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G4PolarizedBhabhaCrossSection.cc
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26 // $Id: G4PolarizedBhabhaCrossSection.cc 69847 2013-05-16 09:36:18Z gcosmo $
27 // -------------------------------------------------------------------
28 //
29 // GEANT4 Class file
30 //
31 //
32 // File name: G4PolarizedBhabhaCrossSection
33 //
34 // Author: Andreas Schaelicke
35 //
36 // Creation date: 12.01.2006
37 //
38 // Modifications:
39 // 16-01-06 included cross section as calculated by P.Starovoitov
40 // 24-08-06 bugfix in total cross section (A. Schaelicke)
41 // 07-11-06 modify reference system for polarisation vectors
42 // (A. Schaelicke & P.Starovoitov)
43 //
44 // Class Description:
45 // * calculates the differential cross section
46 // incomming positron Kpl(along positive z direction) scatters at
47 // an electron Kmn at rest
48 // * phi denotes the angle between the scattering plane (defined by the
49 // outgoing electron) and X-axis
50 // * all stokes vectors refer to spins in the Global System (X,Y,Z)
51 //
52 
53 #include "G4PolarizedBhabhaCrossSection.hh"
54 #include "G4PhysicalConstants.hh"
55 
56 G4PolarizedBhabhaCrossSection::G4PolarizedBhabhaCrossSection() : phi0(1.)
57 {
58 }
59 G4PolarizedBhabhaCrossSection::~G4PolarizedBhabhaCrossSection()
60 {
61 }
62 void G4PolarizedBhabhaCrossSection::Initialize(
63  G4double e,
64  G4double gamma,
65  G4double /*phi*/,
66  const G4StokesVector & pol0,
67  const G4StokesVector & pol1,
68  G4int flag)
69 {
70  SetXmax(1.);
71 
72  G4double re2 = classic_electr_radius * classic_electr_radius;
73  G4double gamma2 = gamma*gamma;
74  G4double gamma3 = gamma2*gamma;
75  G4double gmo = (gamma - 1.);
76  G4double gmo2 = (gamma - 1.)*(gamma - 1.);
77  G4double gmo3 = gmo2*(gamma - 1.);
78  G4double gpo = (gamma + 1.);
79  G4double gpo2 = (gamma + 1.)*(gamma + 1.);
80  G4double gpo3 = gpo2*(gamma + 1.);
81  G4double gpo12 = std::sqrt(gpo);
82  G4double gpo32 = gpo*gpo12;
83  G4double gpo52 = gpo2*gpo12;
84 
85  G4double pref = re2/(gamma - 1.0);
86  G4double sqrttwo=std::sqrt(2.);
87  G4double d = std::sqrt(1./e - 1.);
88  G4double e2 = e*e;
89  G4double e3 = e2*e;
90 
91  // *** new ***
92  G4double gmo12 = std::sqrt(gmo);
93  G4double gmo32 = gmo*gmo12;
94  G4double egmp32 = std::pow(e*(2 + e*gmo)*gpo,(3./2.));
95  G4double e32 = e*std::sqrt(e);
96 
97  G4bool polarized=(!pol0.IsZero())||(!pol1.IsZero());
98 
99  if (flag==0) polarized=false;
100  // Unpolarised part of XS
101  // *AS* UnpME . OK
102  phi0 = 0.;
103  phi0+= e2*gmo3/gpo3;
104  phi0+= -2.*e*gamma*gmo2/gpo3;
105  phi0+= (3.*gamma2 + 6.*gamma + 4.)*gmo/gpo3;
106  phi0+= -(2.*gamma2 + 4.*gamma + 1.)/(e*gpo2);
107  phi0+= gamma2/(e2*(gamma2 - 1.));
108  phi0*=0.25;
109  // Initial state polarisarion dependence
110  if (polarized) {
111  // G4cout<<"Polarized differential Bhabha cross section"<<G4endl;
112  // G4cout<<"Initial state polarisation contributions"<<G4endl;
113  // G4cout<<"Diagonal Matrix Elements"<<G4endl;
114  // *** new ***
115  G4double xx = -((e*gmo - gamma)*(-1 - gamma + e*(e*gmo - gamma)*(3 + gamma)))/(4*e*gpo3);
116  G4double yy = (e3*gmo3 - 2*e2*gmo2*gamma - gpo*(1 + 2*gamma) + e*(-2 + gamma2 + gamma3))/(4*e*gpo3);
117  G4double zz = ((e*gmo - gamma)*(e2*gmo*(3 + gamma) - e*gamma*(3 + gamma) + gpo*(1 + 2*gamma)))/(4*e*gpo3);
118  // ***
119 
120  phi0 += xx*pol0.x()*pol1.x() + yy*pol0.y()*pol1.y() + zz*pol0.z()*pol1.z();
121 
122  {
123  G4double xy = 0;
124  G4double xz = (d*(e*gmo - gamma)*(-1 + 2*e*gmo - gamma))/(2*sqrttwo*gpo52);
125  G4double yx = 0;
126  G4double yz = 0;
127  G4double zx = xz;
128  G4double zy = 0;
129  // G4cout<<"Non-diagonal Matrix Elements"<<G4endl;
130  phi0+=yx*pol0.y()*pol1.x() + xy*pol0.x()*pol1.y();
131  phi0+=zx*pol0.z()*pol1.x() + xz*pol0.x()*pol1.z();
132  phi0+=zy*pol0.z()*pol1.y() + yz*pol0.y()*pol1.z();
133  }
134  }
135  // Final state polarisarion dependence
136  phi2=G4ThreeVector();
137  phi3=G4ThreeVector();
138 
139  if (flag>=1) {
140  //
141  // Final Positron Ppl
142  //
143  // initial positron Kpl
144  if (!pol0.IsZero()) {
145 
146  G4double xxPplKpl = -((-1 + e)*(e*gmo - gamma)*(-(gamma*gpo) + e*(-2 + gamma + gamma2)))/
147  (4*e2*gpo*std::sqrt(gmo*gpo*(-1 + e + gamma - e*gamma)* (1 + e + gamma - e*gamma)));
148  G4double xyPplKpl = 0;
149  G4double xzPplKpl = ((e*gmo - gamma)*(-1 - gamma + e*gmo*(1 + 2*gamma)))/
150  (2*sqrttwo*e32*gmo*gpo2*std::sqrt(1 + e + gamma - e*gamma));
151  G4double yxPplKpl = 0;
152  G4double yyPplKpl = (gamma2*gpo + e2*gmo2*(3 + gamma) -
153  e*gmo*(1 + 2*gamma*(2 + gamma)))/(4*e2*gmo*gpo2);
154  G4double yzPplKpl = 0;
155  G4double zxPplKpl = ((e*gmo - gamma)*(1 + e*(-1 + 2*e*gmo - 2*gamma)*gmo + gamma))/
156  (2*sqrttwo*e*gmo*gpo2*std::sqrt(e*(1 + e + gamma - e*gamma)));
157  G4double zyPplKpl = 0;
158  G4double zzPplKpl = -((e*gmo - gamma)*std::sqrt((1 - e)/(e - e*gamma2 + gpo2))*
159  (2*e2*gmo2 + gamma + gamma2 - e*(-2 + gamma + gamma2)))/
160  (4*e2*(-1 + gamma2));
161 
162  phi2[0] += xxPplKpl*pol0.x() + xyPplKpl*pol0.y() + xzPplKpl*pol0.z();
163  phi2[1] += yxPplKpl*pol0.x() + yyPplKpl*pol0.y() + yzPplKpl*pol0.z();
164  phi2[2] += zxPplKpl*pol0.x() + zyPplKpl*pol0.y() + zzPplKpl*pol0.z();
165  }
166  // initial electron Kmn
167  if (!pol1.IsZero()) {
168  G4double xxPplKmn = ((-1 + e)*(e*(-2 + gamma)*gmo + gamma))/(4*e*gpo32*std::sqrt(1 + e2*gmo + gamma - 2*e*gamma));
169  G4double xyPplKmn = 0;
170  G4double xzPplKmn = (-1 + e*gmo + gmo*gamma)/(2*sqrttwo*gpo2* std::sqrt(e*(1 + e + gamma - e*gamma)));
171  G4double yxPplKmn = 0;
172  G4double yyPplKmn = (-1 - 2*gamma + e*gmo*(3 + gamma))/(4*e*gpo2);
173  G4double yzPplKmn = 0;
174  G4double zxPplKmn = (1 + 2*e2*gmo2 + gamma + gamma2 + e*(1 + (3 - 4*gamma)*gamma))/
175  (2*sqrttwo*gpo2*std::sqrt(e*(1 + e + gamma - e*gamma)));
176  G4double zyPplKmn = 0;
177  G4double zzPplKmn = -(std::sqrt((1 - e)/(e - e*gamma2 + gpo2))*
178  (2*e2*gmo2 + gamma + 2*gamma2 + e*(2 + gamma - 3*gamma2)))/(4*e*gpo);
179 
180  phi2[0] += xxPplKmn*pol1.x() + xyPplKmn*pol1.y() + xzPplKmn*pol1.z();
181  phi2[1] += yxPplKmn*pol1.x() + yyPplKmn*pol1.y() + yzPplKmn*pol1.z();
182  phi2[2] += zxPplKmn*pol1.x() + zyPplKmn*pol1.y() + zzPplKmn*pol1.z();
183  }
184 //
185 // Final Electron Pmn
186 //
187  // initial positron Kpl
188  if (!pol0.IsZero()) {
189  G4double xxPmnKpl = ((-1 + e*gmo)*(2 + gamma))/(4*gpo* std::sqrt(e*(2 + e*gmo)*gpo));
190  G4double xyPmnKpl = 0;
191  G4double xzPmnKpl = (std::sqrt((-1 + e)/(-2 + e - e*gamma))*
192  (e + gamma + e*gamma - 2*(-1 + e)*gamma2))/(2*sqrttwo*e*gpo2);
193  G4double yxPmnKpl = 0;
194  G4double yyPmnKpl = (-1 - 2*gamma + e*gmo*(3 + gamma))/(4*e*gpo2);
195  G4double yzPmnKpl = 0;
196  G4double zxPmnKpl = -((-1 + e)*(1 + 2*e*gmo)*(e*gmo - gamma))/
197  (2*sqrttwo*e*std::sqrt(-((-1 + e)*(2 + e*gmo)))*gpo2);
198  G4double zyPmnKpl = 0;
199  G4double zzPmnKpl = (-2 + 2*e2*gmo2 + gamma*(-1 + 2*gamma) +
200  e*(-2 + (5 - 3*gamma)*gamma))/(4*std::sqrt(e*(2 + e*gmo))* gpo32);
201 
202  phi3[0] += xxPmnKpl*pol0.x() + xyPmnKpl*pol0.y() + xzPmnKpl*pol0.z();
203  phi3[1] += yxPmnKpl*pol0.x() + yyPmnKpl*pol0.y() + yzPmnKpl*pol0.z();
204  phi3[2] += zxPmnKpl*pol0.x() + zyPmnKpl*pol0.y() + zzPmnKpl*pol0.z();
205  }
206  // initial electron Kmn
207  if (!pol1.IsZero()) {
208  G4double xxPmnKmn = -((2 + e*gmo)*(-1 + e*gmo - gamma)*(e*gmo - gamma)*
209  (-2 + gamma))/(4*gmo*egmp32);
210  G4double xyPmnKmn = 0;
211  G4double xzPmnKmn = ((e*gmo - gamma)*
212  std::sqrt((-1 + e + gamma - e*gamma)/(2 + e*gmo))*
213  (e + gamma - e*gamma + gamma2))/
214  (2*sqrttwo*e2*gmo32*gpo2);
215  G4double yxPmnKmn = 0;
216  G4double yyPmnKmn = (gamma2*gpo + e2*gmo2*(3 + gamma) -
217  e*gmo*(1 + 2*gamma*(2 + gamma)))/(4*e2*gmo*gpo2);
218  G4double yzPmnKmn = 0;
219  G4double zxPmnKmn = -((-1 + e)*(e*gmo - gamma)*(e*gmo + 2*e2*gmo2 - gamma*gpo))/
220  (2*sqrttwo*e2*std::sqrt(-((-1 + e)*(2 + e*gmo)))* gmo*gpo2);
221  G4double zyPmnKmn = 0;
222  G4double zzPmnKmn = ((e*gmo - gamma)*std::sqrt(e/((2 + e*gmo)*gpo))*
223  (-(e*(-2 + gamma)*gmo) + 2*e2*gmo2 + (-2 + gamma)*gpo))/(4*e2*(-1 + gamma2));
224 
225  phi3[0] += xxPmnKmn*pol1.x() + xyPmnKmn*pol1.y() + xzPmnKmn*pol1.z();
226  phi3[1] += yxPmnKmn*pol1.x() + yyPmnKmn*pol1.y() + yzPmnKmn*pol1.z();
227  phi3[2] += zxPmnKmn*pol1.x() + zyPmnKmn*pol1.y() + zzPmnKmn*pol1.z();
228  }
229  }
230  phi0 *= pref;
231  phi2 *= pref;
232  phi3 *= pref;
233 
234 }
235 
236 G4double G4PolarizedBhabhaCrossSection::XSection(const G4StokesVector & pol2,
237  const G4StokesVector & pol3)
238 {
239  G4double xs=0.;
240  xs+=phi0;
241 
242  G4bool polarized=(!pol2.IsZero())||(!pol3.IsZero());
243  if (polarized) {
244  xs+=phi2*pol2 + phi3*pol3;
245  }
246  return xs;
247 }
248 
249 G4double G4PolarizedBhabhaCrossSection::TotalXSection(
250  G4double xmin, G4double xmax, G4double gamma,
251  const G4StokesVector & pol0,const G4StokesVector & pol1)
252 {
253  G4double xs=0.;
254 
255  G4double x=xmin;
256 
257  if (xmax != 1.) G4cout<<" warning xmax expected to be 1 but is "<<xmax<< G4endl;
258 
259  // re -> electron radius^2;
260  G4double re2 = classic_electr_radius * classic_electr_radius;
261  G4double gamma2=gamma*gamma;
262  G4double gmo2 = (gamma - 1.)*(gamma - 1.);
263  G4double gpo2 = (gamma + 1.)*(gamma + 1.);
264  G4double gpo3 = gpo2*(gamma + 1.);
265  G4double logMEM = std::log(x);
266  G4double pref = twopi*re2/(gamma - 1.0);
267  // unpolarise XS
268  G4double sigma0 = 0.;
269  sigma0 += -gmo2*(gamma - 1.)*x*x*x/3. + gmo2*gamma*x*x;
270  sigma0 += -(gamma - 1.)*(3.*gamma*(gamma + 2.) +4.)*x;
271  sigma0 += (gamma*(gamma*(gamma*(4.*gamma - 1.) - 21.) - 7.)+13.)/(3.*(gamma - 1.));
272  sigma0 /= gpo3;
273  sigma0 += logMEM*(2. - 1./gpo2);
274  sigma0 += gamma2/((gamma2 - 1.)*x);
275  // longitudinal part
276  G4double sigma2=0.;
277  sigma2 += logMEM*gamma*(gamma + 1.)*(2.*gamma + 1.);
278  sigma2 += gamma*(7.*gamma*(gamma + 1.) - 2.)/3.;
279  sigma2 += -(3.*gamma + 1.)*(gamma2 + gamma - 1.)*x;
280  sigma2 += (gamma - 1.)*gamma*(gamma + 3.)*x*x;
281  sigma2 += -gmo2*(gamma + 3.)*x*x*x/3.;
282  sigma2 /= gpo3;
283  // transverse part
284  G4double sigma3=0.;
285  sigma3 += 0.5*(gamma + 1.)*(3.*gamma + 1.)*logMEM;
286  sigma3 += (gamma*(5.*gamma - 4.) - 13.)/6.;
287  sigma3 += 0.5*(gamma2 + 3.)*x;
288  sigma3 += - 2.*(gamma - 1.)*gamma*x*x; // *AS* changed sign
289  sigma3 += 2.*gmo2*x*x*x/3.;
290  sigma3 /= gpo3;
291  // total cross section
292  xs+=pref*(sigma0 + sigma2*pol0.z()*pol1.z() + sigma3*(pol0.x()*pol1.x()+pol0.y()*pol1.y()));
293 
294  return xs;
295 }
296 
297 
298 G4StokesVector G4PolarizedBhabhaCrossSection::GetPol2()
299 {
300  // Note, mean polarization can not contain correlation
301  // effects.
302  return 1./phi0 * phi2;
303 }
304 G4StokesVector G4PolarizedBhabhaCrossSection::GetPol3()
305 {
306  // Note, mean polarization can not contain correlation
307  // effects.
308  return 1./phi0 * phi3;
309 }
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