Abstract
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 performed within the perturbed function approach for the Pr+3 ion.
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