Dramatic advances in the understanding of x-ray absorption fine structure (XAFS) have been made over the past few decades, which have led ultimately to a highly quantitative theory. This review covers these developments from a unified multiple-scattering viewpoint. The authors focus on extended x-ray absorption fine structure (EXAFS) well above an x-ray edge, and, to a lesser extent, on x-ray absorption near-edge structure (XANES) closer to an edge. The discussion includes both formal considerations, derived from a many-electron formulation, and practical computational methods based on independent-electron models, with many-body effects lumped into various inelastic losses and energy shifts. The main conceptual issues in XAFS theory are identified and their relative importance is assessed; these include the convergence of the multiple-scattering expansion, curved-wave effects, the scattering potential, inelastic losses, self-energy shifts, and vibrations and structural disorder. The advantages and limitations of current computational approaches are addressed, with particular regard to quantitative experimental comparisons.

DOI:https://doi.org/10.1103/RevModPhys.72.621