The Stokes' Shift in Impurity Spectral Lines. I. Mathematical Technique

Abstract

A new method of deriving the Stokes' shift in impurity spectral lines is presented. The adiabatic approximation is not used. The method makes use of the fact that at most one electron can be bound at the impurity site and reduces the problem in a systematic fashion to the evaluation of traces over only phonon states. A new method is given of evaluating these traces for a particular electron–phonon system which has the chief features required to discuss the Stokes' shift.