A Algorithm for the Calculation of ThreeElectron Matrix Elements.
Abstract
Matrix elements of the threeelectron 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 oneelectron 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.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1990
 Bibcode:
 1990PhDT........83F
 Keywords:

 VOLUMES IIV) (MATRIX ELEMENTS;
 Physics: Atomic