Energy expressions for atomic configurations in the L-S coupling scheme

Abstract

The matrix elements of the spin-free Hamiltonian between two atomic configuration state functions (CSF'S) in the L-S coupling scheme are expressed in terms of the atomic integrals F_k's and G_k's. Using these general expressions, the matrix elements have been obtained for all the atomic configurations with three valence electrons that have not been solved so far by earlier methods. The scope for applying this new approach to obtain the Auger line energies and the promotion energies of metals that involve more than two partially filled shells is indicated. The energy expressions for some of the relevant configurations are tabulated.