Decay rates of tunneling centers coupled to phonons: An instanton approach

Abstract

In this paper, we continue our study of defect tunneling in the presence of phonon modes. We compute the zero-temperature decay rate of the excited state of an asymmetric double well coupled to phonons. We compare the instanton decay rate with that of the traditional models of atomic tunneling (which either treat the defect as a two-level "spin" system or which work in the Condon approximation). We conclude that the traditional models are usually accurate only in a renormalized sense; any attempts to use bare tunneling matrix elements must apply the more sophisticated techniques proposed here. To illustrate this point we use instanton methods to study O${\mathrm{H}}^{-}$ defect tunneling in alkali halides.