Coulomb wave functions in momentum space

Abstract

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 SummaryProgram title: libcwfnCatalogue identifier: AEUQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUQ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 864503No. of bytes in distributed program, including test data, etc.: 7178021Distribution format: tar.gzProgramming 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 MbytesClassification: 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.