Dynamical effects on nearly degenerate electronic levels in solids

Abstract

We consider the optical absorption of a model system consisting of a two‐level ’’ion’’ interacting with a continuum of lattice vibrations. The two‐level system represents localized electronic energy levels such as are found on transition metal ions. The separation of the electronic energies is taken to lie within the phonon band and the interaction with the lattice vibrations is linear. For a single band of phonons the absorption is shown to consist of three peaks—a homogeneously broadened central peak flanked by two sharp lines. The existence of three absorption peaks is in contrast to the predictions of either a static crystal field or of the two‐level system interacting with a single harmonic oscillator. Our results reduce to the latter case when the phonon bandwidth becomes very narrow and to the former when the phonon bandwidth becomes very large.