Multiple-scattering corrections to the extended x-ray absorption fine structure

Multiple-scattering corrections to the extended x-ray absorption fine structure (EXAFS) are investigated using exactly solvable, one-dimensional model systems with a Bloch wave basis, together with expansions appropriate to three dimensions. These one-dimensional models exhibit EXAFS analogous to that observed in real solids, yet their solutions lack many of the complications of full three-dimensional calculations. In particular the models enable one to examine to all orders forward multiple-scattering effects, which lead to nonphysical divergences in ordinary perturbation theory. We find that the exact EXAFS spectra are characterized by "renormalized" values of the electron wave number $k$ and the phase shift $\delta$. However, for the first shell, multiple-scattering effects are absent altogether, and the unrenormalized parameters are correct. Contrary to the situation in low-energy-electron diffraction, these renormalized values cannot in general be realized by suitable adjustment of the inner potential.