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