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Physical Review A

Strong-couplingSmatrices for the generalized exponential models of nonadiabatic transitions

Predrag Krstić, R.K. Janev

Published Jun 1, 1988• 10 citations
Publisher

Abstract

Strong-coupling S matrices for the anti-Demkov, Nikitin, and Demkov models of nonadiabatic transitions are derived. On this basis, analytic expressions for the channel probabilities, which include the effects of the turning point, are also derived. The two states are assumed quasistationary and coupled by a complex interaction.
DOI
10.1103/physreva.37.4625

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We consider a two-state model which extends the exponential time-dependent Demkov model of non-adiabatic coupling to complex energies and interactions. Using the method of steepest descent, exact and practicable asymptotic expansions of the Hankel functions H v j (1) (λ), H v j (2) (λ) are obtained when | v j | and | λ | are large and of the same order. The semiclassical scattering two channel matrix within the strong-coupling Demkov model and embracing non-adiabatic parameters is derived. Closed form expressions for the transition probabilities, which incorporate the effects of the classical turning point, are also derived. The matrix elements are shown to reduce correctly in known limiting cases. These include the case of exact symmetric resonance, the Landau-Zener and Callaway-Bartling model and the Stueckelberg noncrossing formula. In the case of a Hamiltonian matrix which is complex Hermitian on the real t axis, Berry has shown that the phenomenon of anholonomy arises as the physical manifestation of a non-integrable real geometric phase in adiabatic parallel transport round a closed circuit in real space. More recently Berry has reinterpreted this theory as arising from transport around a circuit in complex time. The geometric amplitude factor, which is simply the anholonomic phase corresponding to the connection on a complex fibre bundle, occurs naturally in the Demkov model which is an example of a closed system in parameter space driven by a complex Hermitian Hamiltonian. It is shown that the Berry phase phenomenon also involves contributions from both real and complex circuit adiabatic phases.
A certain two-state exponential potential model is solved quantum mechanically exactly. Compact expressions for nonadibatic transition matrices are obtained. Interesting quantum mechanical threshold effects are found. Simple very accurate expressions are found from a semiclassical viewpoint for the nonadiabatic transition probabilities, indicating that the exponential model may present a third important basic model in addition to the Landau–Zener–Stueckelberg and the Rosen–Zener–Demkov models. Extension to general cases is also briefly discussed.
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We consider two quasimolecular states, one discrete and one quasistationary, whose dynamical coupling becomes possible only by absorption or emission of laser-field photons. In the presence of the laser field the initially discrete state also becomes quasistationary, with an energy continuum shifted with respect to the continuum into which the initially quasistationary state decays. For such an interacting system, the corresponding system of coupled equations is derived and then solved within the Landau-Zener and Demkov nonadiabatic-coupling models, with various assumptions about the time variation of decay widths. Closed-form expressions for the transition probabilities of the half and full collision are obtained. The considered general physical problem is related to electron-capture processes in slow ion--excited-atom (or atom--excited-ion) collisions in a laser field or to laser-assisted excitation-transfer processes in atom--excited-atom slow collisions.