Theory of Plasmon Damping in Metals. I. General Formulation and Application to an Electron Gas

A new general formulation for calculating the wave-number dependence of plasmon damping in metals, including the effects of both the electron-electron and the electron-ion interactions, is presented. As an important application of the general formalism, the case of an electron gas is investigated. The detailed calculation of the probabilities of plasmon decay by producing two electron-hole pairs is made. The effects of exchange processes are also investigated. The numerical result for the q 2 coefficient of the plasmon damping rate is considerably smaller than that obtained by previous theories. The process of plasmon decay via excitation of one electron-hole pair plus another plasmon is shown to contribute a term of q 6 in contrast with the result of previous theories which predicted it to be of q 4 . The comparison with characteristic energy loss experiments is also discussed briefly.