4f−3demission spectra of the rare earths: An interpretation of the lines observed on both sides of the resonances

Abstract

A general model using a multiconfiguration Dirac-Fock program with Breit interaction and QED corrections is established to calculate the $4f$ core-level transitions in the rare earths. This model is tested by comparing the calculated spectra to the experimental spectra of all the elements of the rare-earth series obtained by electron-induced x-ray emission spectroscopy. Agreement between the ab initio energies calculated in the free-ion model and the energies measured for the solid rare-earth spectra is of the order of $1\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, i.e., better than 0.2%. Each observed structure is interpreted. Variation of the intensity ratios of the various emissions along the lanthanide series is explained. These results prove the validity of our theoretical model to describe the $4f\text{\ensuremath{-}}3d$ transitions in the solids. This general model can be used to interpret the $4f$ core-level transitions observed from other spectroscopies.