Electron-correlation third-order contributions to the electric dipole transition amplitudes of rare earth ions in crystals

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Abstract
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 Pr3+ are presented. Special attention is paid to studying the impact of the incompleteness of the radial basis set upon the radial factors occurring in f ↔ f electric-dipole transition theory.