Inversion of Optical Reflectance in the Fullerenes

Since the discovery of superconductivity in the alkali-doped fullerenes \cite{hebard}, the electron-phonon interaction has been the primary suspect for superconductivity in this class of compounds. In this paper we first provide a pedagogical review of how the question of mechanism has traditionally been settled, and then some well-known properties of the optical reflectance (and the derived conductance) are summarized. Finally we demonstrate how a recently derived inversion procedure can use the optical properties of a metal to infer the magnitude of the electron-phonon interaction. We conclude that in the case of the alkali-doped fullerenes, the electron-phonon interaction is sufficiently strong to explain the transition temperatues found in these the materials.