Average-atom treatment of relaxation time in X-ray Thomson scattering from warm-dense matter

TL;DR

This paper investigates the effect of finite relaxation times on X-ray Thomson scattering in warm-dense plasmas using the Mermin dielectric function within the average-atom model, highlighting differences from the collision-free approach.

Contribution

It introduces a method to include relaxation time explicitly in Thomson scattering calculations using the Mermin dielectric function within the average-atom approximation.

Findings

Relaxation rates agree with static and frequency-dependent conductivity estimates.

Transport cross sections from phase-shift analysis differ from Born approximation at low energies.

Including relaxation time significantly affects the modeling of scattering spectra.

Abstract

The influence of finite relaxation times on Thomson scattering from warm-dense plasmas is examined within the framework of the average-atom approximation. Presently most calculations use the collision-free Lindhard dielectric function to evaluate the free-electron contribution to the Thomson cross section. In this work, we use the Mermin dielectric function, which includes relaxation time explicitly. The relaxation time is evaluated by treating the average atom as an impurity in a uniform electron gas and depends critically on the transport cross section. The calculated relaxation rates agree well with values inferred from the Ziman formula for the static conductivity and also with rates inferred from a fit to the frequency-dependent conductivity. Transport cross sections determined by the phase-shift analysis in the average-atom potential are compared with those evaluated in the commonly used Born approximation. The Born approximation converges to the exact cross sections at high energies; however, differences that occur at low energies lead to corresponding differences in relaxation rates. The relative importance of including relaxation time when modeling X-ray Thomson scattering spectra is examined by comparing calculations of the free-electron dynamic structure function for Thomson scattering using Lindhard and Mermin dielectric functions. Applications are given to warm-dense Be plasmas, with temperatures ranging from 2 to 32~eV and densities ranging from 2 to 64~g/cc.