Low-Lying Energy Levels of Lanthanide Atoms and Intermediate Coupling

Abstract

A detailed examination of the effects of intermediate coupling on the properties of the low-lying levels of lanthanide atoms has been made. Particular attention has been given to the effects of a breakdown of Russell-Saunders coupling on the energies and magnetic properties of the levels of the ground multiplets. The energy levels were calculated by diagonalization of the combined electrostatic and spin-orbit matrices of the ${f}^{n}$ configurations. It is found possible to fit the energy levels of the ground multiplets of Nd i and Sm i to within 2 ${\mathrm{cm}}^{\ensuremath{-}1}$ of their observed energies using $4f$-hydrogenic ratios for the Slater ${F}_{k}$ integrals. The $g$ values are found to agree within the experimental errors of the atomic beam measurements. An explanation for the apparent success of the $4f$-hydrogenic eigenfunctions is offered and it is demonstrated that the success of these eigenfunctions does not imply that the actual eigenfunctions are hydrogen-like. Tables of the calculated energies and eigenvectors for low-lying levels are given together with the $g$ values calculated in intermediate coupling. The effects of intermediate coupling on the realtivistic and diamagnetic corrections to the $g$ values are examined and shown to fall within the range of atomic beam measurements. The importance of intermediate coupling in the actinides is noted.