Calculation of the matrix elements of the Coulomb interaction involving relativistic hydrogenic wave functions

Abstract

A program is presented for calculation of the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ψ f †( r)| R− r| −1ψ i( r) d r . Bound-free transitions are considered. Relativistic hydrogenic wave functions are used for the numerical evaluation of the matrix elements. The applied algorithm is based on the multipole series expansion of the Coulomb potential. The radial part of the terms of this series expansion (known as G functions) can also be obtained.