Phonon-Aided Optical Absorption in Sodium

Abstract

A general expression for the phonon-aided optical absorption in metals is derived. The derivation involves transforming canonically the electron-radiation interaction with the operator that generates the Born-Oppenheimer transformation. The absorption arising from all processes in which a single phonon is exchanged is calculated for sodium. These processes correspond to those obtained by usual second-order perturbation theory. Absorption due to processes which can be described as Drude and interband are treated separately. Interband momentum elements are estimated by combining data from the observed direct absorption with inferences from the band structure calculation of Ham. The calculated interband absorption has the same order of magnitude as the absorption observed at low temperatures in sodium by Mayer and Hietel. When interference with the Drude absorption is considered semiquantitatively, the observed low-temperature shape for sodium is indicated. However, the calculated absorption on the low-energy side of the minimum is found to be considerably too high. Some discussion of the possibility that higher phonon processes can reconcile theory and experiment at all temperatures is given.