3 Input Specifications

FORTRAN 90 namelist input in all cases.
In the descriptions below, R=real, I=integer, L=logical, S=string with ' ' marks.
Arrays are indicated by dimensions, e.g. (1:2).
The notation [R;0.05] Means a real variable with default value 0.05.

Example of Essential Input variables

 &mefile fpot = '1-_l1s0j1t' /
 &sturmin
  Eo(1)=-1.0 egsmin=-1.0 egsmax=+0.0   sturm(1)='T' nsturm=20, 
  stepi = 0.05, rmax=20, wfrmax=40  
  ebeg=0.5 estep=-0.5 emax=5.0 /

Namelist MEFILE:

fpot

[S]: Input files are fpot.spec for channel specifications, fpot.mel for matrix elements, and fpot.occ for forbidden-state projection operators. After some header information in the spec file, successive $J^\pi$ sets are concatenated in all these files.

Namelist STURMIN

Common information:

potcoef(1:npots)

[R;npots*1.0] Coefficients of the npots different potential components in the fpot.mel file. (New in version 83)

kdiag,vdiag(1:2),rdiag(1:2),adiag,nidiag [I,5*R,I; 3,5*0.,0]

Diagonal potential to add to all channels. kdiag=0 for Coulomb, 1 for Woods-Saxon, 2 for Gaussian and 3 for regularised inverse cubic $(r/{\tt rdiag})^{\tt nidiag}/ (1 +(r/{\tt rdiag})^{(3+{\tt nidiag})})$.
Use vdiag(1),rdiag(1) for first $J^\pi$ set, and vdiag(2),rdiag(2) for all others.

Eo(1:2)

[R; 0.,0.]: Energy for sturmians or for logarithmic derivatives
Use Eo(1) for first $J^\pi$ set, and Eo(2) for all others.

sturm(1:2)

[S; 'F','F']:
T=Calculation using sturmian basis;
F=Use basis of energy eigenstates in each channel's diagonal potential;
L=Use Laguerre orthonormal basis.
Use sturm(1) for first $J^\pi$ set, and sturm(2) for all others
Use only sturm='F' when scattering required.

simeq

[L;F] Use linear-equations method to find R-matrix for just one scattering energy, ignoring all eigenvalues.

egsmin

[R;-1] Lower bound on energy of eigenvalues to examine in detail.

egsmax

[R;0.] Upper bound on energy of eigenvalues to examine.

ngsmax

[I;0] Number of eigenvalues to find:
If ngsmax = 0, find all eigenvalues by complete diagonalisation,
If ngsmax = 1 or (estep<0 and this is the first $J^\pi$ set):
use inverse iteration to find eigenstate nearest to egsmin,
If ngsmax = 2 ... 25% of all eigenvalues, use diagonalisation and bisection search to find eigenstates in interval [egsmin,egsmax].
Warning: scattering calculations are only accurate up to $\sim \frac{1}{4}$ of maximum eigenenergy found.
If ngsmax > 25% of all eigenstates, find them all by complete diagonalisation.

meigs

[I;0] Maximum number of eigenvectors to store for a $J^\pi$. If zero, store all eigenvectors.

eeigmax

[R;5000. for 2-body, else 50.] Maximum energy of eigenvector to find for a $J^\pi$

maxset

[I;0] Maximum number of $J^\pi$ sets to be solved. If zero, solve for all sets.

rmax

[R;20.] Maximum radius, used for R-matrix calculations. All couplings up to rmax are always included.

numax

[I;3] Maximum power $\nu=\lambda+1$ for exterior $r^{-\nu}$ extrapolations of exterior coupling potentials.

wfrmax

[R;40.] Maximum radius for wave functions for bound states and matrix elements. Asymptotic forms are used if necessary to extrapolate beyond rmax.

rafin

[R;20.] If rafin > rmax, use asymptotic methods for the radial range rmax <r< rafin. rafin may be extended up to rafix if necessary for convergence.

stepi

[R;0.05] Radial step size for basis states

steps

[R;1.0] Radial step size for storing bound and continuum wave functions.

tinside

[R;-1] If positive, start radial integrations at this distance inside a classical turning point. If starting point is greater than rmax, use uncoupled ADW approximation for the R-matrix, and omit the interior diagonalisation. (You must use asymptotic methods in order then to get non-zero phase shifts!)

lprwf

[I;1] Printing wavefunctions. 0=none; 1=bound-state wfns in file 11;
2=diagonal continuum wfs in file 9; 3=all continuum wfs in file 8.

mlpr

[I;1] Maximum L/K value of channel to print when lprwf=3

prns

[L;F] Print norm matrix for Faddeev equations

fadex

[I;1] Number of Faddeev components to use for solutions

Parameters for interior basis states:

nsturm

[I;20] Number of basis states for each channel, which have 1...nsturm nodes.
If nsturm=0, then start with ADW R-matrix at rmax.

pertcent

[L;F] Move centrifugal barrier from basis potentials to perturbation (useful for strong couplings), so all channels have the same set of radial basis functions.

cutl

[R;1.6] See cutr.

cutr

[R;0] Lower radius for counting nodes of basis wave functions is max(cutr,cutl*stepi*L).

pralpha

[L;F] Print alpha(*) for each basis state to file 4, details of searching for basis states to file 2.

pripot

[L;F] Print all coupling potentials to file 3.

prsturm

[L;F] Print basis wave functions in file 160+channel number

prmats

[L;F] Print normalisation matrix MM and Hamiltonian matrix AA in file 6.

Parameters for Sturmian potentials:

Vsturm

[R;-50.] Depth of central potential for Sturmians.

rsturm

[R;1.2] Reduced radius r₀ for Sturmian potential

asturm

[R;0.6] Diffuseness a for Sturmian potential.

A

[R;10.] Use WS radius R = r₀ A^1/3 for Sturmian potential.

kind

[I;9] Kind of Sturmian potential: 0=Coulomb, 1=Woods-Saxon, 2=Channel diagonal potential, 3=Constant (-1), 4=read in file 36, 5=r^-3 shape, 6=lowest eigenenergy surface, 9=Coulomb(0) for sturm='T' and diagonal(2) for 'F'. (If kind=2, the diagonal potentials must all be sufficiently attractive).

Parameters for scattering calculations:

ebeg

[R;0.1] First scattering energy (MeV).

estep

[R;0.1] Average increment in energy. The energies used will actually be linear in $k \sim \sqrt{E}$.

emax

[R;0.0] Maximum scattering energy

elinear

[L;F] Linear E steps, rather than linear in k.

rmaxsc

[R;0.0] Maximum radius for scattering $J^\pi$ sets. If zero, use rmax.

nogscat

[L;F for 2-body, else T] no scattering for first $J^\pi$ set. Such scattering is also disabled by estep<0.

Buttle

[I;5] 0=no Buttle correction; Buttle=number of interpolation points between poles of uncoupled problem. Buttle=5 usually sufficient. If Buttle<0, do `exact energy' rather than interpolated correction. Note: Buttle corrections only available with energy eigenstate basis (sturm=F), so scattering calculations only advised with that basis.

prbut

[L;F] Print details of Buttle corrections

prrm

[L;F] Print R-matrix for each energy in file 6.

prkm

[L;F] Print K-matrix for each energy in file 6.

prtm

[L;F] Print S-matrix for each energy in file 6.

prtran

[L;F] Print details of B(Ek) calculations

nftt

[I;0] File number for binary storage of S/T-matrix elements

minnop

[I;6] Minimum number of channels with plane waves, if more than this number of channels

maxnop

[I;20] Maximum number of channels with plane waves.

turnmax

[R;-40] Minimum turning point distance to keep a channel. If <0, keep all.

rinte

[R;10.] Radius for integration of diagonal wfs to get `interior norms'

e1only

Calculate only B(E1,2) g.s. $\rightarrow$ E matrix elements, and not any continuum wavefunctions. Only effective if no asymptotic propagations.

wfs

[L;F] Calculate continuum wavefunctions in steps of steps (slow) (Set true, if strfun or rtrans > htrans).

strfun

[L;F] Calculate `strength functions' in steps of steps (slower)

discrete

[L;F] Calculate discrete responses to discretised-continuum eigenstates

htrans,rtrans

[R,R; 0.1,0.] If rtrans > htrans, calculate gs to continuum transition densities in radial steps of htrans up to rtrans (slowest)

prrexp

[L;F] Print R-matrix, Buttle parameters and asymptotic couplings powers in files 150

Parameters for asymptotic propagations:

Asymptotic propagators are only used if rafin > rmaxsc, and for scattering require Eo = 0.

xlrgs

[L;T] Apply to bound state searches too.

ewron

[R;10^-6] The error in the multichannel Wronskian must be less than ewron for all channels for convergence of the asymptotic wavefuncion. The smaller that ewron is set the larger the radius of convergence and the distance of propagation.

betalw

[R;10^-6] Accuracy parameter for Light-Walker propagators

prwr

[L;F] Print Wronskian errors

rafix

[R;10⁵] Absolute maximum radius for evaluating Gailitis expansions

rfact

[R;1.2] Fractional increment to radius for trial evaluation of Gailitis expansions, if the test on the Wronskian fails.

gfact

[R;.3] Factor which decides whether the final radius, rafin, should be the value estimated for the current energy or the value at which the previous energy converged. If the ratio of the maximum coefficient in the Gailitis expansion for the current energy to that of the previous energy is > gfact the radius for the previous energy is taken.

maxtry

[I;100] Maximum number of increments for trial evaluation of Gailitis expansions

degeny

[R;10^-5] Thresholds closer than degeny will be taken as degenerate. With small threshold differences solutions converge at large radii resulting in large propagation distances.

cuplim

[R;0.] Closed channels with a coupling with open channels less than cuplim may be dropped during propagation by the LW method.

deplim

[R;0.] Closed channels more deeply bound than deplim may be dropped during propagation by the LW method.

flwp

[S,'lwra'] File name for scratch storage of LW sectors

flwpr

[S,'lwrmats'] File name for scratch storage of LW global propagators

idiscr

[I;71] File number for flwp; idiscr+1 is file number for flwpr.

prwf

[L;F] Print wave functions after global propagations

prbc

[L;F] Print bound-state combination coefficients

debug

[L;F] Information of LW propagators.

prntv

[L;F] Print local diagonalisations for LW method

apflg(1:5)

[I;0,0,0,1,0] For debug prints in GAL library:

iapflg(1)

=1 print expansion coefficients in subroutine GAILCO.

iapflg(2)

=1 NOT USED.

iapflg(3)

=1 print asymptotic wavefunctions.

iapflg(4)

=1 calculate errors in the wavefunctions and print if greater than apeps described next.

apeps

[R;10^-6] Errors in the wavefunctions greater than apeps are printed under the debug flag apflg(4).

ipflg

[I;0] Print information on Gailitis expansions

iasy

[I;50] Number of terms in expansion of asymptotic wave function (An even number). This number depends on the largest floating point number possible on the machine. If overflow is about to occur the program stops with the instruction to reset iasy to a smaller value.

ncol

[I;10] Number of columns for printing some matrices

msurf

[I;0] Do Not use

mblock

[I;0] Do Not use

efermi

[R;0.] Do Not use

Namelist BSTATE:

Parameters for asymptotic bound state propagations:

Bound state asymptotic propagators are only used if xlrgs, if rafin > rmax, if no bound state has yet been found, and if the interior diagonalisation has found a negative-energy eigenstate.
The bound-state asymptotic propagators can use any Eo value.

emin

[R;egsmin] Minimum bound state energy

emax

[R;egsmax] Maximum bound state energy

ne

[I;10] Number of energy points in first scan. Use bisection if determinant is found to change sign between any two of these points.

eps

[R;10^-5] Accuracy criterion to terminate bisection search

kpole

[I;1] Look for bound state near eigenstate number kpole of interior diagonalisation.

idiag

[I;1] Trace details of bound-state search

ibslt

[I;ngsmax] Number of bound states to find

numaxgs

[I;4] Maximum power $\nu$ of $r^{-\nu}$ couplings included in Gailitis expansions for bound states.