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Manuscript Title: Coulomb functions (negative energies).
Authors: K.L. Bell, N.S. Scott
Program title: COUL
Catalogue identifier: AANB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 20(1980)447
Programming language: Fortran.
Computer: IBM 370/165.
Operating system: OS/MVT RELEASE 21.7.
RAM: 90K words
Word size: 8
Keywords: General purpose, Physics atomic, Reactions, Scattering, Wave function, Coulomb, Whittaker, Chebyshev, Runge-kutta.
Classification: 4.5.

Nature of problem:
The routine COUL calculates the exponentially decaying Whittaker functions VL(c, x) and their radial derivatives, where c = square root (-k**2)/Z and x = Zr, for real negative energy k2 and for all (c, x). It is well suited for all programs which require matching to asymptotic Coulomb wave functions in atomic physics.

Solution method:
The techniques employed are parameter dependent but rely heavily on the work of Curtis. The Chebyshev approximation is used wherever possible, either to evaluate the function at the input values or to obtain values to enable numerical solution of the differential equation to occur. Recourse is also made to power series expansions. In general the L=0 functions are first evaluated and then used to recur upwards in L up to the input value.

Restrictions:
Routine COUL has been programmed for real values of K**2, Z an r,k**2 must be a (non-zero) negative quantity, whilst Z and r must be real positive quantities.

Running time:
Compile time using H-extended compiler 7.0 s; using G compiler 4.0 s. Execution of sample data 0.4 s (370/165).