Splitting of the4d32and4d52levels in the rare-earth elements and their oxides

Systematic measurements have been made on the $L{\beta }_{2,15}[L_3-N_{4,5}]$ and the $L{\gamma }_1[L_2-N_4]$ x-ray emission lines of the rare earths: ${}_{59}{}^{}{}_{}{}^{}\mathrm{P}\mathrm{r},$ ${}_{60}{}^{}{}_{}{}^{}\mathrm{N}\mathrm{d},$ ${}_{62}{}^{}{}_{}{}^{}\mathrm{S}\mathrm{m},$ ${}_{63}{}^{}{}_{}{}^{}\mathrm{E}\mathrm{u},$ ${}_{64}{}^{}{}_{}{}^{}\mathrm{G}\mathrm{d},$ ${}_{65}{}^{}{}_{}{}^{}\mathrm{T}\mathrm{b},$ ${}_{66}{}^{}{}_{}{}^{}\mathrm{D}\mathrm{y},$ ${}_{67}{}^{}{}_{}{}^{}\mathrm{H}\mathrm{o},$ ${}_{68}{}^{}{}_{}{}^{}\mathrm{E}\mathrm{r},$ ${}_{69}{}^{}{}_{}{}^{}\mathrm{T}\mathrm{m},$ and ${}_{70}{}^{}{}_{}{}^{}\mathrm{Yb}.\mathrm{}$ Each element was studied both in the metallic and oxidized states. The exchange interaction between the $4f$ and the $4d$ electrons splits both levels and results in sets of x-ray emission lines that are characteristic of the rare-earth elements alone, and that appear at the low-energy sides of the $L{\beta }_{2,15}$ and $L{\gamma }_1$ lines. A computer program was devised to unfold the complex structures, in order to obtain the energy separation and relative transition probabilities of the constituent lines. The effect of oxidation on the splitting of the $4d$ levels, although insignificant for low- and high-$Z$ elements, was found to be more than expected for elements with atomic number in the neighborhood of 65. It is quite possible that the structures studied consist of more than two discrete emission lines; that is, each of the $4d$ levels splits into more than two levels, expecially in the low-atomic-number elements. A theoretical interpretation of these results as a simple exchange interaction does not fit the results satisfactorily, so that more theoretical work is needed.