The Magnetic Interaction of a Valence Electron with Inner Shells

The magnetic interaction terms between two electrons are well known. By using antisymmetric wave functions the diagonal terms of the energy matrix for this interaction are calculated for an electronic configuration consisting of a valence electron and a closed shell. From the diagonal elements the doublet separation is easily obtained by applying the energy sum rule. The direct integrals, that is, terms which would occur even though the wave functions were not symmetrized for the Pauli principle, yield the expected contribution to the doublet separation; namely the interaction of the spin of the valence electron with the electric field produced by the closed shell. The exchange integrals give a contribution which decreases the doublet separation in the cases examined. They have been evaluated for the $f$ terms of Cs I. Their effect is much too small to explain the inversion of the doublets in this spectrum.