Implicit spatial averaging in inversion of inelastic x-ray scattering data

TL;DR

This paper discusses how inelastic x-ray scattering data, used to image electron dynamics, inherently involves spatial averaging, and demonstrates how to relate these averaged images to the true local responses in materials.

Contribution

It reveals that IXS-derived images are spatial averages and provides a method to relate these to the un-averaged local responses, enhancing interpretation of electron dynamics.

Findings

Images are spatial averages over source locations.

A simple relationship to un-averaged response can be established.

Application demonstrated on graphite IXS data.

Abstract

Inelastic x-ray scattering (IXS) now a widely used technique for studying the dynamics of electrons in condensed matter. We previously posed a solution to the phase problem for IXS [P. Abbamonte, et. al., Phys. Rev. Lett. {\bf 92}, 237401 (2004)], that allows explicit reconstruction of the density propagator of a system. The propagator represents, physically, the response of the system to an idealized, point perturbation, so provides direct, real-time images of electron motion with attosecond time resolution and $\AA$-scale spatial resolution. Here we show that the images generated by our procedure, as it was originally posed, are spatial averages over all source locations. Within an idealized, atomic-like model, we show that in most cases a simple relationship to the complete, un-averaged response can still be determined. We illustrate this concept for recent IXS measurements of single crystal graphite.