Analysis of the absorption spectra 4fN+1to 4fN5d-6s of rare-earth ions in the cubic field. I. General formulae

Abstract

In rare-earth ions incorporated in the crystal, the absorption bands within the 4f^N+1 configuration are of free-ion type, except that they are slightly perturbed by the Stark effect caused by the crystal field. On the other hand, the transitions 4f^N+1 to 4f^N5d show broad absorption bands, since the 5d orbit is strongly affected by the crystal field. Furthermore, the transitions 4f^N+1 to 4f^N6s caused by the configuration interaction between 4f^N5d and 6s orbits. In this paper, the elements of the energy matrix of the 4f^N5d-6s system in the cubic field and the general formula for the shape of the absorption spectra 4f^N+1 to 4f^N5d-6s are calculated.