Static and adiabatic approaches to nonradiative multiphonon transitions: correct transition matrix elements of order Δ

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Abstract
The static base approach (SBA) and adiabatic base approach (ABA) are analysed for an electronic two-level system coupled to a single vibrational mode. In the ABA due account is taken of the non-adiabatic contribution to the oscillatory potential. This permits the introduction of a suitable model potential whose eigensolutions can be calculated exactly. It is proven that the calculation of the non-adiabatic transition matrix elements by means of these model eigenfunctions yields the correct first-order result in the promoting-mode coupling constant Delta and thus provides the same accuracy as the SBA calculation. The analysis evinces the importance of the diagonal non-adiabaticity operator, which has been neglected in earlier work. The transition matrix elements of the two approaches are compared. It is found that the absolute value of the SBA result is always larger than that of the ABA result and rises up to about a factor of two times the latter for higher Huang-Rhys factors. The authors finding resolves an old controversy.