      Documentation for program NUMCBAS  L A Morgan, J. D. Gorfinkiel

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Evaluation/calculation of Bessel and Coulomb functions. Numerical 
integration of the Schrödinger equation from both boundaries and matching 
using de Vogelaere’s algorithm. The program is mainly used to generate
the nhumerical functions to be fitted by GTOBAS.

For a more detailed description of the program see: Faure et al.,
Computer Physics Communications 144 (2002) 224–241.

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      Input is via the NAMELIST /INPUT/

      Format of attributes of entities listed below is 
        Name  Type  Length  [Limits]  Default ! description

      NAMELIST/INPUT/

        TITLE   C    80                  
                 ! title for output

        LUNUMB  I     1            13           
                 ! output unit number for numerical orbitals

        CHARGE  R     1             0.
                 ! Effective charge of the target

        LVAL    I     1             0
                 ! angular momentum

        RLIM    R     1            10.  
                 ! R-matrix radius

        ECMAX   R     1            10.
                 ! upper bound for eigenvalues (Ryd)

        TINY    R     1            1.D-11
                 ! eigenvalue convergence accuracy

        IBUG    I     3            0   
                 ! switches for extra printed output,
                   (1) - potential as function of r
	           (2) - final eigen-solutions as functions of r
                   (3) - brief summary of data written to NFTC


        NIX      I    1  [1:10]    3
                  ! number of subranges to be used.

        IRX      I   10            0.01,0.02,0.02605,7*0.
                  ! number of mesh points to end of each subrange (must
                    be divisible by 2)

        HRX      R   10            30,120,500,7*0
                  ! step length to be used in each subrange

        BTOL    R     1            0.2
                 ! maximum difference between b parameters acceptable
                   at start of final iteration to find eigenvalues

                    
Examples
________

1) Coulomb functions for l=4 and maximum energy 4 Ryd on range 0-12 bohr

 &input
  TITLE='Ionic target l=4, RMAT=10.0',
  lval=4,               
  ECMAX = 4.0D0, CHARGE=1.d0, 
  RLIM = 12.0D0,
 /


2) Bessel functions (model potential = zero) for l=0 and maximum energy 4 Ryd
on range 0-12 bohr
 

cat > basis.data << EOF
 &INPUT
  title='Neutral target',
  lval=0,
  ecmax=4.0D0,
  rlim=12.0D0,
  chrage=0.0D0,
 /


