Evaluation of two-centre one-electron four-orbital overlap integrals involving Coulomb waves

The authors present a very efficient and powerful numerical technique to evaluate two-centre one-electron four-orbital integrals for the overlap of two component wavefunctions, each involving a hydrogenic bound state on one centre and either an outgoing or an ingoing Coulomb wave on the other. Using a double complex inverse Laplace transform for the two Coulomb waves they invert the order of integration. Addressing the space integral as the inner integral they evaluate its angular part in prolate spheroidal coordinates. The radial integral and the two outer complex integrals arising from the double inverse Laplace transform are then evaluated numerically with suitable precision. The accuracy of this technique is checked for some special limiting values, and as a function of nested tolerances. These overlap integrals appear in the distorted-wave theories especially in the impact parameter treatment for elastic as well as rearrangement collisions.