Extension of the Dirac Vector Model to Include Several Configurations

Abstract

The vector model for the electrostatic interactions of a system of $n$ electrons, as originally given by Dirac and as used by J. H. Van Vleck, suffers from the restriction that it allows the energy matrix to be set up completely only for a single spatial configuration. In the present paper this restriction is removed. It is shown how the complete energy matrix may be found by means of the vector model, whatever the number of configurations involved. As an example of the method, the energies of the two ${}_{}{}^2{}_{}{}^{}D$ states arising from the atomic configuration $d^3$ are calculated. Calculations by this method are simpler than the corresponding calculations using Slater wave functions in that the energy matrix factors according to characteristic values of $S$.