Damping of Phonons in Simple Metals

Calculations of the phonon damping due to the electron-phonon coupling are made in ten metals—Li, Na, K, Rb, Cs, Al, Pb, Be, Mg, and Zn—so as to cover all important structures, using Heine-Abarenkov-Animalu pseudopotential and different dielectric screening schemes. Screening is done in the spirit of the local reduction of the pseudopotential with proper considerations for the conduction-electron effective mass $m^{*}$. Comparison with experiments is made for those metals for which experimental results are available and it is found that a substantial contribution to the phonon damping arises from electron-phonon interaction. Li and Cs have a strange behavior in the ($\zeta ,0,0\mathrm{}$) direction, where the damping becomes enormous for certain values of $q$ in the small-$q$ region. From an analysis of the results it is legitimate to divide the different screening theories into two groups. Random-phase-approximation (RPA) theory, Hubbard's modified RPA, and the Geldart-Vosko modification of Hubbard's theory are in the first group. All of these theories have weak screening effects. The second group contains the theories presented by Singwi et al., Kleinman and Langreth, and Toigo and Woodruff. All of these theories have strong screening effects. Overhauser's theory has an intermediate screening effect.