Theory of Isotopic Effects in the Electron-Phonon Interaction

Abstract

Experiments on hydrogen and deuterium in solid argon and on the $U$ center in the alkali halides reveal isotopic effects in the positions and breadths of the optical absorption bands, which are inexplicable in terms of the linear approximation of the electron-phonon interaction. Quadratic effects are treated in the semi-classical approximation with a view to understanding the relative roles of band modes and localized modes. It is found that interactions involving localized modes dominate. Further, if the isotopic effects are interpreted as being solely due to quadratic interactions, the impurity is likely to be dynamically unstable in the excited electronic state. However, estimates of anharmonic interactions indicate that these may make a significant contribution to the isotopic properties of these systems.