Optical Absorption Intensities of Rare-Earth Ions

Electric dipole transitions within the 4f shell of a rare-earth ion are permitted if the surroundings of the ion are such that its nucleus is not situated at a center of inversion. An expression is found for the oscillator strength of a transition between two states of the ground configuration 4f^N, on the assumption that the levels of each excited configuration of the type 4f^Nn^'d or 4f^Nn^'g extend over an energy range small as compared to the energy of the configuration above the ground configuration. On summing over all transitions between the components of the ground level ₉ and those of an excited level {^'}₉^{'}, both of 4f^N, the oscillator strength P corresponding to the transition ₉{^'}₉^{'} of frequency is found to be given by P=T_ ({₉U^ () {^'}₉^{'}) }^2, where U^ () is a tensor operator of rank, and the sum runs over the three values 2, 4, and 6 of. Transitions that also involve changes in the vibrational modes of the complex comprising a rare-earth ion and its surroundings, provide a contribution to P of precisely similar form. It is shown that sets of parameters T_ can be chosen to give a good fit with the experimental data on aqueous solutions of NdCl₃ and ErCl₃. A calculation on the basis of a model, in which the first hydration layer of the rare-earth ion does not possess a center of symmetry, leads to parameters T_ that are smaller than those observed for Nd^3+ and Er^3+ by factors of 2 and 8, respectively. Reasons for the discrepancies are discussed.