A Algorithm for the Calculation of Three-Electron Matrix Elements.

Matrix elements of the three-electron operators r_sp{12}{+/-}r _sp{23}{+/-} and r_sp{12}{+/-}r _sp{23}{mp} decompose into a finite sum of products of angular and radial integrals when a one-electron basis of the form psi _{l,n,m}(vec r) = R _{l,n}(alpha,beta; br)Y_ {l,m}(theta,phi) is used. Techniques for evaluating the radial integrals are developed, and general recursive expressions are given for the choice R_{l,n}(alpha,beta; br) = N_{l,n}(br)^ {l}e^{-beta r}L_sp {n}{(alpha)}(br), where L_sp{n}{(alpha)} is a generalized Laguerre polynomial and N _{l,n} is a normalizing factor. By setting beta = b/2, b = constant, and alpha = 2l + 1, the matrix elements can be evaluated to almost machine accuracy via exact integer arithmetic.