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28 // V.Ivanchenko 26.02.2018
29 //
30
31 #include "G4KalbachCrossSection.hh"
32 #include "G4Exp.hh"
33 #include "G4Pow.hh"
34
35 //from subroutine sigpar of PRECO-2000 by Constance Kalbach Walker
36 // Calculate optical model reaction cross sections
37 // using the empirical parameterization
38 // of Narasimha Murthy, Chaterjee, and Gupta
39 // going over to the geometrical limit at high energy.
40 //
41 // Proton cross sections scaled down with signor for a<100
42 // (appropriate for becchetti-greenlees potential).
43 // p2 reduced and global red'n factor introduced below Bc
44 // Neutron cross sections scaled down with signor for a<40
45 // Scaled up for A>210 (added June '98 to conform with
46 // my published papers)
47 // (appropriate for Mani et al potential)
48 //
49
50 // index: 0-neutron, 1-proton, 2-deuteron, 3-triton, 4-He3, 5-He4
51 // parameters: p0, p1, p2, lambda0, lambda1, mu0, mu1, nu0, nu1, nu2, ra
52
53 static const G4double paramK[6][11] = {
54 // n from mani, melkanoff and iori
55 {-312., 0., 0., 12.10, -11.27, 234.1, 38.26, 1.55, -106.1, 1280.8, 0.0},
56 // p from becchetti and greenlees (but modified with sub-barrier
57 // correction function and p2 changed from -449)
58 {15.72, 9.65, -300., 0.00437,-16.58, 244.7, 0.503, 273.1, -182.4, -1.872, 0.0},
59 // d from o.m. of perey and perey
60 {0.798, 420.3,-1651., 0.00619, -7.54, 583.5, 0.337, 421.8, -474.5, -3.592, 0.8},
61 // t from o.m. of hafele, flynn et al
62 {-21.45,484.7,-1608., 0.0186, -8.9, 686.3, 0.325, 368.9, -522.2, -4.998, 0.8},
63 // 3he from o.m. of gibson et al
64 {-2.88,205.6, -1487.,0.00459,-8.93, 611.2, 0.35 , 473.8, -468.2, -2.225, 0.8},
65 // alpha from huizenga and igo
66 { 10.95,-85.2, 1146., 0.0643,-13.96, 781.2, 0.29, -304.7,-470.0, -8.580, 1.2}
67 };
68
69 G4double G4KalbachCrossSection::ComputePowerParameter(G4int resA, G4int idx)
70 {
71 return G4Pow::GetInstance()->powZ(resA, paramK[idx][6]);
72 }
73
74 G4double
75 G4KalbachCrossSection::ComputeCrossSection(G4double K, G4double cb,
76 G4double resA13, G4double amu1,
77 G4int idx, G4int Z, G4int A,
78 G4int resA)
79 {
80 G4double sig = 0.0;
81 G4double signor = 1.0;
82 G4double lambda, mu, nu;
83 G4double ec = std::min(4.0, 100./(G4double)resA); // in MeV
84 if(0 < Z) { ec = cb; }
85
86 G4double ecsq = ec*ec;
87 G4double elab = K * (A + resA) / G4double(resA);
88
89 if(idx == 0) { // parameterization for neutron
90
91 if(resA < 40) { signor =0.7 + resA*0.0075; }
92 else if(resA > 210) { signor = 1. + (resA-210)*0.004; }
93 lambda = paramK[idx][3]/resA13 + paramK[idx][4];
94 mu = (paramK[idx][5] + paramK[idx][6]*resA13)*resA13;
95 // JMQ 20.11.2008 very low energy behaviour corrected
96 // (problem for A (apprx.)>60) fix for avoiding
97 // neutron xs going to zero at very low energies
98 nu = std::abs((paramK[idx][7]*resA + paramK[idx][8]*resA13)*resA13
99 + paramK[idx][9]);
100
101 } else { // parameterization for charged
102 // proton correction
103 if(idx == 1) {
104 if (resA <= 60) { signor = 0.92; }
105 else if (resA < 100) { signor = 0.8 + resA*0.002; }
106 }
107 lambda = paramK[idx][3]*resA + paramK[idx][4];
108 mu = paramK[idx][5]*amu1;
109 nu = amu1* (paramK[idx][7] + paramK[idx][8]*ec + paramK[idx][9]*ecsq);
110 }
111 /*
112 G4cout << "## idx=" << idx << " K=" << K << " elab=" << elab
113 << " ec=" << ec << " lambda=" << lambda << " mu=" << mu
114 << " nu=" << nu << G4endl;
115 */
116 // threashold cross section
117 if(elab < ec) {
118 G4double p = paramK[idx][0];
119 if(0 < Z) { p += paramK[idx][1]/ec + paramK[idx][2]/ecsq; }
120 G4double a = -2*p*ec + lambda - nu/ecsq;
121 G4double b = p*ecsq + mu + 2*nu/ec;
122 G4double det = a*a - 4*p*b;
123 G4double ecut = (det > 0.0) ? (std::sqrt(det) - a)/(2*p) : -a/(2*p);
124
125 //G4cout << " elab= " << elab << " ecut= " << ecut << " sig= " << sig
126 // << " sig1= " << (p*elab*elab + a*elab + b)*signor << G4endl;
127 // If ecut>0, sig=0 at elab=ecut
128 if(0 == idx) {
129 sig = (lambda*ec + mu + nu/ec)*signor*std::sqrt(elab/ec);
130 } else if(elab >= ecut) {
131 sig = (p*elab*elab + a*elab + b)*signor;
132
133 // extra proton correction
134 if(1 == idx) {
135 // c and w are for global correction factor for
136 // they are scaled down for light targets where ec is low.
137 G4double cc = std::min(3.15, ec*0.5);
138 G4double signor2 = (ec - elab - cc) *3.15/ (0.7*cc);
139 sig /= (1. + G4Exp(signor2));
140 }
141 }
142 //G4cout << " ecut= " << ecut << " a= " << a << " b= " << b
143 // << " signor= " << signor << " sig= " << sig << G4endl;
144
145 // high energy cross section
146 } else {
147 // etest is the energy above which the rxn cross section is
148 // compared with the geometrical limit and the max taken.
149
150 // neutron parameters
151 G4double etest = 32.;
152 G4double xnulam = 1.0;
153
154 // parameters for charged
155 static const G4double flow = 1.e-18;
156 static const G4double spill= 1.e+18;
157 if(0 < Z) {
158 etest = 0.0;
159 xnulam = nu / lambda;
160 xnulam = std::min(xnulam, spill);
161 if (xnulam >= flow) {
162 if(1 == idx) { etest = std::sqrt(xnulam) + 7.; }
163 else { etest = 1.2 *std::sqrt(xnulam); }
164 }
165 }
166 // ** For xnulam.gt.0, sig reaches a maximum at sqrt(xnulam).
167 sig = (lambda*elab + mu + nu/elab)*signor;
168 if (xnulam >= flow && elab >= etest) {
169 G4double geom = std::sqrt(A*K);
170 geom = 1.23*resA13 + paramK[idx][10] + 4.573/geom;
171 geom = 31.416 * geom * geom;
172 sig = std::max(sig, geom);
173 }
174 }
175 sig = std::max(sig, 0.0);
176 //G4cout << " ---- sig= " << sig << G4endl;
177 return sig;
178 }
179