The quantum theory of dispersion in metallic conductors. — II

Abstract

1. Introduction.—In a previous paper* the optical properties of metals were discussed on the basis of Bloch’s theory of metallic conduction, f According to this theory the action on a given conduction electron of the other con­duction electrons and the ions of the metallic lattice is replaced by a periodic field of potential. In its stationary states the electron travels freely through the metal, but when the temperature agitation of the lattice is taken into account, the electron will make transitions to other stationary states due to the collisions which then take place. In Part I it was shown that the optical constants of a metal can be expressed by the well-known formulæ of Drude in terms of its electrical conductivity σ 0 for constant electric fields, provided the period of the incident radiation is large compared with the time of relaxation of the conduction electrons or, what comes to the same thing, large compared with the average time between two collisions of such an electron and the metallic lattice. In the other limiting case of a period small compared with this time of relaxation the theory also took a simple form since then the collisions could be entirely neglected. It was further shown that the transitional region of the spectrum where the period of the radiation is comparable with the time of relaxation in general lies in the neighbourhood of a wave-length λ = 10 μ at ordinary temperatures and shifts toward longer wave-lengths as the tempera­ture gets lower since the chance of collision is thereby reduced and the time of relaxation increased. In section 2 of this paper we shall consider once more the optical behaviour of a metal under circumstances where we may neglect the collisions of the electrons with the lattice. Some points which were still rather obscure when Part I was written will be explained more fully in this connection. In section 3 the theory will be extended to include the transitional region of the spectrum spoken of above, and in section 4 a comparison with the experimental data will be given.