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me_rot.f90
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me_rot.f90
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module me_rot
use accuracy
use timer
implicit none
private
public ME_rotation
integer(ik),parameter :: verbose = 5 ! Verbosity level
!
integer(ik) :: Jmax
!
contains
!
!
! Rotational matrix elements for symmetrized rigid rotor
!
!
subroutine ME_rotation(Jmax_,me)
!
integer(ik),intent(in) :: Jmax_
real(ark),intent(out) :: me(7,(jmax_+1)*(jmax_+2)/2,-2:2,0:1)
!
integer(ik) :: j,k1,k2,tau1,tau2,pm,jk,dk,alloc
real(ark) :: fjk,gjk,minus1,mejx,mejz,mejxy,mejyz,mejx2y2,mejy,mejxz,fjk_t
!
real(ark) ,allocatable :: jzmat(:,:,:)
real(ark) ,allocatable :: jx2y2mat(:,:,:),jxymat(:,:,:),jxmat(:,:,:)
real(ark) ,allocatable :: jymat(:,:,:),jxzmat(:,:,:),jyzmat(:,:,:)
!
!
if (verbose>=5) write (out,"(20('*'),' Rotational matrix elements calculations')")
!
Jmax = Jmax_
!
allocate(jzmat(0:jmax,-jmax:jmax,-jmax:jmax ),stat=alloc)
call ArrayStart('ME_rotation-jzmat',alloc,size(jzmat),kind(jzmat))
allocate(jx2y2mat(0:jmax,-jmax:jmax,-jmax:jmax),stat=alloc)
call ArrayStart('ME_rotation-jx2y2mat',alloc,size(jx2y2mat),kind(jx2y2mat))
allocate(jxymat(0:jmax,-jmax:jmax,-jmax:jmax ),stat=alloc)
call ArrayStart('ME_rotation-jxymat',alloc,size(jxymat),kind(jxymat))
allocate(jxmat(0:jmax,-jmax:jmax,-jmax:jmax ),stat=alloc)
call ArrayStart('ME_rotation-jxmat',alloc,size(jxmat),kind(jxmat))
allocate(jymat(0:jmax,-jmax:jmax,-jmax:jmax ),stat=alloc)
call ArrayStart('ME_rotation-jymat',alloc,size(jymat),kind(jymat))
allocate(jxzmat(0:jmax,-jmax:jmax,-jmax:jmax ),stat=alloc)
call ArrayStart('ME_rotation-jxzmat',alloc,size(jxzmat),kind(jxzmat))
allocate(jyzmat(0:jmax,-jmax:jmax,-jmax:jmax ),stat=alloc)
call ArrayStart('ME_rotation-jyzmat',alloc,size(jyzmat),kind(jyzmat))
!
jxmat = 0
jymat = 0
jzmat = 0
jx2y2mat = 0
jxymat = 0
jxzmat = 0
jyzmat = 0
!
do j =0,jmax
!
do k1 = -j,j
!
do k2 = -j,j
!
pm = sign(1,k2-k1)
!
if (k1==k2) then
jzmat(j,k1,k2) = real(k1,ark)
endif
!
if (abs(k1-k2)==2) then
!
fjk_t = int( j*(j+1)-(k1+pm*2)*(k1+pm*1) ,hik)*int( j*(j+1)-k1*(k1+pm*1 ) ,hik)
!
fjk = 0.5_ark*sqrt( fjk_t )
!
jx2y2mat(j,k1,k2) = fjk
jxymat(j,k1,k2) = real(pm,ark)*fjk
!
if (verbose>=7) write(out,"('j,k1,k2,pm,fjk = ',4i7,3e18.8)") j,k1,k2,pm,fjk,jx2y2mat(j,k1,k2),jxymat(j,k1,k2)
!
endif
!
if (iabs(k1-k2).eq.1) then
!
gjk = 0.5_ark*sqrt( real( j*(j+1) - k1*(k1+pm) , kind=ark ) )
jxmat(j,k1,k2) = gjk
jymat(j,k1,k2) = real(pm,ark)*gjk
jxzmat(j,k1,k2) = gjk*real( 2*k1+pm ,ark)
jyzmat(j,k1,k2) = gjk*real( ( 2*k1+pm )*pm ,ark)
!
endif
!
enddo
enddo
enddo
!
me = 0
!
do j =0,jmax
!
do k1 = 0,j
!
jk=1+k1+(j*(j+1) )/2
!
do tau1 = 0,1
!
if (k1.ne.0.or.mod(j+tau1,2).eq.0) then
!
minus1 = -1.0_ark
!
if (mod(tau1,2).eq.0) minus1 = 1.0_ark
!
do k2=max(0,k1-2),min(j,k1+2)
do tau2 = 0,1
!
if (k2/=0.or.mod(j+tau2,2)==0) then
!
dk = k1-k2
!
mejx2y2 = mult_rot_me(j,k1,k2,tau1,tau2,jx2y2mat)
mejy = -mult_rot_me(j,k1,k2,tau1,tau2,jymat )
mejxz = mult_rot_me(j,k1,k2,tau1,tau2,jxzmat )
mejx = minus1*mult_rot_me(j,k1,k2,tau1,tau2,jxmat )
mejz = minus1*mult_rot_me(j,k1,k2,tau1,tau2,jzmat )
mejxy = minus1*mult_rot_me(j,k1,k2,tau1,tau2,jxymat )
mejyz = minus1*mult_rot_me(j,k1,k2,tau1,tau2,jyzmat )
!
! Here we check for the consistency
!
if (tau1.ne.tau2) then
!
if (mejx2y2/=0) then
write(out,"('ME_rotation: mejx2y2 <>0',5i7,e18.8)") j,k1,k2,tau1,tau2,mejx2y2
stop 'ME_rotation: mejx2y2 <>0'
endif
!
if (mejy/=0) then
write(out,"('ME_rotation: mejy <>0',5i7,e18.8)") j,k1,k2,tau1,tau2,mejy
stop 'ME_rotation: mejy <>0'
endif
!
if (mejxz/=0) then
write(out,"('ME_rotation: mejxz <>0',5i7,e18.8)") j,k1,k2,tau1,tau2,mejxz
stop 'ME_rotation: mejxz <>0'
endif
!
! here we store for different taus, but using only the first tau1 as the reference
!
me(1,jk,dk,tau1) = mejx
me(3,jk,dk,tau1) = mejz
me(5,jk,dk,tau1) = mejxy
me(7,jk,dk,tau1) = mejyz
!
else
!
if (mejx.ne.0) then
write(out,"('ME_rotation: mejx <>0',5i7,e18.8)") j,k1,k2,tau1,tau2,mejx
stop 'ME_rotation: mejx <>0'
endif
!
if (mejz.ne.0) then
write(out,"('ME_rotation: mejz <>0',5i7,e18.8)") j,k1,k2,tau1,tau2,mejz
stop 'ME_rotation: mejz <>0'
endif
!
if (mejxy.ne.0) then
write(out,"('ME_rotation: mejxy <>0',5i7,e18.8)") j,k1,k2,tau1,tau2,mejxy
stop 'ME_rotation: mejxy <>0'
endif
!
if (mejyz.ne.0) then
write(out,"('ME_rotation: mejyz <>0',5i7,e18.8)") j,k1,k2,tau1,tau2,mejyz
stop 'ME_rotation: mejyz <>0'
endif
!
! here we store for the same taus, but using only the first tau1 as the reference
!
me(2,jk,dk,tau1) = mejy
me(4,jk,dk,tau1) = mejx2y2
me(6,jk,dk,tau1) = mejxz
!
endif
!
endif
enddo
enddo
endif
enddo
enddo
enddo
!
deallocate(jzmat,jx2y2mat,jxymat,jxmat,jymat,jxzmat,jyzmat)
!
call ArrayStop('ME_rotation-jzmat')
call ArrayStop('ME_rotation-jx2y2mat')
call ArrayStop('ME_rotation-jxymat')
call ArrayStop('ME_rotation-jxmat')
call ArrayStop('ME_rotation-jymat')
call ArrayStop('ME_rotation-jxzmat')
call ArrayStop('ME_rotation-jyzmat')
!
if (verbose>=5) write (out,"(20('*'),' Rotational matrix elements calculations/end')")
!
end subroutine ME_rotation
!
! Miscelan. routime
!
function mult_rot_me(j,k1,k2,tau1,tau2,me) result (f)
!
integer(ik),intent(in) :: j,k1,k2,tau1,tau2
real(ark),intent(in) :: me(0:jmax,-jmax:jmax,-jmax:jmax)
!
real(ark) :: sigma1,sigma2,minus0,f
real(ark) :: minus1,minus2,minus12,fk1,fk2
!
fk1 = 1.0_ark/sqrt(2.0_ark)
if (k1.eq.0) fk1 = 0.5_ark
!
fk2 = 1.0_ark/sqrt(2.0_ark)
if (k2.eq.0) fk2 = 0.5_ark
!
sigma1 = 1.0_ark
if (tau1.eq.1.and.mod(k1,3).eq.1) sigma1 = -1.0_ark
!
sigma2 = 1.0_ark
if (tau2.eq.1.and.mod(k2,3).eq.1) sigma2 = -1.0_ark
!
minus0 = sigma1*sigma2
!
minus1 = -1.0_ark
if (mod(j+tau1+k1,2).eq.0) minus1 = 1.0_ark
!
minus2 = -1.0_ark
if (mod(j+tau2+k2,2).eq.0) minus2 = 1.0_ark
!
minus12 = -1.0_ark
if (mod(tau1+tau2+k1+k2,2).eq.0) minus12 = 1.0_ark
!
if (verbose>=6) write(out,"('j,k1,k2,minus1,minus1,minus12 = ',3i6,5e18.8)") j,k1,k2,minus1,minus1,minus12
if (verbose>=6) write(out,"('me(j,pm k1, pm k2) = ',4e18.8)") me(j,k1, k2),me(j,-k1, k2),me(j,k1, -k2),me(j,-k1, -k2)
!
f = minus0*fk1*fk2*( me(j,k1, k2) + minus1 *me(j,-k1,k2) &
+ minus2*me(j,k1,-k2) + minus12*me(j,-k1,-k2) )
!
end function mult_rot_me
!
end module me_rot