1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
|
*DECK LIBPRI
SUBROUTINE LIBPRI(MAXTRA,DELI,AWR,IALTER,IL,N,PRI)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Compute the PRI array for various Legendre orders using Gaussian
* integration.
*
*Copyright:
* Copyright (C) 2003 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): A. Hebert
*
*Parameters: input
* MAXTRA allocated dimension of array PRI.
* DELI elementary lethargy width of the equi-width lethargy mesh.
* AWR mass ratio for current isotope.
* IALTER type of approximation (=0: use exponentials; =1: use Taylor
* expansions).
* IL Legendre order (=0: isotropic kernel).
*
*Parameters: output
* N exact dimension of array PRI.
* PRI array containing the slowing-down probabilities defined on
* an equi-width lethargy mesh.
*
*Reference:
* M. Grandotto-Biettoli, "AUTOSECOL, un calcul automatique de
* l'auto-protection des resonances des isotopes lourds,"
* Note CEA-N-1961, Commissariat a l'Energie Atomique, 1977.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER MAXTRA,IALTER,IL,N
REAL DELI,AWR,PRI(MAXTRA)
*----
* LOCAL VARIABLES
*----
PARAMETER(NGPT=6,MAXNL=50)
DOUBLE PRECISION AWRB,ALP,T0,FACT
REAL UI(NGPT),WI(NGPT),UJ(NGPT),WJ(NGPT)
REAL POLY(0:MAXNL),CALC(0:MAXNL,0:2)
CHARACTER HSMG*131
ZMU(AWR,U)=0.5*(AWR+1.0)*EXP(-0.5*U)-0.5*(AWR-1.0)*EXP(0.5*U)
*----
* COMPUTE THE LEGENDRE POLYNOMIAL OF ORDER IL.
*----
IF(IL.GT.MAXNL) CALL XABORT('LIBPRI: IL OVERFLOW.')
IF(IL.EQ.0) THEN
POLY(0)=1.0
ELSE IF(IL.EQ.1) THEN
POLY(0)=0.0
POLY(1)=1.0
ELSE
CALC(0:MAXNL,0:1)=0.0
CALC(0,0)=1.0
CALC(1,1)=1.0
DO 15 J=2,IL
DO 10 I=0,IL
T0=-REAL(J-1)*CALC(I,MOD(J-2,3))
IF(I.GT.0) T0=T0+(2.0*REAL(J-1)+1.0)*CALC(I-1,MOD(J-1,3))
CALC(I,MOD(J,3))=REAL(T0)/REAL(J)
10 CONTINUE
15 CONTINUE
DO 20 I=0,IL
POLY(I)=CALC(I,MOD(IL,3))
20 CONTINUE
ENDIF
*
AWRB=AWR
IF(AWR.LT.1.0001) AWRB=1.0001
ALP=((AWRB-1.D0)/(AWRB+1.D0))**2
REPS=REAL(-DLOG(ALP))
N=INT(REPS/DELI)
IF(N+2.GT.MAXTRA) THEN
WRITE(HSMG,'(25HLIBPRI: MAXTRA OVERFLOW (,I8,2H >,I8,2H).)')
1 N+2,MAXTRA
CALL XABORT(HSMG)
ENDIF
*
IF(N.EQ.0) THEN
* COMPUTE PRI(1).
PRI(1)=0.0
CALL ALGPT(NGPT,0.0,DELI-REPS,UI,WI)
DO 41 I=1,NGPT
CALL ALGPT(NGPT,UI(I),UI(I)+REPS,UJ,WJ)
DO 40 J=1,NGPT
FACT=POLY(0)
T0=1.0D0
DO 30 K=1,IL
T0=T0*ZMU(AWR,UJ(J)-UI(I))
FACT=FACT+POLY(K)*T0
30 CONTINUE
IF(IALTER.EQ.0) THEN
PRI(1)=PRI(1)+WI(I)*WJ(J)*EXP(UI(I)-UJ(J))*REAL(FACT)
ELSE
PRI(1)=PRI(1)+WI(I)*WJ(J)*REAL(FACT)
ENDIF
40 CONTINUE
41 CONTINUE
CALL ALGPT(NGPT,DELI-REPS,DELI,UI,WI)
DO 51 I=1,NGPT
CALL ALGPT(NGPT,UI(I),DELI,UJ,WJ)
DO 50 J=1,NGPT
FACT=POLY(0)
T0=1.0D0
DO 45 K=1,IL
T0=T0*ZMU(AWR,UJ(J)-UI(I))
FACT=FACT+POLY(K)*T0
45 CONTINUE
IF(IALTER.EQ.0) THEN
PRI(1)=PRI(1)+WI(I)*WJ(J)*EXP(UI(I)-UJ(J))*REAL(FACT)
ELSE
PRI(1)=PRI(1)+WI(I)*WJ(J)*REAL(FACT)
ENDIF
50 CONTINUE
51 CONTINUE
*
* COMPUTE PRI(2).
PRI(2)=0.0
CALL ALGPT(NGPT,DELI-REPS,DELI,UI,WI)
DO 61 I=1,NGPT
CALL ALGPT(NGPT,DELI,UI(I)+REPS,UJ,WJ)
DO 60 J=1,NGPT
FACT=POLY(0)
T0=1.0D0
DO 55 K=1,IL
T0=T0*ZMU(AWR,UJ(J)-UI(I))
FACT=FACT+POLY(K)*T0
55 CONTINUE
IF(IALTER.EQ.0) THEN
PRI(2)=PRI(2)+WI(I)*WJ(J)*EXP(UI(I)-UJ(J))*REAL(FACT)
ELSE
PRI(2)=PRI(2)+WI(I)*WJ(J)*REAL(FACT)
ENDIF
60 CONTINUE
61 CONTINUE
ELSE
* COMPUTE PRI(1).
PRI(1)=0.0
CALL ALGPT(NGPT,0.0,DELI,UI,WI)
DO 71 I=1,NGPT
CALL ALGPT(NGPT,REAL(UI(I)),DELI,UJ,WJ)
DO 70 J=1,NGPT
FACT=POLY(0)
T0=1.0D0
DO 65 K=1,IL
T0=T0*ZMU(AWR,UJ(J)-UI(I))
FACT=FACT+POLY(K)*T0
65 CONTINUE
IF(IALTER.EQ.0) THEN
PRI(1)=PRI(1)+WI(I)*WJ(J)*EXP(UI(I)-UJ(J))*REAL(FACT)
ELSE
PRI(1)=PRI(1)+WI(I)*WJ(J)*REAL(FACT)
ENDIF
70 CONTINUE
71 CONTINUE
*
* COMPUTE PRI(L) FOR L=2,N.
CALL ALGPT(NGPT,0.0,DELI,UI,WI)
DO 82 L=2,N
PRI(L)=0.0
DO 81 I=1,NGPT
CALL ALGPT(NGPT,REAL(L-1)*DELI,REAL(L)*DELI,UJ,WJ)
DO 80 J=1,NGPT
FACT=POLY(0)
T0=1.0D0
DO 75 K=1,IL
T0=T0*ZMU(AWR,UJ(J)-UI(I))
FACT=FACT+POLY(K)*T0
75 CONTINUE
IF(IALTER.EQ.0) THEN
PRI(L)=PRI(L)+WI(I)*WJ(J)*EXP(UI(I)-UJ(J))*REAL(FACT)
ELSE
PRI(L)=PRI(L)+WI(I)*WJ(J)*REAL(FACT)
ENDIF
80 CONTINUE
81 CONTINUE
82 CONTINUE
*
* COMPUTE PRI(N+1).
PRI(N+1)=0.0
CALL ALGPT(NGPT,0.0,REAL(N+1)*DELI-REPS,UI,WI)
DO 91 I=1,NGPT
CALL ALGPT(NGPT,REAL(N)*DELI,UI(I)+REPS,UJ,WJ)
DO 90 J=1,NGPT
FACT=POLY(0)
T0=1.0D0
DO 85 K=1,IL
T0=T0*ZMU(AWR,UJ(J)-UI(I))
FACT=FACT+POLY(K)*T0
85 CONTINUE
IF(IALTER.EQ.0) THEN
PRI(N+1)=PRI(N+1)+WI(I)*WJ(J)*EXP(UI(I)-UJ(J))*REAL(FACT)
ELSE
PRI(N+1)=PRI(N+1)+WI(I)*WJ(J)*REAL(FACT)
ENDIF
90 CONTINUE
91 CONTINUE
CALL ALGPT(NGPT,REAL(N+1)*DELI-REPS,DELI,UI,WI)
DO 101 I=1,NGPT
CALL ALGPT(NGPT,REAL(N)*DELI,REAL(N+1)*DELI,UJ,WJ)
DO 100 J=1,NGPT
FACT=POLY(0)
T0=1.0D0
DO 95 K=1,IL
T0=T0*ZMU(AWR,UJ(J)-UI(I))
FACT=FACT+POLY(K)*T0
95 CONTINUE
IF(IALTER.EQ.0) THEN
PRI(N+1)=PRI(N+1)+WI(I)*WJ(J)*EXP(UI(I)-UJ(J))*REAL(FACT)
ELSE
PRI(N+1)=PRI(N+1)+WI(I)*WJ(J)*REAL(FACT)
ENDIF
100 CONTINUE
101 CONTINUE
*
* COMPUTE PRI(N+2).
PRI(N+2)=0.0
CALL ALGPT(NGPT,REAL(N+1)*DELI-REPS,DELI,UI,WI)
DO 111 I=1,NGPT
CALL ALGPT(NGPT,REAL(N+1)*DELI,UI(I)+REPS,UJ,WJ)
DO 110 J=1,NGPT
FACT=POLY(0)
T0=1.0D0
DO 105 K=1,IL
T0=T0*ZMU(AWR,UJ(J)-UI(I))
FACT=FACT+POLY(K)*T0
105 CONTINUE
IF(IALTER.EQ.0) THEN
PRI(N+2)=PRI(N+2)+WI(I)*WJ(J)*EXP(UI(I)-UJ(J))*REAL(FACT)
ELSE
PRI(N+2)=PRI(N+2)+WI(I)*WJ(J)*REAL(FACT)
ENDIF
110 CONTINUE
111 CONTINUE
ENDIF
N=N+2
IF(IALTER.EQ.0) THEN
DO 120 I=1,N
PRI(I)=PRI(I)/DELI/REAL(1.0D0-ALP)
120 CONTINUE
ELSE
DO 130 I=1,N
PRI(I)=PRI(I)/DELI/REPS
130 CONTINUE
ENDIF
RETURN
END
|
