Self-Consistent Theory of Optical Transitions in Simple Metals

Abstract

It is shown that the interaction of Bloch (conduction) electrons moving in the periodic lattice potential of a metal with an electromagnetic field is adequately described by a simple reduced Hamiltonian in which the coupling between a single electron and a single photon is represented by a dynamically screened "optical pseudopotential". Thus, realistic calculation of the transition probabilities for various processes, particularly photoemission and absorption, including the collective effects due to the self-consistent field of the electrons, can be performed without recourse to detailed energy-band-structure computation in simple (nearly-free-electron) metals. Furthermore, a simple Hamiltonian of this type can be used quite generally for other purposes, for example, in calculating the self-energy of the Bloch electron due to emission and reabsorption of single photons. An expression is given for the effective mass of the Bloch electron in an electromagnetic field.