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

Spectroscopic analysis of scattered x rays from Be irradiated by copper-target $K\beta$ 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 $\hslash \overrightarrow{\mathrm{k}}$ smaller than the critical $\hslash {\overrightarrow{\mathrm{k}}}_c$ was observed, as predicted by Bohm and Pines, and Nozières and Pines. The plasmon energy for scattering angle zero was found to be 19.4 ± 0.4 eV. No appreciable dispersion was observed for $\hslash \overrightarrow{\mathrm{k}}>\hslash {\overrightarrow{\mathrm{k}}}_c$. 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 × ${10}^{-16\mathrm{}}$ sec, for scattering angle $\phi =0\mathrm{}$.