A THEORY OF MAGNETIC-X-RAY DIFFRACTION ENHANCED BY AN ELECTRIC QUADRUPOLE (E2) RESONANCE

The electric quadrupole contribution to the scattering length is deriv ed using an atomic model for the resonant ion. At one of the levels of approximation considered, our so-called idealized scattering length i s totally consistent with the standard sum rules for the analysis of t he attenuation coefficient. A superior estimate of the scattering leng th includes the structure of the core state. The two levels of treatme nt are used to discuss the intensity of x-rays Bragg diffracted by res onant lanthanide ions in a crystal. Using a ground state for the valen ce shell specified by Hund's rules, explicit expressions for the ideal ized scattering length are tabulated for the tripositive ions. The gen eral expressions for the scattering length can be evaluated for a vale nce-shell wave function of an arbitrary complexity. Thus, our scatteri ng lengths can accommodate the influence of a crystal-field potential or a full multiplet calculation. Linear and circular polarization in t he primary and secondary beams of x-rays are handled in terms of a Sto kes vector, and several illustrative calculations are given.