Evaluation of Matrix Elements of Spinhyphen;Dependent Operators forNhyphen;Electron Systems. I Onehyphen;Body Operators

摘要

The properties of the symmetric group are utilized to obtain a decomposition of matrix elements of spinhyphen;dependent operators into sums of products of spacehyphen; and spinhyphen;dependent matrix elements. The Wignerhyphen;Eckart theorem is then applied, and results in an expression for the matrix elements in terms of reduced matrix elements in both space and spin and a set of coupling coefficients. The coupling coefficients and the reduced spinhyphen;matrix elements are evaluated forNequals;2, 3, 4, and the corresponding reduced spatial matrix elements are evaluated in the simplest case of an orbital approximation.