In ab initio studies of the impact of electron correlation effects of f↔ f transition probabilities
much numerical work is concerned with evaluating radial factors. These terms are
expressed as products of the radial integrals summed over all excited orbitals including
those in the continuum. To simplify the evaluation of these sums, for the first time in f↔ f
transition theory, the perturbed-function approach has been applied. The detailed analysis
of numerical results obtained for the radial factors contributing to the transition amplitudes for …

A complete expression for the f↔ f transition amplitude defined up to the third order in
perturbation theory is presented. The third-order contributions are due to electron correlation
inside the rare earth ion and arise from the static and dynamic models. The approach is
formulated by means of double perturbation theory and in terms of effective tensor operators
expressed by unit tensor operators. The discussion of the relative importance of various
kinds of effective operators is based on the numerical results of test ab initio calculations …