Optical Absorption and Energy Loss in Sodium in the Hartree Approximation

Abstract

A general formalism for phonon-induced optical absorption in metals is derived. It has been applied to solid sodium. The lattice of sodium is approximated by a single reciprocal-lattice point. Its lattice wave number $G$ is somewhat greater than $2K_F$, the Fermi wave number. The energy-loss function of such an electron gas corresponding to a wave vector q has been calculated. For intermediate q with direction around G, the response function of a noninteracting electron gas has a gap in the continuum. As a result, in the presence of electron-electron Coulomb interactions, a new collective state and a redistribution of the energy-loss function have been found in the vicinity of the gap. The deviation of the phonon-induced optical absorption of sodium from the Drude theory has been calculated by using this energy-loss function and also taking into account the umklapp process. Conventional calculations have only taken into account the effects of single-particle excitations, and have neglected the collective states and the redistribution of the energy-loss functions, which are essential to the optical absorption. We find our results are qualitatively different from those of conventional calculations. But our results show that the effects are too small to explain the anomaly appearing in the infrared absorption of sodium.