Adiabatic Approximation Theory and Static Coupling Theory of Nonradiative Transition

The aim of the present paper is to point out and give solution to certain unsolved problemsof a fundamental nature, which have emerged in the course of development of the theory ofnonradiative transitions in the last two decades. It is shown that the so-called Condon approxi-mation involves an inconsistent and consequently impermissible application of the perturba-tion method, and a clear-cut criterion for correct choice of the non-Condon wave function isestablished. On this basis, a proof is given to show that within the approximation that con-sideration of lattice relaxation is restricted to the diagonal electron-phonon interaction and thenondiagonal interaction is considered as a perturbation taken to the first order, the adiabaticapproximation and static coupling theories are equivalent, thus apparently divergent develop-ments of nonradiative transition theory are unified. This conclusion, apart from its significancefrom the point of view of basic theory, will also facilitate practical calculations of transitionrates.