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*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 in LAB).
*
*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
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