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Manuscript Title: COULCC: a continued-fraction algorithm for Coulomb functions of complex order with complex arguments.
Authors: I.J. Thompson, A.R. Barnett
Program title: COULCC
Catalogue identifier: ACDP_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 36(1985)363
Programming language: Fortran.
Computer: AS/7000, CRAY-1, CDC 7600.
Operating system: OS/MVT WITH VS FORTRAN.
RAM: 822K words
Word size: 32
Keywords: GENERAL PURPOSE, COULOMB, WHITTAKER, HYPERGEOMETRIC, CONTINUED FRACTION, SCATTERING, CLOSED CHANNELS, OFF-SHELL, RESONANCES, REACTIONS, REGGE POLES.
Classification: 4.5.

Revision history:
Type Tit le Reference
correction 000A CORRECTION 20/04/04 See below

Nature of problem:
The routine COULCC calculates both the oscillating and the exponentially varying Coulomb wave functions, and their radial derivatives, for complex eta(Sommerfeld parameter), complex energies and complex angular momenta. The functions for uncharged scattering (spherical Bessels) and cylindrical Bessel functions are special cases which are more easily solved. Two linearly independent solutions are found, in general, to the differential equation f''(x) + g(x) f(x) = 0, where g(x) has x**0, x**-1 and x**-2 terms, with coefficients 1, -2eta and -lambda(lambda + 1) respectively.

Solution method:
The continued fractions of Steed are supplemented, if necessary, by a 1F1 series expansion or by Pade accelerations of a 2F0 asymptotic expansion. Recurrence relations are used for integer steps in lambda in a stable manner. It should be noted that the routine will solve for a single arbitrary lambda without recurrence, if required. For small x a previous restriction on accuracy has been removed by adding a subroutine to evaluate the irregular solution (singular at x=0) by a suitable combination of series.

Restrictions:
On the Coulomb bound-state poles the functions are singular (from their boundary conditions). The program returns the residue polynomial but only one solution exists, and it is found.

Running time:
A direct comparison of COULCC and its predecessor for real arguments shows an increase by a factor of 2 for the new code. The test deck (comprising 36 test values and excluding the error condition) took 1.14 sec for execution on the NAS 7000 and 2.2 sec on the CDC 7600.

CORRECTION SUMMARY
Manuscript Title: COULCC: a continued-fraction algorithm for Coulomb functions of complex order with complex arguments.
Authors: I.J. Thompson
Program title: 000A CORRECTION 20/04/04
Catalogue identifier: ACDP_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 159(2004)241
Classification: 4.5.