Bulk-Plasmon Dispersion Spectrum of Be Using an X-Ray Scattering Technique

Abstract

Spectroscopic analysis of scattered x rays from Be irradiated by copper-target $K\ensuremath{\beta}$ radiation establishes the existence of a first-order bulk-plasmon line. Dispersion of the plasmon energy as a function of the scattering angle for momentum transfer $\ensuremath{\hbar}\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ smaller than the critical $\ensuremath{\hbar}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{c}$ was observed, as predicted by Bohm and Pines, and Nozi\`eres and Pines. The plasmon energy for scattering angle zero was found to be 19.4 \ifmmode\pm\else\textpm\fi{} 0.4 eV. No appreciable dispersion was observed for $\ensuremath{\hbar}\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}>\ensuremath{\hbar}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{c}$. Adopting the Drude-Zener model for the electron gas, the experimental half-width of the unfolded lines gives an estimated plasmon lifetime of the order of 1.4 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}16}$ sec, for scattering angle $\ensuremath{\varphi}=0$.