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27 // -------------------------------------------------------------------
28 //
29 // GEANT4 Class file
30 //
31 //
32 // File name: G4PhotoElectricAngularGeneratorPolarized
33 //
34 // Author: A. C. Farinha, L. Peralta, P. Rodrigues and A. Trindade
35 //
36 // Creation date:
37 //
38 // Modifications:
39 // 10 January 2006
40 // 06 May 2011, Replace FILE with std::ifstream
41 //
42 // Class Description:
43 //
44 // Concrete class for PhotoElectric Electron Angular Polarized Distribution Generation
45 //
46 // Class Description:
47 // PhotoElectric Electron Angular Generator based on the general Gavrila photoelectron angular distribution.
48 // Includes polarization effects for K and L1 atomic shells, according to Gavrila (1959, 1961).
49 // For higher shells the L1 cross-section is used.
50 //
51 // The Gavrila photoelectron angular distribution is a complex function which can not be sampled using
52 // the inverse-transform method (James 1980). Instead a more general approach based on the one already
53 // used to sample bremsstrahlung 2BN cross section (G4Generator2BN, Peralta, 2005) was used.
54 //
55 // M. Gavrila, "Relativistic K-Shell Photoeffect", Phys. Rev. 113, 514-526 (1959)
56 // M. Gavrila, "Relativistic L-Shell Photoeffect", Phys. Rev. 124, 1132-1141 (1961)
57 // F. James, Rept. on Prog. in Phys. 43, 1145 (1980)
58 // L. Peralta et al., "A new low-energy bremsstrahlung generator for GEANT4", Radiat. Prot. Dosimetry. 116, 59-64 (2005)
59 //
60 //
61 // -------------------------------------------------------------------
62 //
63 //
64
65 #include "G4PhotoElectricAngularGeneratorPolarized.hh"
66 #include "G4PhysicalConstants.hh"
67 #include "G4RotationMatrix.hh"
68 #include "Randomize.hh"
69 #include "G4Exp.hh"
70
71 G4PhotoElectricAngularGeneratorPolarized::G4PhotoElectricAngularGeneratorPolarized()
72 :G4VEmAngularDistribution("AngularGenSauterGavrilaPolarized")
73 {
74 const G4int arrayDim = 980;
75
76 //minimum electron beta parameter allowed
77 betaArray[0] = 0.02;
78 //beta step
79 betaArray[1] = 0.001;
80 //maximum index array for a and c tables
81 betaArray[2] = arrayDim - 1;
82
83 // read Majorant Surface Parameters. This are required in order to generate
84 //Gavrila angular photoelectron distribution
85 for(G4int level = 0; level < 2; level++){
86 char nameChar0[100] = "ftab0.dat"; // K-shell Majorant Surface Parameters
87 char nameChar1[100] = "ftab1.dat"; // L-shell Majorant Surface Parameters
88
89 G4String filename;
90 if(level == 0) filename = nameChar0;
91 if(level == 1) filename = nameChar1;
92
93 const char* path = G4FindDataDir("G4LEDATA");
94 if (!path)
95 {
96 G4String excep = "G4EMDataSet - G4LEDATA environment variable not set";
97 G4Exception("G4PhotoElectricAngularGeneratorPolarized::G4PhotoElectricAngularGeneratorPolarized",
98 "em0006",FatalException,"G4LEDATA environment variable not set");
99 return;
100 }
101
102 G4String pathString(path);
103 G4String dirFile = pathString + "/photoelectric_angular/" + filename;
104 std::ifstream infile(dirFile);
105 if (!infile.is_open())
106 {
107 G4String excep = "data file: " + dirFile + " not found";
108 G4Exception("G4PhotoElectricAngularGeneratorPolarized::G4PhotoElectricAngularGeneratorPolarized",
109 "em0003",FatalException,excep);
110 return;
111 }
112
113 // Read parameters into tables. The parameters are function of incident electron
114 // energy and shell level
115 G4float aRead=0,cRead=0, beta=0;
116 for(G4int i=0 ; i<arrayDim ;++i){
117 infile >> beta >> aRead >> cRead;
118 aMajorantSurfaceParameterTable[i][level] = aRead;
119 cMajorantSurfaceParameterTable[i][level] = cRead;
120 }
121 infile.close();
122 }
123 }
124
125 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
126
127 G4PhotoElectricAngularGeneratorPolarized::~G4PhotoElectricAngularGeneratorPolarized()
128 {}
129
130 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
131
132 G4ThreeVector&
133 G4PhotoElectricAngularGeneratorPolarized::SampleDirection(
134 const G4DynamicParticle* dp,
135 G4double eKinEnergy,
136 G4int shellId,
137 const G4Material*)
138 {
139 // (shellId == 0) - K-shell - Polarized model for K-shell
140 // (shellId > 0) - L1-shell - Polarized model for L1 and higher shells
141
142 // Calculate Lorentz term (gamma) and beta parameters
143 G4double gamma = 1 + eKinEnergy/electron_mass_c2;
144 G4double beta = std::sqrt((gamma - 1)*(gamma + 1))/gamma;
145
146 const G4ThreeVector& direction = dp->GetMomentumDirection();
147 const G4ThreeVector& polarization = dp->GetPolarization();
148
149 G4double theta, phi = 0;
150 // Majorant surface parameters
151 // function of the outgoing electron kinetic energy
152 G4double aBeta = 0;
153 G4double cBeta = 0;
154
155 // For the outgoing kinetic energy
156 // find the current majorant surface parameters
157 PhotoElectronGetMajorantSurfaceAandCParameters(shellId, beta, &aBeta, &cBeta);
158
159 // Generate pho and theta according to the shell level
160 // and beta parameter of the electron
161 PhotoElectronGeneratePhiAndTheta(shellId, beta, aBeta, cBeta, &phi, &theta);
162
163 // Determine the rotation matrix
164 const G4RotationMatrix rotation =
165 PhotoElectronRotationMatrix(direction, polarization);
166
167 // Compute final direction of the outgoing electron
168 fLocalDirection = PhotoElectronComputeFinalDirection(rotation, theta, phi);
169
170 return fLocalDirection;
171 }
172
173 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
174
175 void
176 G4PhotoElectricAngularGeneratorPolarized::PhotoElectronGeneratePhiAndTheta(
177 G4int shellLevel, G4double beta, G4double aBeta, G4double cBeta,
178 G4double *pphi, G4double *ptheta) const
179 {
180 G4double rand1, rand2, rand3 = 0;
181 G4double phi = 0;
182 G4double theta = 0;
183 G4double crossSectionValue = 0;
184 G4double crossSectionMajorantFunctionValue = 0;
185 G4double maxBeta = 0;
186
187 do {
188
189 rand1 = G4UniformRand();
190 rand2 = G4UniformRand();
191 rand3 = G4UniformRand();
192
193 phi=2*pi*rand1;
194
195 if(shellLevel == 0){
196 // Polarized Gavrila Cross-Section for K-shell (1959)
197 theta=std::sqrt(((G4Exp(rand2*std::log(1+cBeta*pi*pi)))-1)/cBeta);
198 crossSectionMajorantFunctionValue =
199 CrossSectionMajorantFunction(theta, cBeta);
200 crossSectionValue = DSigmaKshellGavrila1959(beta, theta, phi);
201 } else {
202 // Polarized Gavrila Cross-Section for other shells (L1-shell) (1961)
203 theta = std::sqrt(((G4Exp(rand2*std::log(1+cBeta*pi*pi)))-1)/cBeta);
204 crossSectionMajorantFunctionValue =
205 CrossSectionMajorantFunction(theta, cBeta);
206 crossSectionValue = DSigmaL1shellGavrila(beta, theta, phi);
207 }
208
209 maxBeta=rand3*aBeta*crossSectionMajorantFunctionValue;
210 if(crossSectionValue < 0.0) { crossSectionValue = maxBeta; }
211
212 } while(maxBeta > crossSectionValue || theta > CLHEP::pi);
213
214 *pphi = phi;
215 *ptheta = theta;
216 }
217
218 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
219
220 G4double
221 G4PhotoElectricAngularGeneratorPolarized::CrossSectionMajorantFunction(
222 G4double theta, G4double cBeta) const
223 {
224 // Compute Majorant Function
225 G4double crossSectionMajorantFunctionValue = 0;
226 crossSectionMajorantFunctionValue = theta/(1+cBeta*theta*theta);
227 return crossSectionMajorantFunctionValue;
228 }
229
230 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
231
232 G4double
233 G4PhotoElectricAngularGeneratorPolarized::DSigmaKshellGavrila1959(
234 G4double beta, G4double theta, G4double phi) const
235 {
236 //Double differential K shell cross-section (Gavrila 1959)
237
238 G4double beta2 = beta*beta;
239 G4double oneBeta2 = 1 - beta2;
240 G4double sqrtOneBeta2 = std::sqrt(oneBeta2);
241 G4double oneBeta2_to_3_2 = std::pow(oneBeta2,1.5);
242 G4double cosTheta = std::cos(theta);
243 G4double sinTheta2 = std::sin(theta)*std::sin(theta);
244 G4double cosPhi2 = std::cos(phi)*std::cos(phi);
245 G4double oneBetaCosTheta = 1-beta*cosTheta;
246 G4double dsigma = 0;
247 G4double firstTerm = 0;
248 G4double secondTerm = 0;
249
250 firstTerm = sinTheta2*cosPhi2/std::pow(oneBetaCosTheta,4)-(1 - sqrtOneBeta2)/(2*oneBeta2) *
251 (sinTheta2 * cosPhi2)/std::pow(oneBetaCosTheta,3) + (1-sqrtOneBeta2)*
252 (1-sqrtOneBeta2)/(4*oneBeta2_to_3_2) * sinTheta2/std::pow(oneBetaCosTheta,3);
253
254 secondTerm = std::sqrt(1 - sqrtOneBeta2)/(std::pow(2.,3.5)*beta2*std::pow(oneBetaCosTheta,2.5)) *
255 (4*beta2/sqrtOneBeta2 * sinTheta2*cosPhi2/oneBetaCosTheta + 4*beta/oneBeta2 * cosTheta * cosPhi2
256 - 4*(1-sqrtOneBeta2)/oneBeta2 *(1+cosPhi2) - beta2 * (1-sqrtOneBeta2)/oneBeta2 * sinTheta2/oneBetaCosTheta
257 + 4*beta2*(1-sqrtOneBeta2)/oneBeta2_to_3_2 - 4*beta*(1-sqrtOneBeta2)*(1-sqrtOneBeta2)/oneBeta2_to_3_2 * cosTheta)
258 + (1-sqrtOneBeta2)/(4*beta2*oneBetaCosTheta*oneBetaCosTheta) * (beta/oneBeta2 - 2/oneBeta2 * cosTheta * cosPhi2 +
259 (1-sqrtOneBeta2)/oneBeta2_to_3_2 * cosTheta - beta * (1-sqrtOneBeta2)/oneBeta2_to_3_2);
260
261 dsigma = ( firstTerm*(1-pi*fine_structure_const/beta) + secondTerm*(pi*fine_structure_const) )*std::sin(theta);
262
263 return dsigma;
264 }
265
266 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
267
268 G4double
269 G4PhotoElectricAngularGeneratorPolarized::DSigmaL1shellGavrila(
270 G4double beta, G4double theta, G4double phi) const
271 {
272 //Double differential L1 shell cross-section (Gavrila 1961)
273 // 26Oct2022: included factor (1/8) in dsigma from eqn 20 of paper
274 G4double beta2 = beta*beta;
275 G4double oneBeta2 = 1-beta2;
276 G4double sqrtOneBeta2 = std::sqrt(oneBeta2);
277 G4double oneBeta2_to_3_2=std::pow(oneBeta2,1.5);
278 G4double cosTheta = std::cos(theta);
279 G4double sinTheta2 =std::sin(theta)*std::sin(theta);
280 G4double cosPhi2 = std::cos(phi)*std::cos(phi);
281 G4double oneBetaCosTheta = 1-beta*cosTheta;
282
283 G4double dsigma = 0;
284 G4double firstTerm = 0;
285 G4double secondTerm = 0;
286
287 firstTerm = sinTheta2*cosPhi2/std::pow(oneBetaCosTheta,4)-(1 - sqrtOneBeta2)/(2*oneBeta2)
288 * (sinTheta2 * cosPhi2)/std::pow(oneBetaCosTheta,3) + (1-sqrtOneBeta2)*
289 (1-sqrtOneBeta2)/(4*oneBeta2_to_3_2) * sinTheta2/std::pow(oneBetaCosTheta,3);
290
291 secondTerm = std::sqrt(1 - sqrtOneBeta2)/(std::pow(2.,3.5)*beta2*std::pow(oneBetaCosTheta,2.5)) *
292 (4*beta2/sqrtOneBeta2 * sinTheta2*cosPhi2/oneBetaCosTheta + 4*beta/oneBeta2 * cosTheta * cosPhi2
293 - 4*(1-sqrtOneBeta2)/oneBeta2 *(1+cosPhi2) - beta2 * (1-sqrtOneBeta2)/oneBeta2 * sinTheta2/oneBetaCosTheta
294 + 4*beta2*(1-sqrtOneBeta2)/oneBeta2_to_3_2 - 4*beta*(1-sqrtOneBeta2)*(1-sqrtOneBeta2)/oneBeta2_to_3_2 * cosTheta)
295 + (1-sqrtOneBeta2)/(4*beta2*oneBetaCosTheta*oneBetaCosTheta) * (beta/oneBeta2 - 2/oneBeta2 * cosTheta * cosPhi2 +
296 (1-sqrtOneBeta2)/oneBeta2_to_3_2*cosTheta - beta*(1-sqrtOneBeta2)/oneBeta2_to_3_2);
297
298 dsigma = ( firstTerm*(1-pi*fine_structure_const/beta) + secondTerm*(pi*fine_structure_const) )*std::sin(theta) / 8.;
299
300 return dsigma;
301 }
302
303 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
304
305 G4RotationMatrix
306 G4PhotoElectricAngularGeneratorPolarized::PhotoElectronRotationMatrix(
307 const G4ThreeVector& direction,
308 const G4ThreeVector& polarization)
309 {
310 G4double mK = direction.mag();
311 G4double mS = polarization.mag();
312 G4ThreeVector polarization2 = polarization;
313 const G4double kTolerance = 1e-6;
314
315 if(!(polarization.isOrthogonal(direction,kTolerance)) || mS == 0){
316 G4ThreeVector d0 = direction.unit();
317 G4ThreeVector a1 = PerpendicularVector(d0);
318 G4ThreeVector a0 = a1.unit();
319 G4double rand1 = G4UniformRand();
320 G4double angle = twopi*rand1;
321 G4ThreeVector b0 = d0.cross(a0);
322 G4ThreeVector c;
323 c.setX(std::cos(angle)*(a0.x())+std::sin(angle)*b0.x());
324 c.setY(std::cos(angle)*(a0.y())+std::sin(angle)*b0.y());
325 c.setZ(std::cos(angle)*(a0.z())+std::sin(angle)*b0.z());
326 polarization2 = c.unit();
327 mS = polarization2.mag();
328 }else
329 {
330 if ( polarization.howOrthogonal(direction) != 0)
331 {
332 polarization2 = polarization
333 - polarization.dot(direction)/direction.dot(direction) * direction;
334 }
335 }
336
337 G4ThreeVector direction2 = direction/mK;
338 polarization2 = polarization2/mS;
339
340 G4ThreeVector y = direction2.cross(polarization2);
341
342 G4RotationMatrix R(polarization2,y,direction2);
343 return R;
344 }
345
346 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
347
348 void
349 G4PhotoElectricAngularGeneratorPolarized::PhotoElectronGetMajorantSurfaceAandCParameters(G4int shellId, G4double beta, G4double *majorantSurfaceParameterA, G4double *majorantSurfaceParameterC) const
350 {
351 // This member function finds for a given shell and beta value
352 // of the outgoing electron the correct Majorant Surface parameters
353 G4double aBeta,cBeta;
354 G4double bMin,bStep;
355 G4int indexMax;
356 G4int level = 0;
357 if(shellId > 0) { level = 1; }
358
359 bMin = betaArray[0];
360 bStep = betaArray[1];
361 indexMax = (G4int)betaArray[2];
362 const G4double kBias = 1e-9;
363
364 G4int k = (G4int)((beta-bMin+kBias)/bStep);
365
366 if(k < 0)
367 k = 0;
368 if(k > indexMax)
369 k = indexMax;
370
371 if(k == 0)
372 aBeta = std::max(aMajorantSurfaceParameterTable[k][level],aMajorantSurfaceParameterTable[k+1][level]);
373 else if(k==indexMax)
374 aBeta = std::max(aMajorantSurfaceParameterTable[k-1][level],aMajorantSurfaceParameterTable[k][level]);
375 else{
376 aBeta = std::max(aMajorantSurfaceParameterTable[k-1][level],aMajorantSurfaceParameterTable[k][level]);
377 aBeta = std::max(aBeta,aMajorantSurfaceParameterTable[k+1][level]);
378 }
379
380 if(k == 0)
381 cBeta = std::max(cMajorantSurfaceParameterTable[k][level],cMajorantSurfaceParameterTable[k+1][level]);
382 else if(k == indexMax)
383 cBeta = std::max(cMajorantSurfaceParameterTable[k-1][level],cMajorantSurfaceParameterTable[k][level]);
384 else{
385 cBeta = std::max(cMajorantSurfaceParameterTable[k-1][level],cMajorantSurfaceParameterTable[k][level]);
386 cBeta = std::max(cBeta,cMajorantSurfaceParameterTable[k+1][level]);
387 }
388
389 *majorantSurfaceParameterA = aBeta;
390 *majorantSurfaceParameterC = cBeta;
391 }
392
393 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
394
395 G4ThreeVector G4PhotoElectricAngularGeneratorPolarized::PhotoElectronComputeFinalDirection(const G4RotationMatrix& rotation, G4double theta, G4double phi) const
396 {
397 //computes the photoelectron momentum unitary vector
398 G4double sint = std::sin(theta);
399 G4double px = std::cos(phi)*sint;
400 G4double py = std::sin(phi)*sint;
401 G4double pz = std::cos(theta);
402
403 G4ThreeVector samplingDirection(px,py,pz);
404
405 G4ThreeVector outgoingDirection = rotation*samplingDirection;
406 return outgoingDirection;
407 }
408
409 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
410
411 void G4PhotoElectricAngularGeneratorPolarized::PrintGeneratorInformation() const
412 {
413 G4cout << "\n" << G4endl;
414 G4cout << "Polarized Photoelectric Angular Generator" << G4endl;
415 G4cout << "PhotoElectric Electron Angular Generator based on the general Gavrila photoelectron angular distribution" << G4endl;
416 G4cout << "Includes polarization effects for K and L1 atomic shells, according to Gavrilla (1959, 1961)." << G4endl;
417 G4cout << "For higher shells the L1 cross-section is used." << G4endl;
418 G4cout << "(see Physics Reference Manual) \n" << G4endl;
419 }
420
421 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
422
423 G4ThreeVector
424 G4PhotoElectricAngularGeneratorPolarized::PerpendicularVector(
425 const G4ThreeVector& a) const
426 {
427 G4double dx = a.x();
428 G4double dy = a.y();
429 G4double dz = a.z();
430 G4double x = dx < 0.0 ? -dx : dx;
431 G4double y = dy < 0.0 ? -dy : dy;
432 G4double z = dz < 0.0 ? -dz : dz;
433 if (x < y) {
434 return x < z ? G4ThreeVector(-dy,dx,0) : G4ThreeVector(0,-dz,dy);
435 }else{
436 return y < z ? G4ThreeVector(dz,0,-dx) : G4ThreeVector(-dy,dx,0);
437 }
438 }
439