Many-Electron Wave Functions

Abstract

In the last two chapters we have applied the central-field model mainly to systems with two electrons in open shell(s). The extension to more general systems provides no fundamental difficulty. Using the standard technique of Condon and Shortley [1935], described in Chap. 5, one can set up the matrix of the Hamiltonian with Slater determinants as basis functions. The zeroth-order wave function and the first-order energy splitting are then obtained from the eigenvectors and the eigenvalues of this matrix. This procedure, which is still widely used, is for all but the very simplest cases quite tedious, however. The technique of fractional parentage, developed by Racah [1943, 1949], represents an enormous improvement. This technique has been described in several textbooks and monographs [Slater 1960; Judd 1963a, 1967; Wybourne 1965a; Judd and Elliott 1970].