Nonperturbative theory of temperature-dependent optical dephasing in crystals. II. Pseudolocal phonons

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Abstract
We continue our discussion of the nonperturbative theory of zero-phonon impurity lines in crystals formulated by Osad’ko and more recently by us. In Paper I of this series we evaluated our general results for the linewidth and shift for models of electronic coupling to both acoustic and optical phonons. Here we evaluate our general results for a simple model of electronic coupling to a pseudolocal phonon. The pseudolocal phonon is characterized by its frequency and lifetime in both the ground and excited electronic states. In addition to providing exact analytic expressions (reduced to quadrature) for the width and shift, we derive an approximate analytic expression for the linewidth that is bi-Arrhenius, with activation energies corresponding to the ground and excited state pseudolocal phonon frequencies. We discuss how our theoretical approach and results are related to the exchange theory of Harris, the optical Redfield theory of deBree and Wiersma, and the perturbation theory of Small and Jones and Zewail. In Paper III of this series, we compare the results of this paper and of Paper I to experiment.