Description of nonradiative multiphonon transitions in the static coupling scheme II. Approximations

Abstract

For sufficiently large phonon dispersion the general rate-expression for nonradiative multiphonon transitions reduces to a gentle analytical approximate expression suitable, due to its compactness, for numerical calculations too. Simple explicit formulae are obtained in classical and semiclassical approximation frequently used in earlier papers, the severe limitations imposed to their actual applicability being discussed. On the basis of the concept of a mean phonon energy effective at medium temperatures, we derive explicit overlap-factor formulae applying to the experimentally most typical cases when the spacings of the electronic levels involved in the nonradiative multiphonon transitions considered are larger than the corresponding readjustment energies of the phonon field by a factor 10^1/2.