A program to compute exact hydrogenic radial integrals and Einstein coefficients

• Published in: Computer physics communications 2009-10, Vol.180 (10), p.2020-2020
• Main Author: Dy, Hoang-Binh
• Format: Article
• Language: English
• Subjects: Astrophysics; Einstein coefficients; Hydrogenic radial integrals; Lifetimes; Physics
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2009.06.003

An exact expression for the dipole radial integral of hydrogen has been given by Gordon [Ann. Phys. 2 (1929) 1031]. It contains two hypergeometric functions F ( a , b ; c ; x ) , which are difficult to calculate directly, when the (negative) integers a, b are large, as in the case of high Rydberg states of hydrogenic ions. We have derived a simple method [D. Hoang-Binh, Astron. Astrophys. 238 (1990) 449], using a recurrence relation to calculate exactly F, starting from two initial values, which are very easy to compute. We present here a numerical code using this method. The code computes exact hydrogenic radial integrals, oscillator strengths, Einstein coefficients, and lifetimes, for principal quantum numbers up to 1000. Program title: ba5.2 Catalogue identifier: ADUU_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADUU_v2_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.: 1400 No. of bytes in distributed program, including test data, etc.: 11 737 Distribution format: tar.gz Programming language: Fortran 77 Computer: PC, iMac Operating system: Linux/Unix, MacOS 9.0 RAM: Less than 1 MB Classification: 2, 2.2 Catalogue identifier of previous version: ADUU_v1_0 Journal reference of previous version: Comput. Phys. Comm. 166 (2005) 191 Does the new version supersede the previous version?: Yes Nature of problem: Exact calculation of atomic data. Solution method: Use of a recurrence relation to compute hypergeometric functions. Reasons for new version: This new version computes additional important related data, namely, the total Einstein coefficients, and radiative lifetimes. Summary of revisions: Values of the total Einstein transition probability from an upper level n to a lower level n ′ are computed, as well as the radiative lifetime of a level n. Running time: About 2 seconds