Fermi density effect on the stopping power of metallic aluminum

The density-effect correction $\delta$ to the Bethe stopping-power formula for fast charged particles is evaluated for metallic aluminum from the dielectric-response function $\epsilon \mathrm{}\left(E\right)\mathrm{}$. The latter has been accurately determined over the entire range of excitation energy $E$ by Shiles, Sasaki, Inokuti, and Smith through comprehensive analysis of all pertinent experimental data. The resulting values of $\delta$ (which is a function of the particle speed $\beta c$) should be the most reliable to date. The present result agrees well with that of Sternheimer, who used a simpler and less rigorous procedure, and thus corroborates the general view that $\delta$ is insensitive to fine details of the behavior of $\epsilon \mathrm{}\left(E\right)\mathrm{}$. We also present general remarks on the evaluation of $\delta$ and on the analytic continuation of $\epsilon \mathrm{}\left(E\right)\mathrm{}$ as a function of the complex energy $E$.