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25 // 25 //
26 // INCL++ intra-nuclear cascade model 26 // INCL++ intra-nuclear cascade model
27 // Alain Boudard, CEA-Saclay, France << 27 // Pekka Kaitaniemi, CEA and Helsinki Institute of Physics
28 // Joseph Cugnon, University of Liege, Belgium << 28 // Davide Mancusi, CEA
29 // Jean-Christophe David, CEA-Saclay, France << 29 // Alain Boudard, CEA
30 // Pekka Kaitaniemi, CEA-Saclay, France, and H << 30 // Sylvie Leray, CEA
31 // Sylvie Leray, CEA-Saclay, France << 31 // Joseph Cugnon, University of Liege
32 // Davide Mancusi, CEA-Saclay, France <<
33 // 32 //
34 #define INCLXX_IN_GEANT4_MODE 1 33 #define INCLXX_IN_GEANT4_MODE 1
35 34
36 #include "globals.hh" 35 #include "globals.hh"
37 36
38 /** \file G4INCLDeuteronDensity.cc 37 /** \file G4INCLDeuteronDensity.cc
39 * \brief Deuteron density in r and p accordin 38 * \brief Deuteron density in r and p according to the Paris potential.
40 * 39 *
41 * \date 6 March 2012 40 * \date 6 March 2012
42 * \author Davide Mancusi 41 * \author Davide Mancusi
43 */ 42 */
44 43
45 #include "G4INCLDeuteronDensity.hh" 44 #include "G4INCLDeuteronDensity.hh"
46 #include "G4INCLGlobals.hh" 45 #include "G4INCLGlobals.hh"
47 // #include <cassert> 46 // #include <cassert>
48 #include <algorithm> 47 #include <algorithm>
49 48
50 namespace G4INCL { 49 namespace G4INCL {
51 50
52 namespace DeuteronDensity { 51 namespace DeuteronDensity {
53 52
54 namespace { 53 namespace {
55 54
56 const G4int coeffTableSize = 13; 55 const G4int coeffTableSize = 13;
57 56
58 /// \brief Coefficients for the deuteron 57 /// \brief Coefficients for the deuteron wave function
59 const G4double coeff1[coeffTableSize] = 58 const G4double coeff1[coeffTableSize] = {
60 0.88688076e+0, 59 0.88688076e+0,
61 -0.34717093e+0, 60 -0.34717093e+0,
62 -0.30502380e+1, 61 -0.30502380e+1,
63 0.56207766e+2, 62 0.56207766e+2,
64 -0.74957334e+3, 63 -0.74957334e+3,
65 0.53365279e+4, 64 0.53365279e+4,
66 -0.22706863e+5, 65 -0.22706863e+5,
67 0.60434469e+5, 66 0.60434469e+5,
68 -0.10292058e+6, 67 -0.10292058e+6,
69 0.11223357e+6, 68 0.11223357e+6,
70 -0.75925226e+5, 69 -0.75925226e+5,
71 0.29059715e+5, 70 0.29059715e+5,
72 -0.48157368e+4 71 -0.48157368e+4
73 }; 72 };
74 73
75 /// \brief Coefficients for the deuteron 74 /// \brief Coefficients for the deuteron wave function
76 const G4double coeff2[coeffTableSize] = 75 const G4double coeff2[coeffTableSize] = {
77 0.23135193e-1, 76 0.23135193e-1,
78 -0.85604572e+0, 77 -0.85604572e+0,
79 0.56068193e+1, 78 0.56068193e+1,
80 -0.69462922e+2, 79 -0.69462922e+2,
81 0.41631118e+3, 80 0.41631118e+3,
82 -0.12546621e+4, 81 -0.12546621e+4,
83 0.12387830e+4, 82 0.12387830e+4,
84 0.33739172e+4, 83 0.33739172e+4,
85 -0.13041151e+5, 84 -0.13041151e+5,
86 0.19512524e+5, 85 0.19512524e+5,
87 -0.15634324e+5, 86 -0.15634324e+5,
88 0.66231089e+4, 87 0.66231089e+4,
89 -0.11698185e+4 88 -0.11698185e+4
90 }; 89 };
91 90
92 /// \brief Normalisation coefficient for 91 /// \brief Normalisation coefficient for the r-space deuteron wave function
93 const G4double normalisationR = std::sqr 92 const G4double normalisationR = std::sqrt(32. * Math::pi) * 0.28212;
94 93
95 /// \brief Normalisation coefficient for 94 /// \brief Normalisation coefficient for the p-space deuteron wave function
96 const G4double normalisationP = normalis 95 const G4double normalisationP = normalisationR / (std::sqrt(4. * Math::pi) * std::pow(PhysicalConstants::hc,1.5));
97 96
98 /// \brief Mysterious coefficient that a 97 /// \brief Mysterious coefficient that appears in the wavefunctions
99 const G4double al = 0.23162461; 98 const G4double al = 0.23162461;
100 99
101 } 100 }
102 101
103 G4double densityR(const G4double r) { 102 G4double densityR(const G4double r) {
104 const G4double sWave = wavefunctionR(0, 103 const G4double sWave = wavefunctionR(0, r);
105 const G4double dWave = wavefunctionR(2, 104 const G4double dWave = wavefunctionR(2, r);
106 return r*r*(sWave*sWave + dWave*dWave); 105 return r*r*(sWave*sWave + dWave*dWave);
107 } 106 }
108 107
109 G4double derivDensityR(const G4double r) { 108 G4double derivDensityR(const G4double r) {
110 const G4double sWave = wavefunctionR(0, 109 const G4double sWave = wavefunctionR(0, r);
111 const G4double dWave = wavefunctionR(2, 110 const G4double dWave = wavefunctionR(2, r);
112 const G4double sWaveDeriv = derivWavefun 111 const G4double sWaveDeriv = derivWavefunctionR(0, r);
113 const G4double dWaveDeriv = derivWavefun 112 const G4double dWaveDeriv = derivWavefunctionR(2, r);
114 return (sWave*sWaveDeriv + dWave*dWaveDe 113 return (sWave*sWaveDeriv + dWave*dWaveDeriv) / Math::twoPi;
115 } 114 }
116 115
117 G4double densityP(const G4double p) { 116 G4double densityP(const G4double p) {
118 const G4double sWave = wavefunctionP(0, 117 const G4double sWave = wavefunctionP(0, p);
119 const G4double dWave = wavefunctionP(2, 118 const G4double dWave = wavefunctionP(2, p);
120 return p*p*(sWave*sWave + dWave*dWave); 119 return p*p*(sWave*sWave + dWave*dWave);
121 } 120 }
122 121
123 G4double wavefunctionR(const G4int l, cons 122 G4double wavefunctionR(const G4int l, const G4double theR) {
124 // assert(l==0 || l==2); // only s- and d-wave 123 // assert(l==0 || l==2); // only s- and d-waves in a deuteron
125 const G4double r = 2. * std::max(theR, 1 124 const G4double r = 2. * std::max(theR, 1.e-4);
126 125
127 G4double result = 0.; 126 G4double result = 0.;
128 G4double fmr; 127 G4double fmr;
129 128
130 for(G4int i=0; i<coeffTableSize; ++i) { 129 for(G4int i=0; i<coeffTableSize; ++i) {
131 fmr = r * (al+i); 130 fmr = r * (al+i);
132 if(l==0) { // s-wave 131 if(l==0) { // s-wave
133 result += coeff1[i] * std::exp(-fmr) 132 result += coeff1[i] * std::exp(-fmr);
134 } else { // d-wave 133 } else { // d-wave
135 result += coeff2[i] * std::exp(-fmr) 134 result += coeff2[i] * std::exp(-fmr) * (1.+3./fmr+3./(fmr*fmr));
136 } 135 }
137 } 136 }
138 137
139 result *= normalisationR/r; 138 result *= normalisationR/r;
140 return result; 139 return result;
141 } 140 }
142 141
143 G4double derivWavefunctionR(const G4int l, 142 G4double derivWavefunctionR(const G4int l, const G4double theR) {
144 // assert(l==0 || l==2); // only s- and d-wave 143 // assert(l==0 || l==2); // only s- and d-waves in a deuteron
145 const G4double r = 2. * std::max(theR, 1 144 const G4double r = 2. * std::max(theR, 1.e-4);
146 145
147 G4double result = 0.; 146 G4double result = 0.;
148 G4double fmr; 147 G4double fmr;
149 148
150 for(G4int i=0; i<coeffTableSize; ++i) { 149 for(G4int i=0; i<coeffTableSize; ++i) {
151 fmr = r * (al+i); 150 fmr = r * (al+i);
152 if(l==0) { // s-wave 151 if(l==0) { // s-wave
153 result += coeff1[i] * std::exp(-fmr) 152 result += coeff1[i] * std::exp(-fmr) * (fmr + 1.);
154 } else { // d-wave 153 } else { // d-wave
155 result += coeff2[i] * std::exp(-fmr) 154 result += coeff2[i] * std::exp(-fmr) * (fmr + 4. + 9./fmr + 9./(fmr*fmr));
156 } 155 }
157 } 156 }
158 157
159 result *= -normalisationR/(r*r); 158 result *= -normalisationR/(r*r);
160 return result; 159 return result;
161 } 160 }
162 161
163 G4double wavefunctionP(const G4int l, cons 162 G4double wavefunctionP(const G4int l, const G4double theQ) {
164 // assert(l==0 || l==2); // only s- and d-wave 163 // assert(l==0 || l==2); // only s- and d-waves in a deuteron
165 const G4double q = theQ / PhysicalConsta 164 const G4double q = theQ / PhysicalConstants::hc;
166 const G4double q2 = q*q; 165 const G4double q2 = q*q;
167 G4double result=0.; 166 G4double result=0.;
168 G4double fmq, alPlusI; 167 G4double fmq, alPlusI;
169 for(G4int i=0; i<coeffTableSize; ++i) { 168 for(G4int i=0; i<coeffTableSize; ++i) {
170 alPlusI = al+i; 169 alPlusI = al+i;
171 fmq = q2 + alPlusI*alPlusI; 170 fmq = q2 + alPlusI*alPlusI;
172 if(l==0) { // s-wave 171 if(l==0) { // s-wave
173 result += coeff1[i] / fmq; 172 result += coeff1[i] / fmq;
174 } else { // d-wave 173 } else { // d-wave
175 result += coeff2[i] / fmq; 174 result += coeff2[i] / fmq;
176 } 175 }
177 } 176 }
178 177
179 result *= normalisationP; 178 result *= normalisationP;
180 return result; 179 return result;
181 } 180 }
182 181
183 } 182 }
184 183
185 } 184 }
186 185