A theoretical framework for absorption (dichroism) and the resonance-enhanced scattering of x-rays by magnetic materials: I

The scattering length common to the attenuation coefficient and cross-sections for the resonance-enhanced scattering of x-rays suffers from a dependence on a spectrum of virtual, intermediate states which contain next to no useful information about the environment of the atoms. It is the dependence of the scattering length on intermediate states that sets the x-ray techniques apart from neutron scattering and other techniques which directly probe properties of magnetic materials, and limits the usefulness of physical intuition in the interpretation of empirical x-ray data. As a step toward a legible interpretation, in a language of standard atomic variables, an investigation is reported of a modified scattering length constructed to possess a structure similar to the scattering length for magnetic neutron scattering, namely, it has the mathematical structure of a spherical tensor operator, to which all Racah's methods for electrons in an open valence shell can be applied. In the process of reaching this goal, the influence of the intermediate states on the scattering length is reduced by summing over a limited set of quantum numbers for the intermediate states. Topics covered in the investigation include the attenuation coefficient for x-rays passing through a foil of magnetic material, dichroism, and the cross-sections for resonance-enhanced elastic (Bragg) and inelastic scattering of x-rays by magnetic materials. The treatment of polarization in the primary beam admits states of partial polarization, described by a Stokes vector. Both jj-coupling and Russell - Saunders coupling schemes for the valence states are explored.