Abstract
Electric dipole transitions within the 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 , on the assumption that the levels of each excited configuration of the type or 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 and those of an excited level , both of , the oscillator strength corresponding to the transition of frequency is found to be given by where 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 of precisely similar form. It is shown that sets of parameters can be chosen to give a good fit with the experimental data on aqueous solutions of Nd and Er. 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 that are smaller than those observed for and by factors of 2 and 8, respectively. Reasons for the discrepancies are discussed.
- Received 12 March 1962
DOI:https://doi.org/10.1103/PhysRev.127.750
©1962 American Physical Society