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pe-REALbox-rate-pow.f
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pe-REALbox-rate-pow.f
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implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension ca(4,4),cb(4,4),cgamma(0:3,4,4),
1 cgamma5(4,4),gmunu(0:3,0:3),cu1bar(4),cu2(4),cukbar(4),
2 cue(4),p1(0:3),p2(0:3),pk(0:3),cs1(2),cs2(2),csk(2),
3 cleft(4,4),cGVGA(4,4),xg(100),wxg(100),pg(100),wpg(100),
4 pe(0:3),cse(2)
common /dirac/ ci,cgamma,cgamma5,gmunu
common /con/ pi,hbarc,rc,alpha,GF,GV,GA,dMp,dMn,dme,dmnu,dMd,gnpd,
1 dkapp,dkapn,dufac,dN0,e
call const
call cdirac
nx = 8
call gaus(xg,wxg,nx)
np = 8
call gaus(pg,wpg,np)
do ip =1,np
pg(ip) =(pg(ip)+1.d0)*pi
wpg(ip) = wpg(ip)*pi
enddo
PRINT '(A)','PNLL code'
PRINT '(A)','PG'
write(*,*) pg(1),pg(2),pg(3),pg(4),pg(5),pg(6),pg(7),pg(8)
PRINT '(A)','WPG'
write(*,*) wpg(1),wpg(2),wpg(3),wpg(4),wpg(5),wpg(6),wpg(7),wpg(8)
Ekemin =((dMn + dmnu - dme)**2 - dMp**2)/(2.d0*(dMn+dmnu))
pmin = dsqrt((Ekemin+dme)**2 - dme**2)
E2check =((dMn + dmnu)**2 -(dMp+dme)**2)/(2.d0*dMp)
PRINT '(A)','EKemin,pmin,E2check'
write(*,*) Ekemin,pmin,E2check
call copyg(cgamma5,ca)
call chsgng(ca)
cscal = 1.d0
call saddg(cscal,ca,cleft)
call copyg(cgamma5,ca)
cscal = GA
call smultg(cscal,ca,ca)
call chsgng(ca)
cscal = GV
call saddg(cscal,ca,cGVGA)
do is1 =1,2
cs1(is1) = 0.d0
enddo
do is2 =1,2
cs2(is2) = 0.d0
enddo
do ise =1,2
cse(ise) = 0.d0
enddo
do isk =1,2
csk(isk) = 0.d0
enddo
tran2 = 0.d0
densep = 7.d0 ! g/cc NiH density ??
dNiMW = 28.d0 ! g/mol NiH MW ??
dndens = dN0*densep/dNiMW
open(9,file='plot.dat',status='UNKNOWN')
do iep =1,500
pep =(pmin + dexp(dlog(1.d-11)+ dfloat(iep)*
1 (dlog(100.d0)-dlog(1.d-11))/500.d0))/ dsqrt(3.d0)
rlconf = 1.d-5*hbarc*pi/pep
tran2 = 0.d0
do ix =1,nx
do ip =1,np
do is1 =1,2
cs1(is1) = 1.d0
do is2 =1,2
cs2(is2) = 1.d0
do ise =1,2
cse(ise) = 1.d0
do isk =1,2
csk(isk) = 1.d0
do isgn1 = 1,2
do isgn2 = 1,2
do isgn3 = 1,2
camp2 = 0.d0
pep1 = pep*((-1.d0)**isgn1)
pep2 = pep*((-1.d0)**isgn2)
pep3 = pep*((-1.d0)**isgn3)
call pekin(xg(ix),pg(ip),pep1,pep2,pep3,pe,p1,p2,pk)
call spinubar(p1,dMn,cs1,cu1bar)
call spinu(p2,dMp,cs2,cu2)
call spinu(pe,dme,cse,cue)
call spinubar(pk,dmnu,csk,cukbar)
call vcopyg(0,cgamma,cb)
call multg(cGVGA,cb,cb)
call ubaru(cu1bar,cb,cu2,chad0)
call vcopyg(0,cgamma,cb)
call multg(cb,clef t,cb)
call ubaru(cukbar,cb,cue,clep0)
call vcopyg(1,cgamma,cb)
call multg(cGVGA,cb,cb)
call ubaru(cu1bar,cb,cu2,chad1)
call vcopyg(1,cgamma,cb)
call multg(cb,clef t,cb)
call ubaru(cukbar,cb,cue,clep1)
call vcopyg(2,cgamma,cb)
call multg(cGVGA,cb,cb)
call ubaru(cu1bar,cb,cu2,chad2)
call vcopyg(2,cgamma,cb)
call multg(cb,clef t,cb)
call ubaru(cukbar,cb,cue,clep2)
call vcopyg(3,cgamma,cb)
call multg(cGVGA,cb,cb)
call ubaru(cu1bar,cb,cu2,chad3)
call vcopyg(3,cgamma,cb)
call multg(cb,clef t,cb)
call ubaru(cukbar,cb,cue,clep3)
camp2 = camp2 +
1 (chad0* clep0 - chad1* clep1 - chad2* clep2 - chad3* clep3)
enddo
enddo
enddo
fact =rc*((pep/(2.d0*pi))**3)*(GF**2)*(dsqrt(pk(0)**2-dmnu**2))**3
1 /(512.d0 *(pi **2)* p2(0)* pe(0)* hbarc * 1.d-15*
1 dabs((pk(1) *(p1(0)* pk(1)-pk(0)* p1(1))) +
1 (pk(2)*(p1(0)* pk(2)-pk(0)* p1(2))) +
1 (pk(3)*(p1(0)* pk(3)-pk(0)* p1(3)))))
EKn = p1(0) - dMn
EKe = pe(0) - dme
tran2 = tran2 + wxg(ix)*wpg(ip)*
1 dreal(camp2* dconjg(camp2)) * fact *dndens
csk(isk) = 0.d0
enddo
cse(ise) = 0.d0
enddo
cs2(is2) = 0.d0
enddo
cs1(is1) = 0.d0
enddo
enddo
enddo
EKp = p2(0) - dMp
EKn = p1(0) - dMn
EKe = pe(0) - dme
EKnu = pk(0) - dmnu
C write(*,*) iep,rlconf,tran2,tran2/dndens,EKe,EKn
write(*,*) "tran2",iep,rlconf,tran2,tran2/dndens
write(9,*) rlconf,tran2,
1 tran2 *((pe(0) - dme)+(p2(0) - dMp)) * e * 1.d-7,
1 tran2 *(2.2d0+(p1(0) - dMn)) * e * 1.d-7,EKe,EKn,EKnu,Ekp
enddo
close(9)
STOP
END
subroutine const
implicit real*8(a-h,o-z)
common /con/ pi,hbarc,rc,alpha,GF,GV,GA,dMp,dMn,dme,dmnu,dMd,gnpd
1 ,dkapp,dkapn,dufac,dN0,e
pi = 4.d0*datan(1.d0)
hbarc = 197.3269631d0 ! MeV-fm
rc = 299792458.d0 ! m/s
alpha = 7.2973525376d-3
e = 1.602176487d-13 ! J/MeV
dN0 = 6.02214179d23 ! molˆ-1
dMp = 938.272013d0 ! MeV
dMn = 939.565346d0 ! MeV
dme = 0.510998910d0 ! MeV
dmnu = 1.d-8 ! MeV
dMd = 1875.612793d0 ! MeV
GF = 1.16637d-11 ! 1/MeVˆ2
GV = 1.d0 ! 1.013d0
GA = -1.285d0*GV ! -1.267
gnpd = 10.6617553d0 ! 11.3 in 9704031 v5.pdf(pg 8-9)
dkapp= 1.793d0
dkapn= -1.913d0
dufac= 0.d0
RETURN
end
subroutine cdirac
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension cgamma(0:3,4,4),cgamma5(4,4),gmunu(0:3,0:3)
common /dirac/ ci,cgamma,cgamma5,gmunu
ci =(0.d0,1.d0)
do i1 =1,4
do i2 =1,4
cgamma5(i1,i2) =(0.d0,0.d0)
do imu = 0,3
cgamma(imu,i1,i2) =(0.d0,0.d0)
enddo
enddo
enddo
cgamma(0,1,1) = 1.d0
cgamma(0,2,2) = 1.d0
cgamma(0,3,3) = -1.d0
cgamma(0,4,4) = -1.d0
cgamma(1,1,4) = 1.d0
cgamma(1,2,3) = 1.d0
cgamma(1,3,2) = -1.d0
cgamma(1,4,1) = -1.d0
cgamma(2,1,4) = -ci
cgamma(2,2,3) = ci
cgamma(2,3,2) = ci
cgamma(2,4,1) = -ci
cgamma(3,1,3) = 1.d0
cgamma(3,2,4) = -1.d0
cgamma(3,3,1) = -1.d0
cgamma(3,4,2) = 1.d0
cgamma5(1,3) = 1.d0
cgamma5(2,4) = 1.d0
cgamma5(3,1) = 1.d0
cgamma5(4,2) = 1.d0
RETURN
end
subroutine spinu(p,rm,cs,cu)
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension cgamma(0:3,4,4),cgamma5(4,4),cwu(4,2)
dimension cu(4),gmunu(0:3,0:3),cs(2),cphi(2),p(0:3)
common /dirac/ ci,cgamma,cgamma5,gmunu
fac = dsqrt(p(0) + rm)
cphi(1) = cs(1)*fac
cphi(2) = cs(2)*fac
cwu(1,1) = 1.d0
cwu(1,2) = 0.d0
cwu(2,1) = 0.d0
cwu(2,2) = 1.d0
cwu(3,1) =(p(3))/(p(0) + rm)
cwu(3,2) =(p(1)- ci*p(2))/(p(0) + rm)
cwu(4,1) =(p(1)+ ci*p(2))/(p(0) + rm)
cwu(4,2) =(-p(3))/(p(0) + rm)
do i1 =1,4
cu(i1) = 0.d0
doi2 = 1,2
cu(i1) = cu(i1) + cwu(i1,i2)*cphi(i2)
enddo
enddo
RETURN
end
subroutine spinubar(p,rm,cs,cubar)
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension cgamma(0:3,4,4),cgamma5(4,4),gmunu(0:3,0:3)
dimension cwu(4,2),cu(4),cubar(4),cs(2),cphi(2),p(0:3)
common /dirac/ ci,cgamma,cgamma5,gmunu
fac = dsqrt(p(0) + rm)
cphi(1) = cs(1)*fac
cphi(2) = cs(2)*fac
cwu(1,1) = 1.d0
cwu(1,2) = 0.d0
cwu(2,1) = 0.d0
cwu(2,2) = 1.d0
cwu(3,1) =(p(3))/(p(0) + rm)
cwu(3,2) =(p(1)- ci*p(2))/(p(0) + rm)
cwu(4,1) =(p(1)+ ci*p(2))/(p(0) + rm)
cwu(4,2) =(-p(3))/(p(0) + rm)
do i1 =1,4
cu(i1) = 0.d0
do i2 =1,2
cu(i1) = cu(i1) + cwu(i1,i2)*cphi(i2)
enddo
enddo
cubar(1) = dconjg(cu(1))
cubar(2) = dconjg(cu(2))
cubar(3) = -dconjg(cu(3))
cubar(4) = -dconjg(cu(4))
RETURN
end
subroutine ubaru(cubar,ca,cu,cscal)
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension cubar(4),ca(4,4),cu(4)
cscal = 0.d0
do i1 =1,4
do i2 =1,4
cscal = cscal + cubar(i1)*ca(i1,i2)*cu(i2)
enddo
enddo
return
end
subroutine chsgng(ca)
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension ca(4,4)
do i1 =1,4
do i2 =1,4
ca(i1,i2) = -ca(i1,i2)
enddo
enddo
RETURN
end
subroutine vcopyg(mu,caa,cb)
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension caa(0:3,4,4),cb(4,4)
do i1 =1,4
do i2 =1,4
cb(i1,i2) = caa(mu,i1,i2)
enddo
enddo
RETURN
end
subroutine subg(ca,cb,cc)
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension ca(4,4),cb(4,4),cc(4,4)
do i1 =1,4
do i2 =1,4
cc(i1,i2) = ca(i1,i2) - cb(i1,i2)
enddo
enddo
RETURN
end
subroutine copyg(ca,cb)
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension ca(4,4),cb(4,4)
do i1 =1,4
do i2 =1,4
cb(i1,i2) = ca(i1,i2)
enddo
enddo
RETURN
end
subroutine saddg(cscal,ca,cb)
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension ca(4,4),cb(4,4)
do i1 =1,4
do i2 =1,4
cb(i1,i2) = ca(i1,i2)
enddo
enddo
do i1 =1,4
cb(i1,i1) = cb(i1,i1) + cscal
enddo
RETURN
end
subroutine addg(ca,cb,cc)
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension ca(4,4),cb(4,4),cc(4,4)
do i1 =1,4
do i2 =1,4
cc(i1,i2) = ca(i1,i2) + cb(i1,i2)
enddo
enddo
RETURN
end
subroutine smultg(cscal,ca,cb)
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension ca(4,4),cb(4,4)
do i1 =1,4
do i2 =1,4
cb(i1,i2) = ca(i1,i2)*cscal
enddo
enddo
RETURN
end
subroutine multg(ca,cb,cc)
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension ca(4,4),cb(4,4),cc(4,4),cd(4,4)
do i1 =1,4
do i2 =1,4
cd(i1,i2) =(0.d0,0.d0)
do j =1,4
cd(i1,i2) = cd(i1,i2) + ca(i1,j)*cb(j,i2)
enddo
enddo
enddo
do i1 =1,4
do i2 =1,4
cc(i1,i2) = cd(i1,i2)
enddo
enddo
RETURN
end
subroutine pekin(x,phi,pep1,pep2,pep3,pe,p1,p2,pk)
implicit real*8(a-b,d-h,o-z)
implicit complex*16(c)
dimension p1(0:3),p2(0:3),pk(0:3),pe(0:3)
common /con/ pi,hbarc,rc,alpha,GF,GV,GA,dMp,dMn,dme,dmnu,dMd,gnpd
1 ,dkapp,dkapn,dufac,dN0,e
p2(0) = dsqrt(dMp**2 + pep1**2 + pep2**2 + pep3**2)
p2(1) = -pep1
p2(2) = -pep2
p2(3) = -pep3
pe(0) = dsqrt(dme**2 + pep1**2 + pep2**2 + pep3**2)
pe(1) = pep1
pe(2) = pep2
pe(3) = pep3
Etot = p2(0) + pe(0)
Eknu =((Etot-dmnu)**2 - dMn**2)/(2.d0*Etot)
Ekn =((Etot-dMn)**2 - dmnu**2)/(2.d0*Etot)
pnu = dsqrt((Eknu+dmnu)**2 - dmnu**2)
pk(0) = Eknu + dmnu
pk(1) = pnu*dsqrt(1.d0 - x**2)*dcos(phi)
pk(2) = pnu*dsqrt(1.d0 - x**2)*dsin(phi)
pk(3) = pnu*x
p1(0) = p2(0) + pe(0) - pk(0)
p1(1) = p2(1) + pe(1) - pk(1)
p1(2) = p2(2) + pe(2) - pk(2)
p1(3) = p2(3) + pe(3) - pk(3)
RETURN
end
SUBROUTINE GAUS(Y,WY,N)
IMPLICIT REAL*8(A-H,O-Z)
C THIS ROUTINE DETERMINES THE N/2 POSITIVE ZEROS(X(N/2)) OF THE
C LEGENDRE POLYNOMIAL OF ORDER N. ALSO THE N/2 DISTINCT WEIGHTS
C FOR GAUSS QUADRATURE ARE CALCULATED. N IS EVEN AND LESS THAN 101.
DOUBLE PRECISION V,Z,Z1,P,P1,DP,POL
DIMENSION X(50),W(50),POL(101)
DIMENSION Y(*),WY(*)
NP1=N+1
M = N/2
MP1=M+1
Z = 3.14159265358979D0/(2.0D0*FLOAT(N))
DO 20 L=1,M
DO 5 K=1,100
CALL PL(Z,N,POL)
P=POL(NP1)
DP=N*(Z*POL(NP1)-POL(N))/(Z*Z-1.D0)
Z = Z - P/DP
IF(DABS(P).LT..1D-11) GO TO 15
5 CONTINUE
WRITE(6,1000) L
RETURN
15 X(L) = Z
V = 2.0D0/((1.0D0 - Z*Z)*DP*DP)
W(L) = V
IF(L.EQ.M) GO TO 30
DZ=Z
IF (L.GT.1) DZ=(X(L)-X(L-1))*.5D0
DO 17 K=1,200
Z = Z + DZ
CALL PL(Z,N,POL)
P=POL(NP1)
Z1 = Z + DZ
CALL PL(Z1,N,POL)
P1=POL(NP1)
IF(P*P1.LT.0.0D0) GO TO 18
17 CONTINUE
18 Z = (P1*Z - P*Z1)/(P1 - P)
20 CONTINUE
30 DO 40 NEG=1,N
IF(NEG.LE.M)Y(NEG)=-X(MP1-NEG)
IF(NEG.GT.M)Y(NEG)=X(NEG-M)
IF(NEG.LE.M)WY(NEG)=W(MP1-NEG)
IF(NEG.GT.M)WY(NEG)=W(NEG-M)
40 CONTINUE
RETURN
1000 FORMAT(5X,40HFAILURE TO GET ZEROS OF LEGENDRES FOR L=,I3)
END
SUBROUTINE PL(X,L,POL)
IMPLICIT REAL*8(A-H,O-Z)
C COMPUTES LEGENDRE POLYNOMINALS OF ORDER ZERO TO ORDER
C (L) FOR A GIVEN ARGUMENT (X=COS(THETA))
DOUBLE PRECISION S,X,POL
DIMENSION POL(*)
POL(1)=1.0D0
POL(2)=X
IF(L.LE.1)GOTO20
DO 10 JJ=2,L
S=JJ
10 POL(JJ+1)=((2.D0*S-1.D0)*X*POL(JJ)-(S-1.D0)*POL(JJ-1))/S
20 RETURN
END