Analysis of some integrals arising in the atomic four-electron problem

Abstract

An analysis is presented for the evaluation of the one-center integrals of the form ∫ri1rj2rk3rl4rm12 rn13rp14rq23rs24 rt34e−ar1−br2−cr3−dr4 dr1 dr2 dr3 dr4 which arise in the solution of the atomic four-electron problem when a Hylleraas expansion is employed. A majority of the cases that arise can be solved by a reduction of the four-electron integrals to integrals arising in the three-electron problem. A second general approach is developed which is able to handle almost all cases that arise in practical calculations.