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We show rigorously, within the two-state approximation, that in the semiclassical limit h/→0 a nonadiabatic transition induced by an analytic time-dependent Hamiltonian is localized to the vicinity of a complex crossing of the two adiabatic potential curves, with transition amplitude independent of the nonadiabatic coupling and given by a simple formula of A. M.Dykhne.
Davis et al. (Thu,) studied this question.
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