Plasmon Properties in bcc Potassium and Sodium

Plasmon dispersion curves and line shapes for bcc potassium and sodium have been obtained for plasmon propagation along the [110] and [100] directions by calculating the peak positions of Im[$\frac{-1\mathrm{}}{{\epsilon }_l(\overrightarrow{\mathrm{q}},\omega )}$], where ${\epsilon }_l(\overrightarrow{\mathrm{q}},\omega )$ is the wave-vector-and frequency-dependent longitudinal dielectric function. The augmented-plane-wave energy band structure of these solids was incorporated into the theory through ${\epsilon }_l(\overrightarrow{\mathrm{q}},\omega )$ which was calculated in the self-consistent-field formalism. The calculated dispersion relations show striking deviations from the corresponding free-electron calculations in three respects. First, the plasmons are considerably damped by the presence of interband transitions, with general trend towards increased damping for increasing values of the wave vector. Second, the zero-wave-vector plasma frequency is smaller than the corresponding free-electron plasma frequency. Finally, the dispersion curves are very different from those for free electrons. Results for potassium for the [110] direction are in good agreement with experiment.