Ionic energy levels in trigonal and tetragonal fields

Abstract

The aim of this paper is that of finding the ionic energy levels in an electric field, if in addition to this field the ion is acted upon by a field of lower symmetry, in our case crystalline fields of trigonal or tetragonal type. Following the work of Bethe, and the work of Schönfeld on the cubic field, we shall reduce the representations of the cubic group, by restricting to its trigonal and tetragonal subgroups, and then utilizing the technique developed by Racah, we shall be able to write down the field matrices for every irreducible representation of the trigonal and the tetragonal groups. In this paper we shall consider only the electronic configurations d 2 and d 3, but it must be mentioned that the same technique can be applied to other electronic configurations, assuming that the cubic splitting in these configurations is already known.