Inelastic X-Ray Scattering as a Probe of the Many-Body Local-Field Factor in Metals

Abstract

We report the first measurement of the many-body local-field factor $G(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})$ for a simple metal (Al) at large wave vectors. Inelastic x-ray measurements of the dynamical structure factor are analyzed using ab initio calculations of the noninteracting polarizability. Our measured $G(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})$ is in agreement with available theory for $q<{1.5k}_{F}$, unlike earlier electron energy-loss results; however, for $q\ensuremath{\sim}{2k}_{F}$ our $G(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})$ is a factor of 2 stronger than most theoretical predictions. We have also measured the polarizability for noninteracting electrons at a wave vector for which $G(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})\ensuremath{\cong}1$.