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pe-gauss-coefs.f
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pe-gauss-coefs.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
write(*,*) wxg(1),wxg(2),wxg(3),wxg(4),wxg(5),wxg(6),wxg(7),wxg(8)
write(*,*) wpg(1),wpg(2),wpg(3),wpg(4),wpg(5),wpg(6),wpg(7),wpg(8)
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