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Electric-dipole absorption and the scattering of x-rays: analytic results for a ion in an octahedral crystal field

A formulation describing electric-dipole absorption and resonance-enhanced diffraction of x-rays is applied to a ion in an octahedral crystal field and subject to a magnetic field. Analytical results are given for both the idealized and the complete forms of the scattering length. The contributing atomic quantities are discussed in detail, e.g. the spin - orbit interaction and the quadrupole moment of the valence holes. The model calculation was chosen to illustrate the use of a completely general formulation of the scattering length, from which one obtains the attenuation coefficient and cross-sections for elastic and inelastic scattering. Relevant tensor operators are referred both to unit tensors, and to appropriately coupled operators of spin and orbital angular momentum. The quantities that appear in the linear dichroic signal differ from corresponding results in the literature, and reasons for this finding are discussed.