Rev A10, p477, f25
538
539 if (verboseLevel>0) G4cout << " coulombDeflectionFunction_l2 =" << coulombDeflectionFunction_l2 << G4endl;
540
541 G4double crossSection_L2 = coulombDeflectionFunction_l2 * sigmaPSSR_l2;
542 //ECPSSR L2 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
543 //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
544
545 if (verboseLevel>0) G4cout << " crossSection_L2 =" << crossSection_L2 << G4endl;
546
547 if (crossSection_L2 >= 0)
548 {
549 return crossSection_L2 * barn;
550 }
551 else {return 0;}
552}
553
554//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
555
556
557G4double G4ecpssrBaseLixsModel::CalculateL3CrossSection(G4int zTarget,G4double massIncident, G4double energyIncident)
558
559{
560 if (zTarget <=13) return 0.;
561
562 //this L3-CrossSection calculation method is done according to Werner Brandt and Grzegorz Lapicki, Phys.Rev.A20 N2 (1979),
563 //and using data tables of O. Benka et al. At.Data Nucl.Data Tables Vol.22 No.3 (1978).
564
565 G4NistManager* massManager = G4NistManager::Instance();
566
567 G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
568
569 G4double zIncident = 0;
570
571 G4Proton* aProtone = G4Proton::Proton();
572 G4Alpha* aAlpha = G4Alpha::Alpha();
573
574 if (massIncident == aProtone->GetPDGMass() )
575
576 zIncident = (aProtone->GetPDGCharge())/eplus;
577
578 else
579 {
580 if (massIncident == aAlpha->GetPDGMass())
581
582 zIncident = (aAlpha->GetPDGCharge())/eplus;
583
584 else
585 {
586 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateL3CrossSection : Proton or Alpha incident particles only. " << G4endl;
587 G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
588 return 0;
589 }
590 }
591
592 G4double l3BindingEnergy = transitionManager->Shell(zTarget,3)->BindingEnergy();
593
594 G4double massTarget = (massManager->GetAtomicMassAmu(zTarget))*amu_c2;
595
596 G4double systemMass =((massIncident*massTarget)/(massIncident+massTarget))/electron_mass_c2;//Mass of the system (projectile, target)
597
598 const G4double zlshell= 4.15;
599
600 G4double screenedzTarget = zTarget-zlshell;//Effective nuclear charge as seen by electrons in L3-subshell
601
602 const G4double rydbergMeV= 13.6056923e-6;
603
604 const G4double nl= 2.;
605
606 G4double tetal3 = (l3BindingEnergy*nl*nl)/((screenedzTarget*screenedzTarget)*rydbergMeV);//Screening parameter
607
608 if (verboseLevel>0) G4cout << " tetal3=" << tetal3<< G4endl;
609
610 G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
611
612 const G4double bohrPow2Barn=(Bohr_radius*Bohr_radius)/barn ;//Bohr radius of hydrogen
613
614 G4double sigma0 = 8.*pi*(zIncident*zIncident)*bohrPow2Barn*std::pow(screenedzTarget,-4.);
615
616 G4double velocityl3 = CalculateVelocity(3, zTarget, massIncident, energyIncident);// Scaled velocity
617
618 if (verboseLevel>0) G4cout << " velocityl3=" << velocityl3<< G4endl;
619
620 const G4double l23AnalyticalApproximation= 1.25;
621
622 G4double x3 = (nl*l23AnalyticalApproximation)/velocityl3;
623
624 if (verboseLevel>0) G4cout << " x3=" << x3<< G4endl;
625
626 G4double electrIonizationEnergyl3=0.;
627
628 if ( x3<=0.035) electrIonizationEnergyl3= 0.75*pi*(std::log(1./(x3*x3))-1.);
629 else
630 {
631 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));
632 else
633 {
634 if ( x3<=11.) electrIonizationEnergyl3 =2.*G4Exp(-2.*x3)/std::pow(x3,1.6);}
635 }
636
637 G4double hFunctionl3 =(electrIonizationEnergyl3*2.*nl)/(tetal3*std::pow(velocityl3,3));//takes into account the polarization effect
638
639 if (verboseLevel>0) G4cout << " hFunctionl3=" << hFunctionl3<< G4endl;
640
641 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.);
642 //takes into account the reduced binding effect
643
644 if (verboseLevel>0) G4cout << " gFunctionl3=" << gFunctionl3<< G4endl;
645
646 G4double sigmaPSS_l3 = 1.+(((2.*zIncident)/(screenedzTarget*tetal3))*(gFunctionl3-hFunctionl3));//Binding-polarization factor
647
648 if (verboseLevel>0) G4cout << "sigmaPSS_l3 =" << sigmaPSS_l3<< G4endl;
649
650 const G4double cNaturalUnit= 137.;
651
652 G4double yl3Formula=0.15*(screenedzTarget/cNaturalUnit)*(screenedzTarget/cNaturalUnit)/(velocityl3/sigmaPSS_l3);
653
654 G4double l3relativityCorrection = std::pow((1.+(1.1*yl3Formula*yl3Formula)),0.5)+yl3Formula; // Relativistic correction parameter
655
656 G4double L3etaOverTheta2;
657
658 G4double universalFunction_l3 = 0.;
659
660 G4double sigmaPSSR_l3;
661
662 if ( velocityl3 < 20. )
663 {
664
665 L3etaOverTheta2 = (reducedEnergy* l3relativityCorrection)/((sigmaPSS_l3*tetal3)*(sigmaPSS_l3*tetal3));
666
667 if ( (tetal3*sigmaPSS_l3>=0.2) && (tetal3*sigmaPSS_l3<=2.6670) && (L3etaOverTheta2>=0.1e-3) && (L3etaOverTheta2<=0.866e2) )
668
669 universalFunction_l3 = 2.*FunctionFL2((tetal3*sigmaPSS_l3), L3etaOverTheta2 );
670
671 sigmaPSSR_l3 = (sigma0/(tetal3*sigmaPSS_l3))*universalFunction_l3;
672
673 if (verboseLevel>0) G4cout << " sigma PWBA L3 CS at low velocity range = " << sigmaPSSR_l3<< G4endl;
674
675 }
676
677 else
678
679 {
680
681 L3etaOverTheta2 = reducedEnergy/(tetal3*tetal3);
682
683 if ( (tetal3>=0.2) && (tetal3<=2.6670) && (L3etaOverTheta2>=0.1e-3) && (L3etaOverTheta2<=0.866e2) )
684
685 universalFunction_l3 = 2.*FunctionFL2(tetal3, L3etaOverTheta2 );
686
687 sigmaPSSR_l3 = (sigma0/tetal3)*universalFunction_l3;
688
689 if (verboseLevel>0) G4cout << " sigma PWBA L3 CS at medium and high velocity range = " << sigmaPSSR_l3<< G4endl;
690 }
691
692 G4double pssDeltal3 = (4./(systemMass*sigmaPSS_l3*tetal3))*(sigmaPSS_l3/velocityl3)*(sigmaPSS_l3/velocityl3);
693
694 if (verboseLevel>0) G4cout << " pssDeltal3=" << pssDeltal3<< G4endl;
695
696 if (pssDeltal3>1) return 0.;
697
698 G4double energyLossl3 = std::pow(1-pssDeltal3,0.5);
699
700 if (verboseLevel>0) G4cout << " energyLossl3=" << energyLossl3<< G4endl;
701
702 G4double coulombDeflectionl3 =
703 (8.*pi*zIncident/systemMass)*std::pow(tetal3*sigmaPSS_l3,-2.)*std::pow(velocityl3/sigmaPSS_l3,-3.)*(zTarget/screenedzTarget);
704
705 G4double cParameterl3 = 2.*coulombDeflectionl3/(energyLossl3*(energyLossl3+1.));
706
707 G4double coulombDeflectionFunction_l3 = 11.*ExpIntFunction(12,cParameterl3);//Coulomb-deflection effect correction
708 // *** see Brandt, Phys Rev A10, p477, f25
709
710 if (verboseLevel>0) G4cout << " coulombDeflectionFunction_l3 =" << coulombDeflectionFunction_l3 << G4endl;
711
712 G4double crossSection_L3 = coulombDeflectionFunction_l3 * sigmaPSSR_l3;
713 //ECPSSR L3 -subshell cross section is estimated at perturbed-stationnairy-state(PSS)
714 //and reduced by the energy-loss(E),the Coulomb deflection(C),and the relativity(R) effects
715
716 if (verboseLevel>0) G4cout << " crossSection_L3 =" << crossSection_L3 << G4endl;
717
718 if (crossSection_L3 >= 0)
719 {
720 return crossSection_L3 * barn;
721 }
722 else {return 0;}
723}
724
725//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
726
727G4double G4ecpssrBaseLixsModel::CalculateVelocity(G4int subShell, G4int zTarget, G4double massIncident, G4double energyIncident)
728
729{
730
731 G4AtomicTransitionManager* transitionManager = G4AtomicTransitionManager::Instance();
732
733 G4double liBindingEnergy = transitionManager->Shell(zTarget,subShell)->BindingEnergy();
734
735 G4Proton* aProtone = G4Proton::Proton();
736 G4Alpha* aAlpha = G4Alpha::Alpha();
737
738 if (!((massIncident == aProtone->GetPDGMass()) || (massIncident == aAlpha->GetPDGMass())))
739 {
740 G4cout << "*** WARNING in G4ecpssrBaseLixsModel::CalculateVelocity : Proton or Alpha incident particles only. " << G4endl;
741 G4cout << massIncident << ", " << aAlpha->GetPDGMass() << " (alpha)" << aProtone->GetPDGMass() << " (proton)" << G4endl;
742 return 0;
743 }
744
745 const G4double zlshell= 4.15;
746
747 G4double screenedzTarget = zTarget- zlshell;
748
749 const G4double rydbergMeV= 13.6056923e-6;
750
751 const G4double nl= 2.;
752
753 G4double tetali = (liBindingEnergy*nl*nl)/(screenedzTarget*screenedzTarget*rydbergMeV);
754
755 G4double reducedEnergy = (energyIncident*electron_mass_c2)/(massIncident*rydbergMeV*screenedzTarget*screenedzTarget);
756
757 G4double velocity = 2.*nl*std::pow(reducedEnergy,0.5)/tetali;
758 // *** see Brandt, Phys Rev A10, p10, f4
759
760 return velocity;
761}
762
763//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
764
765G4double G4ecpssrBaseLixsModel::FunctionFL1(G4double k, G4double theta)
766{
767
768 G4double sigma = 0.;
769 G4double valueT1 = 0;
770 G4double valueT2 = 0;
771 G4double valueE21 = 0;
772 G4double valueE22 = 0;
773 G4double valueE12 = 0;
774 G4double valueE11 = 0;
775 G4double xs11 = 0;
776 G4double xs12 = 0;
777 G4double xs21 = 0;
778 G4double xs22 = 0;
779
780 // PROTECTION TO ALLOW INTERPOLATION AT MINIMUM AND MAXIMUM Eta/Theta2 values
781
782 if (
783 theta==8.66e-4 ||
784 theta==8.66e-3 ||
785 theta==8.66e-2 ||
786 theta==8.66e-1 ||
787 theta==8.66e+00 ||
788 theta==8.66e+01
789 ) theta=theta-1e-12;
790
791 if (
792 theta==1.e-4 ||
793 theta==1.e-3 ||
794 theta==1.e-2 ||
795 theta==1.e-1 ||
796 theta==1.e+00 ||
797 theta==1.e+01
798 ) theta=theta+1e-12;
799
800 // END PROTECTION
801
802 std::vector<double>::iterator t2 = std::upper_bound(dummyVec1.begin(),dummyVec1.end(), k);
803 std::vector<double>::iterator t1 = t2-1;
804
805 std::vector<double>::iterator e12 = std::upper_bound(aVecMap1[(*t1)].begin(),aVecMap1[(*t1)].end(), theta);
806 std::vector<double>::iterator e11 = e12-1;
807
808 std::vector<double>::iterator e22 = std::upper_bound(aVecMap1[(*t2)].begin(),aVecMap1[(*t2)].end(), theta);
809 std::vector<double>::iterator e21 = e22-1;
810
811 valueT1 =*t1;
812 valueT2 =*t2;
813 valueE21 =*e21;
814 valueE22 =*e22;
815 valueE12 =*e12;
816 valueE11 =*e11;
817
818 xs11 = FL1Data[valueT1][valueE11];
819 xs12 = FL1Data[valueT1][valueE12];
820 xs21 = FL1Data[valueT2][valueE21];
821 xs22 = FL1Data[valueT2][valueE22];
822
823 if (verboseLevel>0)
824 G4cout
825 << valueT1 << " "
826 << valueT2 << " "
827 << valueE11 << " "
828 << valueE12 << " "
829 << valueE21 << " "
830 << valueE22 << " "
831 << xs11 << " "
832 << xs12 << " "
833 << xs21 << " "
834 << xs22 << " "
835 << G4endl;
836
837 G4double xsProduct = xs11 * xs12 * xs21 * xs22;
838
839 if (xs11==0 || xs12==0 ||xs21==0 ||xs22==0) return (0.);
840
841 if (xsProduct != 0.)
842 {
843 sigma = QuadInterpolator( valueE11, valueE12,
844 valueE21, valueE22,
845 xs11, xs12,
846 xs21, xs22,
847 valueT1, valueT2,
848 k, theta );
849 }
850
851 return sigma;
852}
853
854//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
855
856G4double G4ecpssrBaseLixsModel::FunctionFL2(G4double k, G4double theta)
857{
858
859 G4double sigma = 0.;
860 G4double valueT1 = 0;
861 G4double valueT2 = 0;
862 G4double valueE21 = 0;
863 G4double valueE22 = 0;
864 G4double valueE12 = 0;
865 G4double valueE11 = 0;
866 G4double xs11 = 0;
867 G4double xs12 = 0;
868 G4double xs21 = 0;
869 G4double xs22 = 0;
870
871 // PROTECTION TO ALLOW INTERPOLATION AT MINIMUM AND MAXIMUM Eta/Theta2 values
872
873 if (
874 theta==8.66e-4 ||
875 theta==8.66e-3 ||
876 theta==8.66e-2 ||
877 theta==8.66e-1 ||
878 theta==8.66e+00 ||
879 theta==8.66e+01
880 ) theta=theta-1e-12;
881
882 if (
883 theta==1.e-4 ||
884 theta==1.e-3 ||
885 theta==1.e-2 ||
886 theta==1.e-1 ||
887 theta==1.e+00 ||
888 theta==1.e+01
889 ) theta=theta+1e-12;
890
891 // END PROTECTION
892
893 std::vector<double>::iterator t2 = std::upper_bound(dummyVec2.begin(),dummyVec2.end(), k);
894 std::vector<double>::iterator t1 = t2-1;
895
896 std::vector<double>::iterator e12 = std::upper_bound(aVecMap2[(*t1)].begin(),aVecMap2[(*t1)].end(), theta);
897 std::vector<double>::iterator e11 = e12-1;
898
899 std::vector<double>::iterator e22 = std::upper_bound(aVecMap2[(*t2)].begin(),aVecMap2[(*t2)].end(), theta);
900 std::vector<double>::iterator e21 = e22-1;
901
902 valueT1 =*t1;
903 valueT2 =*t2;
904 valueE21 =*e21;
905 valueE22 =*e22;
906 valueE12 =*e12;
907 valueE11 =*e11;
908
909 xs11 = FL2Data[valueT1][valueE11];
910 xs12 = FL2Data[valueT1][valueE12];
911 xs21 = FL2Data[valueT2][valueE21];
912 xs22 = FL2Data[valueT2][valueE22];
913
914 if (verboseLevel>0)
915 G4cout
916 << valueT1 << " "
917 << valueT2 << " "
918 << valueE11 << " "
919 << valueE12 << " "
920 << valueE21 << " "
921 << valueE22 << " "
922 << xs11 << " "
923 << xs12 << " "
924 << xs21 << " "
925 << xs22 << " "
926 << G4endl;
927
928 G4double xsProduct = xs11 * xs12 * xs21 * xs22;
929
930 if (xs11==0 || xs12==0 ||xs21==0 ||xs22==0) return (0.);
931
932 if (xsProduct != 0.)
933 {
934 sigma = QuadInterpolator( valueE11, valueE12,
935 valueE21, valueE22,
936 xs11, xs12,
937 xs21, xs22,
938 valueT1, valueT2,
939 k, theta );
940 }
941
942 return sigma;
943}
944
945//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
946
947G4double G4ecpssrBaseLixsModel::LinLinInterpolate(G4double e1,
948 G4double e2,
949 G4double e,
950 G4double xs1,
951 G4double xs2)
952{
953 G4double value = xs1 + (xs2 - xs1)*(e - e1)/ (e2 - e1);
954 return value;
955}
956
957//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
958
959G4double G4ecpssrBaseLixsModel::LinLogInterpolate(G4double e1,
960 G4double e2,
961 G4double e,
962 G4double xs1,
963 G4double xs2)
964{
965 G4double d1 = std::log(xs1);
966 G4double d2 = std::log(xs2);
967 G4double value = G4Exp(d1 + (d2 - d1)*(e - e1)/ (e2 - e1));
968 return value;
969}
970
971//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
972
973G4double G4ecpssrBaseLixsModel::LogLogInterpolate(G4double e1,
974 G4double e2,
975 G4double e,
976 G4double xs1,
977 G4double xs2)
978{
979 G4double a = (std::log10(xs2)-std::log10(xs1)) / (std::log10(e2)-std::log10(e1));
980 G4double b = std::log10(xs2) - a*std::log10(e2);
981 G4double sigma = a*std::log10(e) + b;
982 G4double value = (std::pow(10.,sigma));
983 return value;
984}
985
986//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
987
988G4double G4ecpssrBaseLixsModel::QuadInterpolator(G4double e11, G4double e12,
989 G4double e21, G4double e22,
990 G4double xs11, G4double xs12,
991 G4double xs21, G4double xs22,
992 G4double t1, G4double t2,
993 G4double t, G4double e)
994{
995// Log-Log
996 G4double interpolatedvalue1 = LogLogInterpolate(e11, e12, e, xs11, xs12);
997 G4double interpolatedvalue2 = LogLogInterpolate(e21, e22, e, xs21, xs22);
998 G4double value = LogLogInterpolate(t1, t2, t, interpolatedvalue1, interpolatedvalue2);
999
1000/*
1001// Lin-Log
1002 G4double interpolatedvalue1 = LinLogInterpolate(e11, e12, e, xs11, xs12);
1003 G4double interpolatedvalue2 = LinLogInterpolate(e21, e22, e, xs21, xs22);
1004 G4double value = LinLogInterpolate(t1, t2, t, interpolatedvalue1, interpolatedvalue2);
1005*/
1006
1007/*
1008// Lin-Lin
1009 G4double interpolatedvalue1 = LinLinInterpolate(e11, e12, e, xs11, xs12);
1010 G4double interpolatedvalue2 = LinLinInterpolate(e21, e22, e, xs21, xs22);
1011 G4double value = LinLinInterpolate(t1, t2, t, interpolatedvalue1, interpolatedvalue2);
1012*/
1013 return value;
1014
1015}
FatalException
@ FatalException
Definition: G4ExceptionSeverity.hh:61
G4Exception
void G4Exception(const char *originOfException, const char *exceptionCode, G4ExceptionSeverity severity, const char *description)
Definition: G4Exception.cc:35
G4Exp
G4double G4Exp(G4double initial_x)
Exponential Function double precision.
Definition: G4Exp.hh:179
G4double
double G4double
Definition: G4Types.hh:83
G4int
int G4int
Definition: G4Types.hh:85
G4endl
#define G4endl
Definition: G4ios.hh:57
G4cout
G4GLOB_DLL std::ostream G4cout
G4Alpha::Alpha
static G4Alpha * Alpha()
Definition: G4Alpha.cc:88
G4AtomicShell::BindingEnergy
G4double BindingEnergy() const
Definition: G4AtomicShell.hh:79
G4AtomicTransitionManager::Shell
G4AtomicShell * Shell(G4int Z, size_t shellIndex) const
Definition: G4AtomicTransitionManager.cc:94
G4AtomicTransitionManager::Instance
static G4AtomicTransitionManager * Instance()
Definition: G4AtomicTransitionManager.cc:44
G4NistManager::Instance
static G4NistManager * Instance()
Definition: G4NistManager.cc:70
G4NistManager::GetAtomicMassAmu
G4double GetAtomicMassAmu(const G4String &symb) const
Definition: G4NistManager.hh:376
G4ParticleDefinition::GetPDGCharge
G4double GetPDGCharge() const
Definition: G4ParticleDefinition.hh:112
G4Proton::Proton
static G4Proton * Proton()
Definition: G4Proton.cc:92
G4ecpssrBaseLixsModel::CalculateL1CrossSection
G4double CalculateL1CrossSection(G4int zTarget, G4double massIncident, G4double energyIncident)
Definition: G4ecpssrBaseLixsModel.cc:191
G4ecpssrBaseLixsModel::CalculateL2CrossSection
G4double CalculateL2CrossSection(G4int zTarget, G4double massIncident, G4double energyIncident)
Definition: G4ecpssrBaseLixsModel.cc:394
G4ecpssrBaseLixsModel::ExpIntFunction
G4double ExpIntFunction(G4int n, G4double x)
Definition: G4ecpssrBaseLixsModel.cc:121
G4ecpssrBaseLixsModel::CalculateVelocity
G4double CalculateVelocity(G4int subShell, G4int zTarget, G4double massIncident, G4double energyIncident)
Definition: G4ecpssrBaseLixsModel.cc:727
G4ecpssrBaseLixsModel::CalculateL3CrossSection
G4double CalculateL3CrossSection(G4int zTarget, G4double massIncident, G4double energyIncident)
Definition: G4ecpssrBaseLixsModel.cc:557