Evaluation of negative energy Coulomb (Whittaker) functions

Abstract

This paper describes a code for evaluating exponentially decaying negative energy Coulomb functions and their first derivatives with respect to the radial variable. The functions, which correspond to Whittaker functions of the second kind, are obtained to high accuracy for a wide range of parameters using recurrence techniques. Program summary Title of program: whittaker_w Catalog identifier: ADSZ Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADSZ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer: Cray T3E, Sun Ultra-5_10 sparc, Origin2000, Compaq EV67, IBM SP3, Toshiba 460CDT Operating systems under which the program has been tested: Windows NT4, Redhat Linux, SunOS 5.8 Programming language used: Fortran 95 Memory required to run with typical data: 500 KB Number of bytes in distributed program, including test data, etc.: 39728 Number of lines in distributed program, including test data, etc.: 2900 Distribution format: tar gzip file Nature of physical 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. Method of solution: Recurrence relations, power series expansion, numerical quadrature. Restrictions on the complexity of the problem: 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.