ANALYSIS OF SOME INTEGRALS ARISING IN THE ATOMIC 4-ELECTRON PROBLEM

An analysis is presented for the evaluation of the one-center integral s of the form integral r1i r2j r3k r4l r12m r13n r14p r23q r24s r34t e (-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 that arise can be solved by a reduction of the four-e lectron 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.