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fun.f95
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MODULE modulo
!***********************************************************************************************
!* This module contains all functions and subroutines for frescoPRC tool: *
!* *
!* Subroutine CLEBSCH: Compute C-G coefficients *
!* *
!* Subroutine wigner: Compute matrix element of Wigner's functions accoding to B.14 and B.19 *
!* from PRC 94 6 (2016), 064605 (even and odd nuclei). *
!* *
!* Dispersive functions pack: Calculation of Analytical dispersive integrals. *
!* *
!* Subroutine FORMFACT: Numerical calculation of form factors using *
!* Gauss-Legendre quadrature. Those form factors are part of *
!* FRESCO's input [fort.4]. *
!* *
!* Subroutine steps: Build the couplings between G.S band and excited bands for *
!* even and odd nuclei according to equations B.12 and B.16 from *
!* PRC 94 6 (2016), 064605. * *
!***********************************************************************************************
CONTAINS
SUBROUTINE CLEBSCH(AJ,BJ,CJ,AM,BM,CM,CG)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION Q(100,100)
DOUBLE PRECISION CG
DOUBLE PRECISION AJ,BJ,CJ,AM,BM,CM
INTEGER ZZ
ZZ=MAX(2*AJ+1,2*BJ+1,2*CJ+1,AJ+BJ+CJ,AJ+AM,BJ+BM,CJ+CM)+2
DO 2 I=1,ZZ
Q(I,1)=1.d0
Q(I,I)=1.d0
2 CONTINUE
DO 3 I=2,ZZ-1
DO 3 K=2,I
Q(I+1,K)=Q(I,K-1)+Q(I,K)
3 CONTINUE
CG=0.d0
JA=AJ+AM+1.01d0
MA=AJ-AM+1.01d0
JB=BJ+BM+1.01d0
MB=BJ-BM+1.01d0
JC=CJ+CM+1.01d0
MC=CJ-CM+1.01d0
LA=BJ+CJ-AJ+1.01d0
LB=CJ+AJ-BJ+1.01d0
LC=AJ+BJ-CJ+1.01d0
LT=AJ+BJ+CJ+1.01d0
D=DABS(AM+BM-CM)-0.01d0
IF (D) 10,10,20
10 LD=MIN0(JA,JB,JC,MA,MB,MC,LA,LB,LC)
IF (LD) 20,20,30
30 JA2=AJ+AJ+AM+AM
JB2=BJ+BJ+BM+BM
JC2=CJ+CJ-CM-CM
I2=JA2+JB2+JC2-JA2/2*2-JB2/2*2-JC2/2*2
IF (I2) 20,40,20
40 FN=Q(JA+MA-1,LC)/Q(LT,JC+MC-1)
FN=FN*Q(JB+MB-1,LC)/Q(LT+1,2)
FN=FN/Q(JA+MA-1,JA)
FN=FN/Q(JB+MB-1,JB)
FN=FN/Q(JC+MC-1,JC)
K0=MAX(0,LC-JA,LC-MB)+1
K1=MIN(LC,MA,JB)
X=0.d0
DO 50 K=K0,K1
X=-X-Q(LC,K)*Q(LB,MA-K+1)*Q(LA,JB-K+1)
50 CONTINUE
IP=K1+LB+JC
P=1-2*(IP-IP/2*2)
CG=P*X*DSQRT(FN)
CG=CG*DSQRT(2*CJ+1)*(-1)**IDNINT(AJ-BJ-CM)
20 CONTINUE
RETURN
END SUBROUTINE CLEBSCH
SUBROUTINE wigner_even(J1_val,J2_val,K1_val,K2_val,lamd_val,l1,l2, &
reduced_matriz_element)
DOUBLE PRECISION CG(4)
DOUBLE PRECISION reduced_matriz_element
REAL J1_val,J2_val,lamd_val
INTEGER K1_val,K2_val,l1,l2
INTEGER delta, factor,mu
DOUBLE PRECISION f1
INTEGER f2
IF (K2_val==0) THEN
delta=1
ELSE
delta=0
ENDIF
IF (K1_val==0) THEN
delta1=1
ELSE
delta1=0
ENDIF
IF (K2_val==2 .OR. K1_val==2) THEN
mu=2; factor=1
ELSE
mu=0; factor=2
ENDIF
CALL CLEBSCH(DBLE(J2_val),DBLE(lamd_val),DBLE(J1_val),DBLE(K2_val), &
DBLE(mu),DBLE(K1_val),CG(1))
CALL CLEBSCH(DBLE(J2_val),DBLE(lamd_val),DBLE(J1_val),-1d0*DBLE(K2_val), &
DBLE(mu),DBLE(K1_val),CG(2))
CALL CLEBSCH(DBLE(J2_val),DBLE(lamd_val),DBLE(J1_val),DBLE(K2_val), &
DBLE(mu),-1d0*DBLE(K1_val),CG(3))
CALL CLEBSCH(DBLE(J2_val),DBLE(lamd_val),DBLE(J1_val),-1d0*DBLE(K2_val), &
DBLE(mu),-1d0*DBLE(K1_val),CG(4))
f1= DSQRT(2*DBLE(J2_val)+1d0)/(DSQRT((1d0+DBLE(delta1))*(1d0+DBLE(delta))))
f2= (1+(-1)**(lamd_val+K2_val+l1+l2))/2
reduced_matriz_element=f1*f2*(CG(1) + ((-1)**(J2_val+l2))*CG(2) + &
((-1)**(J1_val+l1))*CG(3) + ((-1)**(J1_val+J2_val+l1+l2))*CG(4))
reduced_matriz_element=reduced_matriz_element/factor
END SUBROUTINE wigner_even
SUBROUTINE wigner_odd(J1_val,J2_val,K1_val,K2_val,lamd_val,l1,l2, &
reduced_matriz_element)
DOUBLE PRECISION CG(4)
DOUBLE PRECISION reduced_matriz_element
REAL J1_val,J2_val,lamd_val
REAL K1_val,K2_val
REAL TOL
INTEGER delta, factor,mu,l1,l2
DOUBLE PRECISION f1
INTEGER f2,par1,par2
TOL=1E-07 !!
IF (ABS(K1_val-K2_val) .LT. TOL) THEN
mu=0; factor=2
ELSE
mu=2; factor=1
ENDIF
par1=l1/ABS(l1)
par2=l2/ABS(l2)
f1= DSQRT(2*DBLE(J2_val)+1d0)
f2= (1+((-1)**(lamd_val))*par1*par2)/2
CALL CLEBSCH(DBLE(J2_val),DBLE(lamd_val),DBLE(J1_val),DBLE(K2_val), &
DBLE(mu),DBLE(K1_val),CG(1))
CALL CLEBSCH(DBLE(J2_val),DBLE(lamd_val),DBLE(J1_val),-1d0*DBLE(K2_val), &
DBLE(mu),DBLE(K1_val),CG(2))
CALL CLEBSCH(DBLE(J2_val),DBLE(lamd_val),DBLE(J1_val),DBLE(K2_val), &
DBLE(mu),-1d0*DBLE(K1_val),CG(3))
CALL CLEBSCH(DBLE(J2_val),DBLE(lamd_val),DBLE(J1_val),-1d0*DBLE(K2_val), &
DBLE(mu),-1d0*DBLE(K1_val),CG(4))
reduced_matriz_element=f1*f2*(CG(1) + ((-1)**(NINT(J2_val-0.5)))*par2*CG(2) &
+ ((-1)**(NINT(J1_val-0.5)))*par1*CG(3) + &
((-1)**(NINT(J2_val+J1_val-1)))*par2*par1*CG(4))
reduced_matriz_element=reduced_matriz_element/factor
END SUBROUTINE wigner_odd
! *******************************************************
! START of dispersive PACK
! *******************************************************
!==========================================================================
! AUTHOR: Dr. Roberto Capote Noy
!
! e-mail: [email protected] ; [email protected];
!
! DISPERSIVE OPTICAL MODEL POTENTIAL PACKAGE
!
! Analytical dispersive integrals are included
! see Quesada JM, Capote R et al,
! Computer Physics Communications 153(2003) 97
! Phys. Rev. C67(2003) 067601
!
! Dispersive integral's derivatives calculated by Dr.J.M.Quesada
!
REAL FUNCTION DOM_INT_Wv (Ef,Ep,Av,Bv,n,Einc,DerivIntWv)
IMPLICIT NONE
REAL Ef,Ep,Av,Bv,E,pi,Einc
REAL E0,Ex,Eplus,Emin,Rs,ResEmin,ResEplus
REAL DerEmin, DerEplus, Rds, DerivIntWv
DOUBLE COMPLEX Pj,I,Zj,Ztmp
DOUBLE COMPLEX Fs,Ds
INTEGER N,j,IS
DATA I/(0.d0,1.d0)/
pi=4.d0*atan(1.d0)
IS = 1
E = Einc
IF(Einc.LE.Ef) THEN
E=2.d0*Ef-Einc
IS = -1
ENDIF
E0 = Ep - Ef
Ex = E - Ef
Eplus = Ex + E0
Emin = Ex - E0
DOM_INT_Wv = 0.d0
DerivIntWv = 0.d0
ResEmin = Emin**n / (Emin**n + Bv**n)
DerEmin = Emin**(n-1)* &
( Emin**n + Bv**n*(1.d0 + n*log(ABS(Emin)) ) ) &
/ (Emin**n + Bv**n)**2
ResEplus = -Eplus**n / (Eplus**n + Bv**n)
DerEplus = -Eplus**(n-1) * &
( Eplus**n + Bv**n*(1.d0+n*log(Eplus)) ) &
/ (Eplus**n + Bv**n)**2
Fs = (0.d0,0.d0)
Ds = (0.d0,0.d0)
DO j=1,n
Ztmp = I*(2*j-1)/dble(n)*pi
Pj = Bv*exp(Ztmp)
Zj = Pj * (2*Pj +Eplus -Emin) * Ex
Zj = Zj / ( (Pj+E0) * (Pj+Eplus) * (Pj-Emin) )
Fs = Fs + Zj*log(-Pj)
Ds = Ds + 2*Pj*(Ex*Ex + (Pj+E0)**2)*log(-Pj) &
/( (Pj+Eplus)**2 * (Pj-Emin)**2 )
ENDDO
IF(ABS(IMAG(Fs)).gt.1.d-4) STOP 'Too big imag part in Wv'
IF(ABS(IMAG(Ds)).gt.1.d-4) STOP 'Too big imag deriv in Wv'
Rs = REAL(Fs)
Rds = REAL(Ds)
DOM_INT_Wv = -Av/pi*IS* &
(Rs/n + ResEplus*log(Eplus) + ResEmin*log(ABS(Emin)))
DerivIntWv = Av/pi*IS*( Rds/n + DerEplus + DerEmin)
RETURN
END FUNCTION DOM_INT_Wv
REAL FUNCTION DOM_INT_Ws (Ef,Ep,As,Bs,Cs,m,Einc,DerivIntWs)
IMPLICIT NONE
REAL Ef,Ep,As,Bs,Cs,E,Einc
DOUBLE COMPLEX I,Pj,Zj,Ztmp
REAL E0,Ex,pi
REAL Rs,ResEmin,ResEplus
REAL DerivIntWs,DerEmin,DerEplus,Rds
INTEGER m,j,IS
DOUBLE COMPLEX Fs,Ds
REAL*8 Emin,Eplus
DATA I/(0.d0,1.d0)/
pi=4.d0*atan(1.d0)
IS = 1
E = Einc
IF(Einc.LE.Ef) THEN
E=2.d0*Ef-Einc
IS = -1
ENDIF
E0 = Ep - Ef
Ex = E - Ef
Eplus = Ex + E0
Emin = Ex - E0
DOM_INT_Ws = 0.d0
DerivIntWs = 0.d0
ResEmin = Emin**m / (Emin**m + Bs**m)
DerEmin = -Emin**(m-1) * &
( Emin**m + Bs**m + ( -Cs*Emin**(m+1) + &
Bs**m *(-Cs*Emin+m) ) * exp(-Cs*Emin)*EIn(Cs*Emin) ) &
/ (Emin**m + Bs**m)**2
ResEplus = -Eplus**m / (Eplus**m + Bs**m)
DerEplus = Eplus**(m-1) * &
( Eplus**m + Bs**m + ( Cs*Eplus**(m+1) + &
Bs**m *(Cs*Eplus+m) ) * exp(Cs*Eplus)*EIn(-Cs*Eplus) ) &
/ (Eplus**m + Bs**m)**2
Fs = (0.d0,0.d0)
Ds = (0.d0,0.d0)
DO j=1,m
Ztmp = I*(2*j-1)/dble(m)*pi
Pj = Bs*exp(Ztmp)
Zj = Pj * (2*Pj +Eplus -Emin) * Ex
Zj = Zj / (Pj+E0) / (Pj+Eplus) / (Pj-Emin)
Fs = Fs + Zj* zfi(-Pj*Cs)
Ds = Ds + 2*Pj*(Ex*Ex + (Pj+E0)**2)*zfi(-Pj*Cs) &
/( (Pj+Eplus)**2 * (Pj-Emin)**2 )
ENDDO
IF(ABS(IMAG(Fs)).GT.1.d-4) STOP 'Too big imag part in Ws'
IF(ABS(IMAG(Ds)).GT.1.d-4) STOP 'Too big imag deriv in Ws'
Rs = REAL(Fs)
Rds = REAL(Ds)
DOM_INT_Ws = As/pi*IS*(Rs/m &
- ResEplus*exp(Cs*Eplus)*EIn(-Cs*Eplus) &
- ResEmin*exp(-Cs*Emin)*EIn(Cs*Emin) )
RETURN
END FUNCTION DOM_INT_Ws
REAL FUNCTION WV(A,B,Ep,Ef,E,n)
IMPLICIT NONE
REAL A,B,Ep,Ef,E,ee
INTEGER n
WV=0.d0
IF(E.LE.Ef) E=2.d0*Ef-E
IF(E.LT.Ep) RETURN
ee=(E-Ep)**n
WV=A*ee/(ee+B**n)
RETURN
END FUNCTION WV
REAL FUNCTION WDD(A,B,C,Ep,Ef,E,m)
IMPLICIT NONE
REAL A,B,C,Ep,Ef,E,ee,arg
INTEGER m
WDD=0.d0
IF(E.LE.Ef) E=2.d0*Ef-E
IF(E.LT.Ep) RETURN
arg=C*(E-Ep)
IF(arg.GT.15) RETURN
ee=(E-Ep)**m
WDD=A*ee/(ee+B**m)*EXP(-arg)
RETURN
END FUNCTION WDD
REAL FUNCTION DOM_int_T1(Ef,Ea,E)
IMPLICIT NONE
REAL E,Ea,Ef,Ex,Ea2,Eax,Pi,T11,T12,T13
Pi=4.d0*ATAN(1.d0)
Ex=E-Ef
Ea2=Ea**2
Eax=Ex+Ea
T11 = 0.5d0*log(Ea)/Ex
T12 = ( (2*Ea+Ex)*log(Ea)+0.5d0*pi*Ex ) &
/(2.*(Eax**2 + Ea2))
T13 = -Eax**2*log(Eax)/(Ex*(Eax**2+Ea2))
DOM_int_T1 = Ex/Pi*(T11+T12+T13)
RETURN
END FUNCTION DOM_int_T1
REAL FUNCTION DOM_int_T2(Ef,Ea,E)
IMPLICIT NONE
REAL E,Ea,Ef,EL,Pi
Pi=4.d0*ATAN(1.d0)
EL=Ef+Ea
DOM_int_T2= 1.d0 / Pi * ( &
sqrt(abs(Ef)) * atan( (2*sqrt(EL*abs(Ef)))/(EL-abs(Ef)) ) &
+ EL**1.5d0/(2*Ef)*log(Ea/EL) )
IF(E.GT.EL) THEN
DOM_int_T2 = DOM_int_T2 + 1.d0/Pi* ( &
sqrt(E) * log( (sqrt(E)+sqrt(EL)) / (sqrt(E)-sqrt(EL)) ) + &
1.5d0*sqrt(EL)*log((E-EL)/Ea) + EL**1.5d0/(2*E)*log(EL/(E-EL)) )
ELSEIF(E.EQ.EL) THEN
DOM_int_T2 = DOM_int_T2 + 1.d0/Pi*1.5d0*sqrt(EL) &
*log((2**(4.d0/3.d0)*EL)/Ea)
ELSEIF(E.GT.0.d0 .AND. E.LE.EL) THEN
DOM_int_T2 = DOM_int_T2 + 1.d0/Pi * ( &
sqrt(e) * log( (sqrt(E)+sqrt(EL)) / (sqrt(EL)-sqrt(E)) ) + &
1.5d0*sqrt(EL)*log((EL-E)/Ea)+EL**1.5d0/(2.d0*E)*log(EL/(EL-E)) )
ELSEIF(abs(E)<1e-10) then
DOM_int_T2 = DOM_int_T2 + 1.d0/Pi*( 1.5*sqrt(EL) &
* log(EL/Ea) + 0.5d0*sqrt(EL) )
ELSE
DOM_int_T2 = DOM_int_T2 + 1.d0/Pi * ( &
-sqrt(abs(E))*atan( 2*(sqrt(EL*abs(E))) / (EL-abs(E)) ) + &
1.5d0*sqrt(EL)*log((EL-E)/Ea)+EL**1.5d0/(2.d0*E)*log(EL/(EL-E)) )
ENDIF
!write(101,*) E,DOM_int_T2,Ef,Ea
RETURN
END FUNCTION DOM_int_T2
DOUBLE COMPLEX FUNCTION zfi(za)
IMPLICIT NONE
REAL aj
DOUBLE COMPLEX za,y
INTEGER m,i
zfi=0.d0
IF (za.EQ.0.d0) RETURN
IF (abs(real(za)+18.5d0).GE.25.d0) GO TO 3
IF (SQRT(625.d0-(REAL(za)+18.5d0)**2)/1.665d0.LT.ABS(imag(za))) GO TO 3
zfi=-.57721566490153d0-log(za)
y=1.d0
DO 1 m=1,2000
aj=m
y=-y*za/aj
IF (ABS(y).lt.1.d-15*ABS(zfi)) GO TO 2
1 zfi=zfi-y/aj
2 zfi=EXP(za)*zfi
RETURN
3 DO 4 i=1,20
aj=21-i
zfi=aj/(za+zfi)
4 zfi=aj/(1.d0+zfi)
zfi=1.d0/(zfi+za)
RETURN
END FUNCTION zfi
REAL*8 FUNCTION EIn(X)
IMPLICIT NONE
REAL*8 FAC, H, X
INTEGER N
EIn = 0.57721566490153d0+LOG(ABS(X))
FAC = 1.0
DO N = 1,100
H = FLOAT(N)
FAC = FAC*H
EIn = EIn + X**N/(H*FAC)
ENDDO
RETURN
END FUNCTION EIn
SUBROUTINE dispers2(A,Z,k,eopt, &
v,rvv,avv, dv,drv,dav, dvs,drs,das, w,rw,aw, wd,rwd,awd, &
vso,rvso,avso,dvso, wso,rwso,awso, &
Vlin,Vdep,lambdaHF,Cviso,Vso0,lambdaso,Ccoul, &
AAv,BBv,W0,BBs,CCs,Cwiso,Wso0,BBso, &
Ea,alpha,eferm,Ades, &
rHFl,rHFdep,aHFl,aHFdep,rv,avl,avdep, &
rsl,rsdep,as, &
rso,aso,rc,ac)
REAL eopt,asym,eferm,f,Cviso,viso,Ccoul,Cwiso
REAL lambdaHF,lambdaso,Ades
pi = 4.0*atan(1.)
!
! *** Parameters of Soukhovitskii, Capote, Quesada, Chiba and Martyanov (Nov 25, 2015) ***
! *** with Asymmetrical W energy-dependence
! *** dispers2: T1 integral with correct coefficient
! *** done by Ian Thompson
! k : designator for particle
! Z : charge number of residual nucleus
! A : mass number of residual nucleus
! eopt : incident energy
! asym : asymmetry parameter
! eferm : Fermi energy
! f : eopt-eferm
Au = A-Ades
asym=(A-2.*Z)/A
V0 = Vlin + Vdep*Au
rHF = rHFL + rHFdep * Au
aHF = aHFl + aHFdep * Au
av = avl + avdep * Au
rs = rsl + rsdep * Au
AAHF = V0 * (1 + (-1)**k * Cviso*asym/V0)
AAs = W0 * (1 + (-1)**k * Cwiso*asym/W0)
eoffset = 0.
IF (k==2) eoffset = Ccoul * Z/A**(1./3.)
Eeff = eopt - eoffset
f = Eeff - eferm
v = AAHF * EXP(-lambdaHF*f)
vso=Vso0*EXP(-lambdaso*f)
! sources of dispersive terms
w = AAv * f*f/(f*f + BBv**2)
IF(f < -Ea) THEN
fe = f + Ea
w = w * (1 - fe*fe/(fe*fe + Ea*Ea))
ELSE IF(f>Ea) THEN
w = w + alpha * (SQRT(Eeff) + (eferm+Ea)**1.5d0/(2*Eeff) &
- 1.5d0*SQRT(eferm+Ea))
endif
wd = AAs * f*f/(f*f + BBs**2) * EXP( -CCs * ABS(f))
wso=Wso0* f*f/(f*f + BBso**2)
! dispersive terms to add for real volume and real surface forms
drv= rv; dav = av
drs = rs; das = as
dvs = DOM_INT_Ws (eferm,eferm,AAs,BBs,CCs,2,Eeff,DerivIntWs)
DWv = DOM_INT_Wv (eferm,eferm,AAv,BBv,2,Eeff,DerivIntWv)
T1 = DOM_int_T1(eferm,Ea,Eeff) * AAv * Ea*Ea/(Ea*Ea + BBv**2)
T2 = DOM_int_T2(eferm,Ea,Eeff) * alpha
dv = DWv + T1 + T2
dvso = DOM_INT_Wv (eferm,eferm,Wso0,BBso,2,Eeff,DerivIntWv)
! name translations
rvv = rHF ; avv = aHF
rvso = rso; avso = aso
rwso = rso; awso = aso
rw = rv ; aw = av
rwd = rs ; awd = as
RETURN
END SUBROUTINE dispers2
! ***********************************************************
! * END of dispersive *
! ***********************************************************
!----------------------------------------------------------------------------
! **************************************************************************
! * *
! * Numerical calculation of form factors using Gauss-Legendre quadrature *
! * *
! **************************************************************************
! - Form factors calculated for volume and surface terms with axial deformations up to beta_{60}.
! - Additional 1/sqrt(4*pi) factor added to match FRESCO's convention.
! - Output (extension .form) prepared to be used as FRESCO's external forms input [fort.4].
DOUBLE PRECISION FUNCTION arm(x,L)
DOUBLE PRECISION x,P(0:L),pi
INTEGER L,i
pi=ACOS(-1d0)
IF(L==0) THEN
arm=DSQRT(1.d0/(4d0*pi))
ENDIF
IF(L==1) THEN
arm=DSQRT(3.d0/(4d0*pi))*x
ENDIF
IF(L.GE.2) THEN
P(0)=1d0
P(1)=x
DO i=2,L,1
P(i)=((2d0*DBLE(i)-1d0)*x*P(i-1) - DBLE(i-1)*P(i-2))/(DBLE(i))
END DO
arm=dsqrt((2d0*DBLE(L)+1d0)/(4d0*pi))*P(L)
ENDIF
RETURN
END FUNCTION arm
DOUBLE PRECISION FUNCTION rdef(R,x,BETA2,BETA4,BETA6)
REAL R,BETA2,BETA4,BETA6
DOUBLE PRECISION x
rdef=DBLE(R)*(1d0+DBLE(BETA2)*arm(x,2)+DBLE(BETA4)*arm(x,4)+DBLE(BETA6)*arm(x,6))
RETURN
END FUNCTION rdef
DOUBLE PRECISION FUNCTION vws(r,v0,RR,a,x,L,BETA2,BETA4,BETA6)
REAL r,v0,RR,a,BETA2,BETA4,BETA6
DOUBLE PRECISION x
INTEGER L
vws=(DBLE(v0)/(1d0+EXP((DBLE(r)-rdef(RR,x,BETA2,BETA4,BETA6))/DBLE(a))))*arm(x,L)
RETURN
END FUNCTION vws
DOUBLE PRECISION FUNCTION vs(r,v0,RR,a,x,L,BETA2,BETA4,BETA6)
REAL r,v0,RR,a,BETA2,BETA4,BETA6
DOUBLE PRECISION x,f
INTEGER L
f=EXP((DBLE(r)-rdef(RR,x,BETA2,BETA4,BETA6))/DBLE(a))
vs=-4d0*DBLE(v0)*arm(x,L)*f/(1+f)**2
RETURN
END FUNCTION vs
DOUBLE PRECISION FUNCTION gaussv(r,v0,RR,a,L,BETA2,BETA4,BETA6)
REAL r,v0,RR,a,x(19),w(19),BETA2,BETA4,BETA6
DOUBLE PRECISION pp,pi,p
INTEGER j,L
pi=ACOS(-1d0)
x(1:10)=(/-.992407,-.960208,-.903156,-.822715,-.720966, &
-.600545,-.464571,-.316564,-.160359,0.0/)
w(1:10)=(/.0194618,.0448182,.0690445,.09149,.111567,.128754, &
.142607,.152766,.158969,.161054/)
DO i=1,9,1
x(10+i)=-x(10-i)
w(10+i)=w(10-i)
END DO
p=0d0
DO j=1,19,1
p=p+DBLE(w(j))*vws(r,v0,RR,a,DBLE(x(j)),L,BETA2,BETA4,BETA6)
END DO
gaussv=DSQRT(pi)*p !Factor required by FRESCO's convention.
RETURN
END FUNCTION gaussv
DOUBLE PRECISION FUNCTION gausss(r,v0,RR,a,L,BETA2,BETA4,BETA6)
REAL r,v0,RR,a,x(19),w(19),BETA2,BETA4,BETA6
DOUBLE PRECISION pp,pi,p
INTEGER j,L
pi=ACOS(-1d0)
x(1:10)=(/-.992407,-.960208,-.903156,-.822715,-.720966, &
-.600545,-.464571,-.316564,-.160359,0.0/)
w(1:10)=(/.0194618,.0448182,.0690445,.09149,.111567,.128754, &
.142607,.152766,.158969,.161054/)
DO i=1,9,1
x(10+i)=-x(10-i)
w(10+i)=w(10-i)
END DO
p=0d0
DO j=1,19,1
p=p+DBLE(w(j))*vs(r,v0,RR,a,DBLE(x(j)),L,BETA2,BETA4,BETA6)
END DO
gausss=-DSQRT(pi)*p !Factors required by FRESCO's convention
RETURN
END FUNCTION gausss
SUBROUTINE FORMFACT(VR,RR,AR,dv,drv,dav,W,RW,AW, &
VD,RVD,AVD,WD,RD,AD,N,rmax,BETA2,BETA4,BETA6,A,nexo,sump)
DOUBLE PRECISION deltar,r(0:N)
REAL rmax,BETA2,BETA4,BETA6,A
REAL VR,RR,AR !Real volume
REAL dv,drv,dav,W,RW,AW !Real/imaginary dispersive volume
REAL VD,RVD,AVD,WD,RD,AD!Real/imaginary dispersive surface
INTEGER N,i,nexo,sump
deltar=DBLE(rmax)/(DBLE(N)-1d0)
r(0)=0.0d0
DO i=1,N-1,1
r(i)=r(i-1)+deltar
END DO
IF(sump .NE. 0) THEN
WRITE(94,*) '!Real volume'
WRITE(94,20) N,deltar,R(0)
DO i=0,N-1,1
WRITE(94,10) gaussv(REAL(r(i)),-VR,RR*(A**(1./3.)),AR,2,BETA2,BETA4,BETA6)
END DO
ENDIF
IF(nexo .NE. 0) THEN
WRITE(94,*) '!Real volume'
WRITE(94,20) N,deltar,R(0)
DO i=0,N-1,1
WRITE(94,10) gaussv(REAL(r(i)),-VR,RR*(A**(1./3.)),AR,2,BETA2,BETA4,BETA6)
END DO
ENDIF
IF(sump .NE. 0) THEN
WRITE(94,*) '!Dispersive real and imaginary volume'
WRITE(94,20) N,deltar,R(0)
DO i=0,N-1,1
WRITE(94,10) gaussv(REAL(r(i)),-dv,drv*(A**(1./3.)),dav,2,BETA2,BETA4,BETA6)
WRITE(94,10) gaussv(REAL(r(i)),-W,RW*(A**(1./3.)),AW,2,BETA2,BETA4,BETA6)
END DO
ENDIF
IF(nexo .NE. 0) THEN
WRITE(94,*) '!Dispersive real and imaginary volume'
WRITE(94,20) N,deltar,R(0)
DO i=0,N-1,1
WRITE(94,10) gaussv(REAL(r(i)),-dv,drv*(A**(1./3.)),dav,2,BETA2,BETA4,BETA6)
WRITE(94,10) gaussv(REAL(r(i)),-W,RW*(A**(1./3.)),AW,2,BETA2,BETA4,BETA6)
END DO
ENDIF
IF(sump .NE. 0) THEN
WRITE(94,*) '!Dispersive real and imaginary surface'
WRITE(94,20) N,deltar,R(0)
DO i=0,N-1,1
WRITE(94,10) gausss(REAL(r(i)),-VD,RVD*(A**(1./3.)),AVD,2,BETA2,BETA4,BETA6)
WRITE(94,10) gausss(REAL(r(i)),-WD,RD*(A**(1./3.)),AD,2,BETA2,BETA4,BETA6)
END DO
ENDIF
IF(nexo .NE. 0) THEN
WRITE(94,*) '!Dispersive real and imaginary surface'
WRITE(94,20) N,deltar,R(0)
DO i=0,N-1,1
WRITE(94,10) gausss(REAL(r(i)),-VD,RVD*(A**(1./3.)),AVD,2,BETA2,BETA4,BETA6)
WRITE(94,10) gausss(REAL(r(i)),-WD,RD*(A**(1./3.)),AD,2,BETA2,BETA4,BETA6)
END DO
ENDIF
20 FORMAT(' ',i2,' ',f9.6,' ',f9.6)
10 FORMAT(' ',f9.6)
CLOSE(94)
RETURN
END SUBROUTINE FORMFACT
! **************************************************************************
! * *
! * End of form factors pack *
! * *
! **************************************************************************
!-------------------------------------------------------------------------------
! ****************************************************************************
! * *
! * Interband coupling between ground state band and excited bands for *
! * even and odd nuclei *
! * *
! ****************************************************************************
! - Subroutine used to build &STEPS part of FRESCO's input.
SUBROUTINE steps_even(J1,J2,p1,p2,I1,I2,K1,K2,BETA_VAL)
REAL J1,J2,K1,K2,lamd,BETA_VAL
INTEGER I1,I2,lamd_ph_1,lamd_ph_2
INTEGER p1,p2
DOUBLE PRECISION wigner_val
REAL jmin,jmax,jaux(40)
lamd_ph_1=0 ! No phonons in the G.S band.
IF (p2 .LT. 0) THEN
lamd=3.0
lamd_ph_2=3
ELSE
lamd=2.0
lamd_ph_2=2
ENDIF
2 format('&STEP ia=',i2,' ib=',i2,' k=',i1,' str=',1f9.4,'/')
IF (J1.GE.lamd) THEN
jmin=J1-lamd
jmax=J1+lamd
DO i=0,INT(2*lamd),1
jaux(i+1)=jmin+i
ENDDO
siz=2*lamd+1
ELSE
jmin=lamd-J1
jmax=lamd+J1
DO i=0,2*INT(J1),1
jaux(i+1)=jmin+i
ENDDO
siz=2*J1+1
ENDIF
DO i=1,INT(siz)
IF(jaux(i) .EQ. J2 .AND. J2 .LE. jmax ) THEN
CALL wigner_even(J1,J2,INT(K1),INT(K2),lamd,lamd_ph_1,lamd_ph_2,wigner_val)
WRITE(1,2) I1,I2,INT(lamd),((-1)**((J2-J1+ABS(J2-J1))/2))*wigner_val*BETA_VAL ! Phase accoding to FRESCO's convention.
CALL wigner_even(J2,J1,INT(K2),INT(K1),lamd,lamd_ph_2,lamd_ph_1,wigner_val)
WRITE(1,2) I2,I1,INT(lamd),((-1)**((J1-J2+ABS(J1-J2))/2))*wigner_val*BETA_VAL
ENDIF
ENDDO
RETURN
END SUBROUTINE steps_even
SUBROUTINE steps_odd(J1,J2,p1,p2,I1,I2,K1,K2,BETA_VAL)
REAL J1,J2,K1,K2,lamd,BETA_VAL
INTEGER I1,I2
INTEGER p1,p2,pval
DOUBLE PRECISION wigner_val
REAL jmin,jmax,jaux(40)
pval=p1*p2
IF (pval .LT. 0) THEN
lamd=3.0
ELSE IF (pval .GT. 0) THEN
lamd=2.0
ENDIF
2 format('&STEP ia=',i2,' ib=',i2,' k=',i1,' str=',1f9.4,'/')
IF (J1.GE.lamd) THEN
jmin=J1-lamd
jmax=J1+lamd
DO i=0,INT(2*lamd),1
jaux(i+1)=jmin+i
ENDDO
siz=2*lamd+1
ELSE
jmin=lamd-J1
jmax=lamd+J1
DO i=0,NINT(2*J1),1
jaux(i+1)=jmin+i
ENDDO
siz=2*J1+1
ENDIF
DO i=1,INT(siz)
IF(jaux(i) .EQ. J2 .AND. J2 .LE. jmax ) THEN
CALL wigner_odd(J1,J2,K1,K2,lamd,p1,p2,wigner_val)
WRITE(1,2) I1,I2,INT(lamd),((-1)**(NINT(J2-J1+ABS(J2-J1))/2))*wigner_val*BETA_VAL ! Phase accoding to FRESCO's convention.
CALL wigner_odd(J2,J1,K2,K1,lamd,p2,p1,wigner_val)
WRITE(1,2) I2,I1,INT(lamd),((-1)**(NINT(J1-J2+ABS(J1-J2))/2))*wigner_val*BETA_VAL
ENDIF
ENDDO
RETURN
END SUBROUTINE steps_odd
! - Stop in case of allocation error.
SUBROUTINE error (errval,errtype)
INTEGER errval,errtype
IF(errval.NE.0.AND.errtype.EQ.1) THEN
STOP "Allocation request denied"
ENDIF
IF(errval.NE.0.AND.errtype.EQ.2) THEN
STOP "Deallocation request denied"
ENDIF
RETURN
END SUBROUTINE error
! - Generate a script for Python in case of drawing cross section graphs at the end of the run.
SUBROUTINE Graphs
OPEN(94,form='formatted',file='graphs.py')
WRITE(94,'(a)') 'from pylab import *'
WRITE(94,'(a)') 'import matplotlib.pyplot as plt'
WRITE(94,'(a)') 'f = open("Cross_sections.out")'
WRITE(94,'(a)') 'heading = f.readline()'
WRITE(94,'(a)') 'Energy = []'
WRITE(94,'(a)') 'Elastic_CS = []'
WRITE(94,'(a)') 'Absorption_CS = []'
WRITE(94,'(a)') 'Total_CS = []'
WRITE(94,'(a)') 'for line in f:'
WRITE(94,'(a)') ' dat = line.split()'
WRITE(94,'(a)') ' Energy.append(float(dat[0]))'
WRITE(94,'(a)') ' Elastic_CS.append(float(dat[1]))'
WRITE(94,'(a)') ' Absorption_CS.append(float(dat[2]))'
WRITE(94,'(a)') ' Total_CS.append(float(dat[4]))'
WRITE(94,'(a)') 'f.close()'
WRITE(94,'(a)') 'fig1,axes = plt.subplots()'
WRITE(94,'(a)') 'axes.plot(Energy, Elastic_CS, "x--b")'
WRITE(94,'(a)') 'axes.set_xlabel("Energy (MeV)")'
WRITE(94,'(a)') 'axes.set_ylabel("Cross section (mb)")'
WRITE(94,'(a)') 'axes.set_title("Elastic cross section")'
WRITE(94,'(a)') 'axes.grid(True)'
WRITE(94,'(a)') 'fig1.savefig("Elastic_CS.eps", format="eps")'
WRITE(94,'(a)') '##################################################'
WRITE(94,'(a)') 'fig2,axes = plt.subplots()'
WRITE(94,'(a)') 'axes.plot(Energy, Absorption_CS, "*--r")'
WRITE(94,'(a)') 'axes.set_xlabel("Energy (MeV)")'
WRITE(94,'(a)') 'axes.set_ylabel("Cross section (mb)")'
WRITE(94,'(a)') 'axes.set_title("Absorption cross section")'
WRITE(94,'(a)') 'axes.grid(True)'
WRITE(94,'(a)') 'fig2.savefig("Absorption_CS.eps", format="eps")'
WRITE(94,'(a)') '##################################################'
WRITE(94,'(a)') 'fig3,axes = plt.subplots()'
WRITE(94,'(a)') 'axes.plot(Energy, Total_CS, "x-.b")'
WRITE(94,'(a)') 'axes.set_xlabel("Energy (MeV)")'
WRITE(94,'(a)') 'axes.set_ylabel("Cross section (mb)")'
WRITE(94,'(a)') 'axes.set_title("Total cross section")'
WRITE(94,'(a)') 'axes.grid(True)'
WRITE(94,'(a)') 'fig3.savefig("Total_CS.eps", format="eps")'
CLOSE(94)
END SUBROUTINE Graphs
DOUBLE PRECISION FUNCTION k_val(E,M)
DOUBLE PRECISION hc
REAL E, M, mu
hc = 197.32698d0 !MeV*fm
mu = (M/(M+1.0))*938.494
k_val = DSQRT((2.0d0*E*mu)/(hc*hc))
RETURN
END FUNCTION K_val
END MODULE modulo