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

We report the first measurement of the many-body local-field factor $G(\overrightarrow{q},\omega )$ 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 $G(\overrightarrow{q},\omega )$ is in agreement with available theory for $q<\mathrm{}{1.5k}_F$, unlike earlier electron energy-loss results; however, for $q\sim {2k}_F$ our $G(\overrightarrow{q},\omega )$ 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 $G(\overrightarrow{q},\omega )\cong 1$.