Operator equivalents and matrix elements for the excited states of rare-earth ions

Abstract In recent work on the rare-earth double nitrates, it has been found necessary to extend the theory of crystal fields to cases of C3­v­ symmetry. Operator equivalences are given for the potentials V34 and V36', defined by ∑z(x3 - 3xy2) and Ʃ(11z3 - 3zr2) (x3 - 3xy2) respectively, and their matrix elements tabulated over a range of J (the total angular momentum) which includes the ground states of all the rare-earth ions. Operator-equivalent factors are given for certain excited levels in praseodymium and neodymium ions, and a method is described for finding these factors for levels which derive from terms that occur twice in a configuration of the form fn. The dependence on J and Jz of the matrix elements of the crystal-field interaction between different J levels is given for the components of a crystal field with C3v symmetry.