A Fortran program to calculate the matrix elements of the Coulomb interaction involving hydrogenic wave functions

• Published in: Computer physics communications 2017-03, Vol.212, p.280-282
• Main Author: Sarkadi, L.
• Format: Article
• Language: English
• Subjects: Coulomb functions; Coulomb interaction; Hydrogenic wave functions; Ionization; Matrix elements; Multipole series expansion
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2016.10.018

The program MTRXCOUL [1] calculates the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ψf∗(r)|R−r|−1ψi(r)dr. Bound-free transitions are considered, and non-relativistic hydrogenic wave functions are used. In this revised version a bug discovered in the F3Y CPC Program Library (PL) subprogram [2] is fixed. Furthermore, the COULCC CPC PL subprogram [3] applied for the calculations of the radial wave functions of the free states and the Bessel functions is replaced by the CPC PL subprogram DCOUL [4]. Program Title: MTRXCOUL Program Files doi:http://dx.doi.org/10.17632/xyg9zrmzz2.1 Licensing provisions: GNU GPL v3 Programming language: Fortran 77 Journal reference of previous version: Comput. Phys. Commun. 133 (2000) 119. Does the new version supersede the previous version?: Yes Reasons for the new version:1.In some applications MTRXCOUL led to unexpected results that were traced back to the erroneous execution of the subprogram F3Y [2]. For example, in some cases F3Y yielded completely different values for the inputs (l,m1,l,m2,l′,m′) and (l,m2,l,m1,l′,m′), while, for symmetry reason, one expects equal results. In the new version this error in F3Y was corrected.2.In MTRXCOUL the COULCC subprogram [3] is applied for the calculations of the radial wave functions of the free states RE,l(r) and the Bessel functions Jn(x). Since the publication of MTRXCOUL a relativistic version of the program, MTRDCOUL has also been developed and published [5]. In MTRDCOUL RE,l(r) and Jn(x) are calculated by the subprogram DCOUL written by Salvat et al. [4]. Since the latter program is suitable also for calculations of non-relativistic wave functions, to ensure consistency between MTRXCOUL and MTRDCOUL, in the revised program the COULCC [3] was replaced by DCOUL. Furthermore, in some applications DCOUL turned out to be more efficient than COULCC. Summary of revisions:1.In the line AAQQ0036 of the original F3Y program [2] the incorrect assignment A2=L1−M1−N2 was replaced by A2=L1−M1−N1. The corrected F3Y was tested by comparing its results with those obtained by a program written for the integral of the product of three spherical harmonics using the 369j program [6]. An agreement within 10−14 was found between the two calculations for all possible arguments of the function belonging to the values of li up to 10.2.In the RFINAL function of the revised MTRXCOUL the regular Coulomb function Fl(η,x) is calculated using the code DCOUL [4]