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lagrange_mesh.f
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module lagrange_mesh_single_channel
use mesh
implicit none
! note the delta function structure fi(xj) = \lambda_i^{-1/2} \delta_{ij}
real*8,dimension(:),allocatable :: lagrange_func
real*8,dimension(:,:), allocatable :: kinetic_matrix
real*8,dimension(:,:),allocatable :: l_barrier_matrix
complex*16,dimension(:,:),allocatable :: V_matrix
real*8,dimension(:),allocatable :: mesh_rr, mesh_rw
real*8 :: rmax_rmatrix
contains
c***********************************************************************
subroutine initial_lagrange_func (rmatch_rmatrix)
!
! before calling this subroutine please initial rmax_rmatrix and nr
!
! this subroutine is used to initial the Lagrange function
! for the purpose to reconstruct the scattering wave function
!!!!!! please gives the matching radius
c***********************************************************************
use gauss
use mesh
use precision
implicit none
integer :: ir
real*8 :: rmatch_rmatrix
rmax_rmatrix=rmatch_rmatrix
if(allocated(lagrange_func)) deallocate(lagrange_func)
if(allocated(mesh_rr)) deallocate(mesh_rr)
if(allocated(mesh_rw)) deallocate(mesh_rw)
allocate(lagrange_func(1:nr))
allocate(mesh_rr(1:nr))
allocate(mesh_rw(1:nr))
call gauleg(nr,0.0_dpreal,1.0_dpreal,mesh_rr,mesh_rw)
do ir=1, nr
lagrange_func(ir) = 1/ sqrt(rmax_rmatrix * mesh_rw(ir))
end do
end subroutine
c-----------------------------------------------------------------------
c***********************************************************************
subroutine T_and_Bloch(mu)
! this subroutine is used to compute the kinetic and Bloch operator
! in the matrix form
c***********************************************************************
use precision
use constants
implicit none
integer :: ir, irp
real*8 :: f1,f2,f3
real*8 :: xi, xj
real*8 :: mu
if(allocated(kinetic_matrix)) deallocate(kinetic_matrix)
allocate(kinetic_matrix(1:nr, 1:nr))
do ir=1 , nr
do irp=1, nr
f1=0.0_dpreal
f2=0.0_dpreal
f3=0.0_dpreal
xi= mesh_rr(ir)
xj= mesh_rr(irp)
if(ir==irp) then
f1= hbarc**2 / (6.0_dpreal * rmax_rmatrix**2 * xi * (1-xi) * mu)
f2= 4.0_dpreal * nr * (nr+1) + 3.0
f3= (1.0_dpreal - 6.0_dpreal *xi )/( xi * (1-xi) )
kinetic_matrix(ir,irp)= f1 * ( f2 + f3 )
else
f1= (-1.0_dpreal)**(ir+irp) * hbarc**2 /2.0_dpreal/rmax_rmatrix/rmax_rmatrix/
+ sqrt( xi * xj * (1-xi) * (1-xj) ) / mu
f2= nr * (nr+1) + 1.0 + ( xi + xj - 2.0_dpreal * xi * xj )/( (xi-xj)**2 )
f3= 1.0_dpreal/(1.0_dpreal-xi) + 1.0_dpreal/(1.0_dpreal -xj)
kinetic_matrix(ir,irp)= f1* (f2-f3)
end if
end do
end do
end subroutine
c-----------------------------------------------------------------------
c***********************************************************************
subroutine centrifugal_barrier (l,mu)
! this subroutine is used to compute centrifugal_barrier in
! lagrange mesh basis
! V_l = \frac{\hbarc^2 l (l+1)}{2 * mu * r}
! input : mu in MeV
! l
c***********************************************************************
use constants
use precision
implicit none
integer :: l , ir
real*8 :: mu ,xi
if(allocated(l_barrier_matrix)) deallocate(l_barrier_matrix)
allocate(l_barrier_matrix(1:nr, 1:nr))
l_barrier_matrix=0.0_dpreal
do ir=1 , nr
xi = mesh_rr(ir)
l_barrier_matrix(ir,ir) = ( hbarc**2 * l * (l+1) )/ ( 2.0_dpreal * mu * rmax_rmatrix * rmax_rmatrix * xi * xi )
end do
end subroutine
c-----------------------------------------------------------------------
c***********************************************************************
subroutine lagrange_V(Vpot)
! this subroutine is used to compute the V-matrix in the Lagrange
! mesh basis
! input V is given in the mesh point in the step of hcm
! this subroutine interpolate the Vpot to give the correct mesh sets
c***********************************************************************
use interpolation
use precision
implicit none
complex*16,dimension(0:irmatch),intent(in) :: vpot
integer :: ir
real*8 :: r
if(allocated(V_matrix)) deallocate(V_matrix)
allocate(V_matrix(1:nr,1:nr))
V_matrix=0.0_dpreal
do ir = 1, nr
r = rmax_rmatrix* mesh_rr(ir)
V_matrix(ir,ir) = FFC(r/hcm, vpot, 1+irmatch)
end do
end subroutine
c-----------------------------------------------------------------------
c***********************************************************************
subroutine R_matrix(l,mu,ecm,vpot,cph,gc,gcp,fc,fcp)
! this subroutine is used to compute the single channel R-matrix
c***********************************************************************
use precision
use constants
implicit none
integer :: l
real*8 :: mu, ecm ,k
real*8 :: gc,gcp,fc,fcp
complex*16,dimension(0:irmatch) :: vpot
complex*16,dimension(1:nr,1:nr) :: C_minus_E
complex*16,dimension(1:nr) :: B_vector , X_vector
integer :: ir,INFO,NRHS
integer,dimension(1:nr) :: IPIV
real*8 :: N
complex*16 :: Rmatrix , Zmatrix , Smatrix, Zmatrix_O, Zmatrix_I
complex*16 :: hc ,hc1 !H(+), H(-)
complex*16 :: hcp,hcp1 ! derivatives of H(+),H(-)
complex*16,dimension(1:nr) :: scattwf
complex*16 :: wf_bound
real*8 :: cph
complex*16,dimension(1:nr,1:nr) :: C_minus_E1 ! need to remove
complex *16 :: test
integer :: irp
logical :: nonlocal
complex*16, dimension(1:nr, 1:nr) :: nlpot
real*8 :: delta
k=sqrt(2.*mu*ecm/(hbarc**2))
hc=cmplx(gc,fc,kind=8)
hc1=cmplx(gc,-fc,kind=8)
hcp=cmplx(gcp,fcp,kind=8)
hcp1=cmplx(gcp,-fcp,kind=8)
call lagrange_V(Vpot)
call centrifugal_barrier(l,mu)
C_minus_E=0.0_dpreal
B_vector=0.0_dpreal ! fn(a) in sofia's notes
C_minus_E = kinetic_matrix + l_barrier_matrix + V_matrix
do ir=1, nr
C_minus_E(ir,ir) = C_minus_E(ir,ir) - ecm
B_vector(ir) = (-1.0_dpreal)**ir / sqrt( rmax_rmatrix* mesh_rr(ir) * ( 1.0-mesh_rr(ir) ) ) ! calculate f_n^(a) in the notes
end do
NRHS=1
X_vector= B_vector
C_minus_E1= C_minus_E
call ZGESV( nr, NRHS, C_minus_E, nr, IPIV, X_vector, nr, INFO )
If(INFO/=0) stop "error in calling ZGESV"
! test case for the zgesv
C do ir=1, nr
C test=0.0_dpreal
C do irp=1,nr
C
C test=test + C_minus_E1(ir, irp) * X_vector(irp)
C
C end do
C end do
! normalize factor
N = hbarc**2 / (2.0_dpreal * mu * rmax_rmatrix)
Rmatrix=0.0_dpreal
do ir=1,nr
Rmatrix = Rmatrix + B_vector(ir) * X_vector(ir)
end do
Rmatrix=Rmatrix * N
Zmatrix= (hc-k*rmax_rmatrix*Rmatrix*hcp) / (k*rmax_rmatrix)
Zmatrix_O=Zmatrix
Zmatrix_I= (hc1-k*rmax_rmatrix*Rmatrix*hcp1) / (k*rmax_rmatrix)
C Smatrix= CONJG(Zmatrix) / Zmatrix
Smatrix= Zmatrix_I / Zmatrix_O
delta=0.5d0*ACOS(real(Smatrix))
if (aimag(Smatrix)<0) delta=-delta+pi
DELTA=DELTA*180.0d0/pi
write(*,*) "l=",l,"Smatrix=", Smatrix
! compute the scattering wave function ! still testing
wf_bound = 0.5* iu * (hc1-hc*Smatrix) * exp(iu*cph)
do ir=1,nr
scattwf(ir)=lagrange_func(ir)*X_vector(ir)*wf_bound *N / Rmatrix
write(99,*) mesh_rr(ir)* rmax_rmatrix , real(scattwf(ir)), aimag(scattwf(ir))
end do
stop
end subroutine
c-----------------------------------------------------------------------
end module