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ws_fields.f90
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ws_fields.f90
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module fields
use ws_param
use densita
real (pr) :: t0,x0,t1,t2,x1,x2,t3,x3
real (pr) :: W,gamma,dmshb0
integer :: ifecm,j2terms,ixtls
character*4 force
!
!!
!
real (pr) :: a0,b0,a1,b1
real (pr) :: a2,b2,a3,b3
!
real (pr) :: af1,af2,af3,af4,af5,af6
real (pr) :: af7,af8,af9,af10,af11
real (pr) :: bf1,bf2,bf3,bf4,bf5,bf6,bf7,bf8
real (pr) :: bf9,bf10,bf11,bf14
contains
subroutine buildfield
implicit none
end subroutine buildfield
!------------------------------------------------------------------
subroutine set_force
!this routine fix the parameters of the Skyrme force
! input and output are passed with the module skyrmepar
implicit none
gamma = 1.0d0
dmshb0 = 1.0d0 / 20.7355300000d0
w = 0.0d0
!
!! These three parameters are for testing purposes only...
!
!NOTA: if ifecm=0 it means that we make the one body c.o.m correction
! dmshb = dmshb0 / ( 1- 1 /A )
!
select case (trim(force))
!
case ("t0t3")
j2terms = 0
t0 = -1132.400
x0 = 0.d0
t1 = 0.d0
x1 = 0.000000d0
t2 = 0.d0
x2 = 0.000000d0
t3 = 23610.40d0
x3 = 0.000000d0
w = 0.000000d0
gamma = 1.000000d0
!
ixtls = 0
ifecm = 0
case ("SIII")
!
!! SIII SET OF PARAMETERS
!
j2terms = 0
!
t0 = -1128.750000d0
x0 = 0.450000d0
t1 = 395.000000d0
x1 = 0.000000d0
t2 = -95.000000d0
x2 = 0.000000d0
t3 = 14000.000000d0
x3 = 1.000000d0
w = 120.000000d0
gamma = 1.000000d0
!
ixtls = 0
ifecm = 0
case ("SLY4")
!
!! SLY4 SET OF PARAMETERS
!
j2terms = 0
!
t0 = -2488.913000d0
x0 = 0.834000d0
t1 = 486.818000d0
x1 = -0.344000d0
t2 = -546.395000d0
x2 = -1.000000d0
t3 = 13777.000000d0
x3 = 1.354000d0
w = 123.000000d0
gamma = 1.0d0 / 6.0d0
!
dmshb0 = 1.0d0 / 20.7355300000d0
!
ixtls = 0
ifecm = 0
case ("SLY5")
!
!! SLY5 SET OF PARAMETERS
!
j2terms = 1
!
t0 = -2483.450000d0
x0 = 0.776000d0
t1 = 484.230000d0
x1 = -0.317000d0
t2 = -556.690000d0
x2 = -1.000000d0
t3 = 13757.000000d0
x3 = 1.263000d0
w = 125.000000d0
!
gamma = 1.0d0 / 6.0d0
!
dmshb0 = 1.0d0 / 20.7355300000d0
!
ixtls = 0
ifecm = 0
!
case ("SKM*")
!
j2terms = 0
!
t0 = -2645.00d0
x0 = 0.09d0
t1 = 410.00d0
x1 = 0.00d0
t2 = -135.00d0
x2 = 0.00d0
t3 = 15595.00d0
x3 = 0.00d0
w = 130.00d0
gamma = 1.0d0 / 6.0d0
!
ixtls = 0
ifecm = 0
!
case ("WSso")
!
j2terms = 0
t0 = -1132.400
x0 = 0.d0
t1 = 0.d0
x1 = 0.000000d0
t2 = 0.d0
x2 = 0.000000d0
t3 = 23610.40d0
x3 = 0.000000d0
w = 0.000000d0
gamma = 1.000000d0
!
case default
!
print *, "Unknown force..."
stop
!
end select
!
call paramaux
return
end subroutine set_force
subroutine paramaux
! this routine is used to initialize some parameters used with Skyrme
! no input required, the parameters are initialized in the module
! skyrmepar
implicit none
a0 = t0 * ( 2.d0 + x0 ) / 4.d0
b0 = - t0 * ( 2.d0 * x0 + 1.d0 ) / 4.d0
a1 = ( t1 * ( 2.d0 + x1 ) + t2 * ( 2.d0 + x2 ) ) / 8.d0
b1 = - ( t1 * ( 2.d0 * x1 + 1.d0 ) - t2 * ( 2.d0 * x2 + 1.d0 ) ) / 8.d0
a2 = ( 3.d0 * t1 * ( 2.d0 + x1 ) - t2 * ( 2.d0 + x2 ) ) / 32.d0
b2 = - ( 3.d0 * t1 * ( 2.d0 * x1 + 1.d0 ) + t2 * ( 2.d0 * x2 + 1.d0 ) ) / 32.d0
a3 = t3 * ( 2.d0 + x3 ) / 24.d0
b3 = - t3 * ( 2.d0 * x3 + 1.d0 ) / 24.d0
!
af1 = t0 * ( 2.d0 + x0 ) / 4.d0
af2 = - t0 * ( 2.d0 * x0 + 1.d0 ) / 4.d0
af3 = t3 * ( 2.d0 + x3 ) / 24.d0
af4 = - t3 * ( 2.d0 * x3 + 1.d0 ) / 24.d0
af5 = ( t1 * ( 2.d0 + x1 ) + t2 * ( 2.d0 + x2 ) ) / 8.d0
af6 = - ( 3.d0 * t1 * ( 2.d0 + x1 ) - t2 * ( 2.d0 + x2 ) ) / 32.d0
af7 = - ( t1 * ( 2.d0 * x1 + 1.d0 ) - t2 * ( 2.d0 * x2 + 1.d0 ) ) / 8.d0
af8 = ( 3.d0 * t1 * ( 2.d0 * x1 + 1.d0 ) + t2 * ( 2.d0 * x2 + 1.d0 ) ) / 32.d0
!
if ( j2terms == 1 ) then
af9 = - ( t1 * x1 + t2 * x2 ) / 16.d0
af10 = ( t1 - t2 ) / 16.d0
else
af9 = 0.d0
af10 = 0.d0
end if
!
!!
!
af11 = - w / 2.d0
!
!!
!
bf1 = 2.d0 * af1
bf2 = 2.d0 * af2
bf3 = ( 2.d0 + gamma ) * af3
bf4 = 2.d0 * af4
bf5 = af5
bf6 = 2.d0 * af6
bf7 = af7
bf8 = 2.d0 * af8
bf9 = 2.d0 * af9
bf10 = 2.d0 * af10
bf11 = - af11
bf14 = gamma * af4
return
end subroutine paramaux
!
!!
!
subroutine HFBpotentials(Ngrid1,del1,xmu,Nprot,Neutr,total_energy)
!=========================================================
!abstract: routine that calculates the HF potentials
! based on a skyrme interaction, it calculates the total
! energy using the functional
!
!input
!Ngrid1,del1: box dimension and mesh
!xmu: mixing among the old and new fields
!Nprot,Neutr: N,Z
!output
!total_energy: total energy using the functional
!========================================================
implicit none
integer :: isospin,ngrid1,i,Amass,Nprot,Neutr
real (pr) :: del1,xmu,eps,r,coef,sum1,sum2,t13,t43
real (pr) :: hb,ymu
real (pr), allocatable :: rho_tot(:),rho_gamma(:)
real (pr), allocatable :: tau_tot(:),cur_tot(:)
real (pr), allocatable :: drho(:,:),dtau(:,:),dcur(:,:)
real (pr), allocatable :: d2rho(:,:),d2tau(:,:),d2cur(:,:)
real (pr), allocatable :: tmp(:),drho_tot(:),d2rho_tot(:)
real (pr), allocatable :: dcur_tot(:)
real (pr), allocatable :: VCx(:),HMENx(:,:),VNx(:,:),VSONx(:,:)
real (pr), allocatable :: dhmenx(:,:),d2hmenx(:,:)
real (pr) :: ex_coulomb_energy,coulomb_energy ! for the energy
real (pr) :: kinetic_energy(0:1),kinetic_energy_tot
real (pr) :: spin_orbit_energy,r2,dmshb
real (pr) :: h_rho,h_rhotau,h_drho,h_gamma,h_so
real (pr) :: field_energy, total_energy
!Nota: i prefer to use new vectors
eps = spacing( 1.0d0 )
t13 = 1.d0/3.d0
t43 = 4.d0/3.d0
coef = - 0.75d0 * ( 3.d0 / pi )**t13 * echarg ! Slater coefficient Coulomb potential
total_energy=0.d0
ymu= 1.d0-xmu
amass=Nprot+Neutr
if ( ifecm == 0 ) then ! center of mass correction
dmshb = dmshb0 / ( 1.0d0 - 1.0d0 / amass )
else
dmshb = dmshb0
end if
hb = 1.0d0 / dmshb
allocate(rho_tot(ngrid1),rho_gamma(ngrid1), &
tau_tot(ngrid1),cur_tot(ngrid1), &
drho(ngrid1,0:1),dtau(ngrid1,0:1),dcur(ngrid1,0:1), &
d2rho(ngrid1,0:1),d2tau(ngrid1,0:1),d2cur(ngrid1,0:1), &
tmp(-1:ngrid1),drho_tot(ngrid1),d2rho_tot(ngrid1) &
,dcur_tot(ngrid1))
allocate(VCx(ngrid1),HMENx(ngrid1,0:1),VNx(ngrid1,0:1),VSONx(ngrid1,0:1), &
dHMENx(ngrid1,0:1),d2HMENx(ngrid1,0:1))
do i=1,ngrid1
rho_tot(i)=rho(i,0)+rho(i,1)
rho_gamma(i)=rho_tot(i)**gamma
tau_tot(i)=tau(i,0)+tau(i,1)
cur_tot(i)=cur(i,0)+cur(i,1)
enddo
!---- calculation of the derivatives ----------------------------
!
!! The densities rho and \tilde\rho are extrapolated to 0 using
!! a forth order polynomial P(x) with the assumptions:
!! P'(0) = 0
!! P(-h) = P(h)
!! Outside the box, they are set to 0.
!
!! For J and \tilde J, the extrapolation is:
!! P(0) = 0
!! P(-h) = -P(h)
!
!! The derivatives of the densities nabla(rho), nabla(\tilde\rho),
!! Delta(rho) and Delta(\tilde\rho)
!! are computed using a 5 points formula.
!
do isospin=0,1
do i=1,ngrid1
tmp(i) = rho(i,isospin)
enddo
tmp(-1) = tmp(1)
tmp(0) = ( 15.d0 * tmp(1) - 6.d0 * tmp(2) + tmp(3) ) / 10.d0
call d1_and_d2(ngrid1,del1, tmp, drho(:,isospin), d2rho(:,isospin))
!
do i=1,ngrid1
tmp(i) = tau(i,isospin)
enddo
tmp(-1) = tmp(1)
tmp(0) = ( 15.d0 * tmp(1) - 6.d0 * tmp(2) + tmp(3) ) / 10.d0
call d1_and_d2(ngrid1,del1, tmp, dtau(:,isospin), d2tau(:,isospin))
!
do i=1,ngrid1
tmp(i) = cur(i,isospin)
enddo
tmp(-1) = - tmp(1)
tmp(0) = 0.0d0
call d1_and_d2(ngrid1,del1, tmp, dcur(:,isospin),d2cur(:,isospin))
enddo
do i=1,ngrid1
drho_tot(i)=drho(i,0)+drho(i,1)
d2rho_tot(i)=d2rho(i,0)+d2rho(i,1)
dcur_tot(i)=dcur(i,0)+dcur(i,1)
enddo
!--------------------------------------------------------------------
! Coulomb (direct potential)
vcx=0.d0
sum1 = 0.0d0 ! the funny integral is taken in Skalski paper PRC63 2001
sum2 = 0.0d0
do i = 1, ngrid1
r=i*del1
sum1 = sum1 + fourpi * r*r * rho(i,1)
sum2 = sum2 + fourpi * r * rho(i,1)
vcx(i) = sum1 / r - sum2
end do
do i=1,ngrid1
vcx(i) = echarg * del1 * ( vcx(i) + sum2 )
enddo
!----- here i calculate the energy using the energy functional
!
!!............................................. Energy
!
if ( minval(rho_tot) < -1.E-10 ) then
print '(" Negative density in subroutine ENERGY in points:")'
do i = 1, ngrid1
if ( rho_tot(i) < -1.E-10 ) print *, i
end do
end if
!
!!............................Exchange and Direct Coulomb energy
!
coulomb_energy = 0.d0
ex_coulomb_energy = 0.d0
do i=1,ngrid1
r=i*del1
r2=r*r
coulomb_energy =coulomb_energy +vcx(i) * rho(i,1) * r2 / 2.0d0
ex_coulomb_energy = ex_coulomb_energy+ rho(i,1)**t43 * r2 * coef
enddo
!
!!............................................. Kinetic energy
kinetic_energy(0)=0.d0
kinetic_energy(1)=0.d0
do i=1,ngrid1
r=i*del1
r2=r*r
kinetic_energy(0)=kinetic_energy(0)+tau(i,0)*hb*r2! neutrons
kinetic_energy(1)=kinetic_energy(1)+tau(i,1)*hb*r2! protons
enddo
kinetic_energy_tot=kinetic_energy(0) + kinetic_energy(1)
!
!!............................................. Spin orbit energy
!
if ( ixtls == 0 ) then
spin_orbit_energy =0.d0
do i=1,ngrid1
r=del1*i
r2=r*r
spin_orbit_energy = spin_orbit_energy + r2 * af11 * ( cur_tot(i) * drho_tot(i) &
+ cur(i,0) * drho(i,0) + cur(i,1) * drho(i,1) )
enddo
else
stop 'errore'
end if
!
!!............................................. Field energy
!
field_energy = 0.d0
do i=1,ngrid1
r=del1*i
r2=r*r
h_rho = a0 * rho_tot(i)**2 + b0 * ( rho(i,0)**2 + rho(i,1)**2 )
!
h_rhotau = a1 * rho_tot(i) * tau_tot(i) &
+ b1 * ( rho(i,0) * tau(i,0) + rho(i,1) * tau(i,1) )
!
h_drho = a2 * drho_tot(i)**2 + b2 * ( drho(i,0)**2 + drho(i,1)**2 )
!
h_gamma = a3 * rho_gamma(i) * rho_tot(i)**2 &
+ b3 * rho_gamma(i) * ( rho(i,0)**2 + rho(i,1)**2 )
!
h_so = af9 * cur_tot(i)**2 + af10 * ( cur(i,0)**2 + cur(i,1)**2 )
field_energy=field_energy+( r2 * ( h_rho + h_rhotau + h_drho &
+ h_gamma + h_so ) )
enddo
!
!!............................................. Rearrangement energy
!
!
!!
!
kinetic_energy_tot = kinetic_energy_tot * del1 * fourpi !
field_energy = field_energy * del1 * fourpi !
spin_orbit_energy = spin_orbit_energy * del1 * fourpi !
coulomb_energy = coulomb_energy * del1 * fourpi !
ex_coulomb_energy = ex_coulomb_energy * del1 * fourpi !
!
total_energy = kinetic_energy_tot + field_energy &
+ spin_orbit_energy + coulomb_energy + ex_coulomb_energy
!
!
!-- calculation of the fields ----------------------------------------
!
do isospin = 0,1
do i=1,ngrid1
r=i*del1
!
!!.................................................... Central field
!
vnx(i,isospin) = rho_tot(i)* & ! central field
( bf1 + bf3 * rho_gamma(i)) &
+ rho(i,isospin) &
* ( bf2 + bf4 * rho_gamma(i)) &
+ rho_gamma(i) * ( bf14 * ( rho(i,0)**2 + rho(i,1)**2 ) &
) / ( rho_tot(i) + eps ) &
+ bf5 * tau_tot(i) &
+ bf6 * ( d2rho_tot(i) + 2.d0*drho_tot(i) / r ) &
+ bf7 * tau(i,isospin) &
+ bf8 * ( d2rho(i,isospin) + 2.d0 * drho(i,isospin) / r ) &
+ isospin * (vcx(i) + t43 * coef * rho(i,1)**t13 )
!
!!................................................. Effective mass
!
Hmenx(i,isospin) = bf5 * rho_tot(i) + bf7 * rho(i,isospin) + hb
!
!!................................................. Spin orbit
!
if ( ixtls == 0 ) then
vnx(i,isospin) = vnx(i,isospin) &
+ bf11 * ( dcur_tot(i) + dcur(i,isospin) &
+ 2.d0 * ( cur_tot(i) + cur(i,isospin) ) / r )
vsonx(i,isospin) = bf9 * cur_tot(i) + bf10 * cur(i,isospin) &
- bf11 * ( drho_tot(i) + drho(i,isospin) )
else
stop 'error'
end if
! to make compatible the spin orbit potential with the one used
! by the code in the routine boundary i have to multiply for the factor
! -2/r
vsonx(i,isospin)=-2.d0*vsonx(i,isospin)/r
dhmenx(i,isospin)=bf5 * drho_tot(i) + bf7 * drho(i,isospin)
d2hmenx(i,isospin)=bf5 * d2rho_tot(i) + bf7 * d2rho(i,isospin)
enddo
do i=1,ngrid1
r=i*del1
vnx(i,isospin)=vnx(i,isospin)+ dhmenx(i,isospin)/r
enddo
end do
!putting together Direct Coulomb and exchange
do i=1,ngrid1
vcx(i)=vcx(i) + t43 * coef * rho(i,1)**t13
enddo
!--- mixing the old filed with the new one
! rewind(1000)
! rewind(1001)
do isospin=0,1
do i=1,ngrid1
r=i*del1
!if(ifixws.eq.1)then
Vpot(i,isospin) = xmu*vnx(i,isospin)+ymu*vpot(i,isospin)
vso(i,isospin) = xmu*vsonx(i,isospin)+ymu*vso(i,isospin)
hb2m(i,isospin) = xmu*hmenx(i,isospin)+ymu*hb2m(i,isospin)
dhmen(i,isospin) = xmu*dhmenx(i,isospin)+ymu*dhmen(i,isospin)
d2hmen(i,isospin) = xmu*d2hmenx(i,isospin)+ymu*d2hmen(i,isospin)
! write(1000+isospin,*)r,Vnx(i,isospin),vsonx(i,isospin),hmenx(i,isospin),dhmenx(i,isospin),d2hmenx(i,isospin)
if(isospin.eq.1)then
vc(i)=xmu*vcx(i)+ymu*vc(i)
endif
!endif
enddo
enddo
!11 format(1x,I6,3(1x,F20.15))
!---- deallocating the memory ------------------------------
deallocate(VCx,HMENx,VNx,VSONx,dHmenx,d2Hmenx)
deallocate(rho_tot,rho_gamma,tau_tot,cur_tot, &
drho,dtau,dcur,d2rho,d2tau,d2cur,tmp &
,drho_tot,d2rho_tot,dcur_tot)
return
end subroutine HFBpotentials
!
!!
!
end module fields