Theory of solid-state contributions to the x-ray elastic scattering amplitude

We present a real space Green's function theory of solid-state contribution s and polarization dependence of the x-ray elastic scattering amplitude. In this approach the calculation separates naturally into contributions from the central (embedded) absorbing atom and multiple-scattering contributions from the environment. Both real and imaginary parts of the anomalous x-ray scattering amplitude are calculated simultaneously in the complex energy p lane, without the necessity of a Kramers-Kronig transform. This approach al so takes into account final-state effects, including core-hole lifetime, th e finite temperature Fermi distribution and Debye-Waller factors, as well a s experimental resolution. The approach is implemented in a generalization of the nb initio, self-consistent code, FEFF8.10, which permits application s to a number of x-ray spectroscopies for general, not necessarily periodic systems. The solid-state effect on the fine structure in the anomalous sca ttering amplitude near an absorption edge is illustrated for Cu metal. Calc ulations are also presented of the x-ray anomalous cross scattering amplitu de F-pi sigma for Cd metal, and x-ray natural circular dichroism in LiIO3, which are both due entirely to solid-state effects.