Mean Excitation Energy for the Stopping Power of Silicon from Oscillator-Strength Spectra

The mean excitation energy, $I$, is the sole nontrivial property of matter appearing in Bethe's expression for the stopping power for a charged particle at high speed. When the dipole oscillator-strength spectrum, d$f$/d$E$, is fully known as a function of excitation energy, $E$, the $I$ value may be evaluated from ln($I)=\smallint $ ln($E)$ (d$f$/d$E)$ d$E$ / $\smallint $ (d$f$/d$E)$ d$E$. Following up work on metallic aluminum, we are analyzing experimental data for the dielectric response of crystalline silicon using Kramers-Kronig dispersion relations and sum rules. The experimental data include absorption, refraction, reflection, and EELS. For silicon, the best set of data in our current judgment gives $I$ = 163.5 $\pm $ 2 eV, where the uncertainty arises from using different but apparently equally reliable data and from numerical procedures. Our result is appreciably lower than the standard value, 173 $\pm $ 3 eV. It is noteworthy that our result for silicon is remarkably close to that for aluminum, both in the $I$ value and in the contributions to it from each electron shell (when scaled for electron occupation and shell-edge energy).