An accurate Fortran code for computing hydrogenic continuum wave functions at a wide range of parameters

Abstract

Abstract The accurate computations of hydrogenic continuum wave functions are very important in many branches of physics such as electron-atom collisions, cold atom physics, and atomic ionization in strong laser fields, etc. Although there already exist various algorithms and codes, most of them are only reliable in a certain ranges of parameters. In some practical applications, accurate continuum wave functions need to be calculated at extremely low energies, large radial distances and/or large angular momentum number. Here we provide such a code, which can generate accurate hydrogenic continuum wave functions and corresponding Coulomb phase shifts at a wide range of parameters. Without any essential restrict to angular momentum number, the present code is able to give reliable results at the electron energy range [ 10 − 3 , 10 3 ] eV for radial distances of [ 10 − 2 , 10 4 ] a.u. We also find the present code is very efficient, which should find numerous applications in many fields such as strong field physics. Program summary Program title: HContinuumGautchi Catalogue identifier: AEHD_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEHD_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.: 1233 No. of bytes in distributed program, including test data, etc.: 7405 Distribution format: tar.gz Programming language: Fortran90 in fixed format Computer: AMD Processors Operating system: Linux RAM: 20 MBytes Classification: 2.7, 4.5 Nature of problem: The accurate computation of atomic continuum wave functions is very important in many research fields such as strong field physics and cold atom physics. Although there have already existed various algorithms and codes, most of them can only be applicable and reliable in a certain range of parameters. We present here an accurate FORTRAN program for calculating the hydrogenic continuum wave functions in a very wide range of parameters, which suffices the needs of most practical applications. The Coulomb phases are also calculated. For any given momentum, radial point, and the largest angular momentum number, the code calculates all the angular components at once. The algorithm we adopt has been given in details by Gautchi [1,2], who suggested a stable minimal solution of general three term recurrence relations. Solution method: Minimum solution of three-term recurrence relations developed by W. Gautchi [1,2]. Running time: A few seconds to a few minutes, depending how many different wave functions one needs to calculate.