Abstract
The electric quadrupole contribution to the scattering length is derived using an atomic model for the resonant ion. At one of the levels of approximation considered, our so-called idealized scattering length is totally consistent with the standard sum rules for the analysis of the attenuation coefficient. A superior estimate of the scattering length includes the structure of the core state. The two levels of treatment are used to discuss the intensity of x-rays Bragg diffracted by resonant lanthanide ions in a crystal. Using a ground state for the valence shell specified by Hund's rules, explicit expressions for the idealized scattering length are tabulated for the tripositive ions. The general expressions for the scattering length can be evaluated for a valence-shell wave function of an arbitrary complexity. Thus, our scattering lengths can accommodate the influence of a crystal-field potential or a full multiplet calculation. Linear and circular polarization in the primary and secondary beams of x-rays are handled in terms of a Stokes vector, and several illustrative calculations are given.
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