Coulomb wave functions in momentum space

• Published in: Computer physics communications 2015-02, Vol.187 (C), p.195-203
• Main Authors: Eremenko, V., Upadhyay, N.J., Thompson, I.J., Elster, Ch, Nunes, F.M., Arbanas, G., Escher, J.E., Hlophe, L.
• Format: Article
• Language: English
• Subjects: Algorithms; Coulomb friction; Mathematical analysis; Mathematical models; MATHEMATICS AND COMPUTING; Momentum-space partial-wave Coulomb functions; Running; Summaries; Wave functions; Windows (computer programs)
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2014.10.002

An algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space is presented. The arguments are the Sommerfeld parameter η, the angular momentum l, the asymptotic momentum q and the ‘running’ momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p→q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of |η| in the range of 10−1 to 10, and thus is particularly suited for momentum space calculations of nuclear reactions. Program title: libcwfn Catalogue identifier: AEUQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUQ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 864503 No. of bytes in distributed program, including test data, etc.: 7178021 Distribution format: tar.gz Programming language: Fortran 90, Fortran 77, Python, make (GNU Make dialect), GNU Bash shell interpreter (available as /bin/bash). Computer: Apple Powermac (Intel Xeon), ASUS K53U (AMD E-350 (Dual Core)), DELL Precision T3500 (Intel Xeon), NERSC Carver (Intel Nehalem Quad Core). Operating system: Linux, Windows (using Cygwin). RAM: less than 512 Mbytes Classification: 17.8, 17.13, 17.16. Nature of problem: The calculation of partial wave Coulomb functions with integer l and all other arguments real. Solution method: Computing the value of the function using explicit formulae and algorithms. Running time: Less than 10−3  s.