Theory of the extended x-ray absorption fine structure

TLDR

The extended x‑ray absorption fine structure arises from the modification of the photoelectron final state by scattering from surrounding atoms. The authors present a theory of extended X‑ray absorption fine structure based on theoretically derived electron‑atom scattering phase shifts. The theory models electron scattering with a spherical‑wave expansion that accounts for finite atomic size, incorporates multiple‑scattering paths classified by total length, and treats the fourth‑shell contribution in fcc/bcc lattices as strongly affected by forward scattering from the first shell. The calculations show that multiple‑scattering effects are quantitatively significant but do not alter the qualitative single‑scattering picture, explain the experimentally observed fourth‑shell anomaly in metals, and reproduce copper data with good agreement.

Abstract

The extended x-ray absorption fine structure is a consequence of the modification of the photoelectron final state due to scattering by the surrounding atoms. We present a theory of the absorption fine structure starting from theoretically obtained electron-atom scattering phase shifts. The electron scattering is treated using a spherical wave expansion which takes into account the finite size of the atoms. Multiple-scattering effects are included by classifying multiple-scattering paths by their total path lengths. Their effects are quite large but appear to make quantitative but not qualitative changes on the single-scattering contribution. The exceptional case is the fourth shell in fcc or bcc structure, where it is shadowed by the first-shell atom and is profoundly affected by forward scattering due to the first shell. This may account for the anomaly observed experimentally at the fourth-shell radius in metals. A detailed numerical calculation is carried out for copper and is shown to agree quite well with experiment.