Lattice dynamics of alkali metals in the self-consistent screening theory

The self-consistent treatment of correlations in the electron liquid recently given by Singwi et at. is applied to calculations of the lattice dynamics of alkali metals. With the Ashcroft form for the pseudopotential, in which the only parameter is the core radius, good agreement with the measured dispersion curves is obtained for the four metals for which such data exist. For Na and K the fitted values of this parameter are close to those derived from Fermi-surface and liquid-resistivity data; for Li and Rb the fitted values lie between those obtained from the other physical properties. Phonon lifetimes due to the electron-phonon interaction are calculated for K. Finally, the cohesive energy, lattice parameter, and compressibility are derived; agreement with the measured values of all three quantities is obtained with a not unreasonable adjustment of the Hartree energy. The relation between the compressibility sum rule and the long-wavelength limit of terms containing third and fourth powers of the electron-phonon matrix element is evaluated for the case of Na within the same framework.