A program to compute exact hydrogenic radial integrals and Einstein coefficients

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)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 summaryProgram title: ba5.2Catalogue identifier: ADUU_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUU_v2_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.: 1400No. of bytes in distributed program, including test data, etc.: 11 737Distribution format: tar.gzProgramming language: Fortran 77Computer: PC, iMacOperating system: Linux/Unix, MacOS 9.0RAM: Less than 1 MBClassification: 2, 2.2Catalogue identifier of previous version: ADUU_v1_0Journal reference of previous version: Comput. Phys. Comm. 166 (2005) 191Does the new version supersede the previous version?: YesNature 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′n′ are computed, as well as the radiative lifetime of a level n.Running time: About 2 seconds