The finite-electron-lifetime expressions for the longitudinal and transverse dielectric functions of a free-electron gas obtained by Lindhard in the self-consistent-field approximation are examined. It is shown that these results are incorrect, and appropriate expressions are developed for the case where the system can be characterized by a single relaxation time.

• Received 9 October 1968

DOI:https://doi.org/10.1103/PhysRev.181.552