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Manuscript Title: Evaluation of negative energy Coulomb (Whittaker) functions.
Authors: C.J. Noble
Program title: whittaker_w
Catalogue identifier: ADSZ
Journal reference: Comput. Phys. Commun. 159(2004)55
Programming language: Fortran 95.
Computer: Cray T3E, Sun Ultra-5_10 sparc, Origin2000, Compaq EV67, IBM SP3, Toshiba 460CDT.
Operating system: Windows NT4, Redhat Linux, SunOS 5.8.
Keywords: Negative energy, General purpose, Whittaker, Confluent hypergeometric, Recurrence, Continued fraction, Matching, R-matrix, Coulomb.
Classification: 4.5.

Nature of problem:
The closed-channel components of the asymptotic radial wave function corresponding to electron or positron scattering by atomic or molecular ions may be expressed in terms of negative energy Coulomb functions. The scattering observables are obtained from S or T matrices which in turn are obtained by matching the radial and asymptotic wavefunctions at a finite radial point. Recent large scale scattering calculations have required accurate values of the Coulomb functions at smaller ρ values and larger negative η values than previous work. The present program is designed to extend the range of parameters for which the function may be calculated.

Solution method:
Recurrence relations, power series expansion, numerical quadrature.

The program has been tested for the parameter ranges 0<ρ<= 1000,| η|<= 120 and 0<= l <= 100. These ranges may, with appropriate scaling to avoid underflow and overflow, be extended.