Semiclassical theory of collisionally induced fine-structure transitions in fluorine atoms

Abstract

A calculation of fine-structure transitions in F atoms impinging on both Xe and H+ has been carried out using a novel semiclassical theory that was proposed recently by Miller and George. The theory has the advantage of being conceptually simple and applicable to a wide class of situations. For Xe+F the cross section for the 2P3/2 → 2P1/2 excitation of F rises from its threshold (0.05 eV) to a value of ∼0.1 Å2 at a collision energy of 0.5 eV. The cross section for H++F is much larger, reaching a value of ∼1 Å2 at a collision energy of 0.25 eV, in reasonable agreement with recent quantum mechanical calculations.

Instanton versus traditional WKB approach to the Landau-Zener problem

“…For example, we found in the sections II and III that the wave functions of nuclei moving along the periodic orbits acquire geometrical phases (the effect is analogous to the Aharonov -Bohm effect [38], but in our case it has nothing to do with external magnetic fields and is related to the non-adiabatic interactions). The relation between the both phenomena (the geometrical phases and the periodic orbits) can be established using Lagrangian (instead of Hamiltonian) formulation of the problem, which enables to take into account explicitely, using propagator technique, [34], [35], [36], time dependence of the adiabatic process under consideration (see also, e.g., [4], [43]). However, a proper handling of these aspects is beyond the scope of our work.…”

“…For example, one of the very efficient technique (so-called propagator method) was proposed and elaborated by Miller and his coworkers [34], [35], [36] (see also [26]). This approach uses semiclassic (van Fleck -Gutzwiller types) propagators, taking into account automatically in terms of the general WKB formalism, the contribution coming from the contour around a complex turning point.…”

Comment on the relation between the nonadiabatic coupling and the complex intersection of potential energy curves

“…two-state approximation [ 7,12,19,20]. In these systems, the nonrelat_ly°.stic description of the halogen atom has a degenerate ground state which splits into 2P 3 /2 and 2P 1/ 2 components upon the inclusion of spin-orbit coup?_ ng.…”

“…Preston, Sloane, and Miller [ 7] have fit AV to an exponential function in the internuclear separation, r, AV(r) = A exp (-ar) (16) for the Xe + F system in which V is the ground state. We use this form in the following treatment of fine-otructure transitions.…”

“…In addition, semiclassical calculations have been carried out for electronic transitions in H+ + D2 [3] and H2 + F( and George [5]. Previously, quantum mechanical (6] and semiclassical (7] calculations had been reported for fine --structure transitions in atom-atom collisions. In the quantum mechanical studies, electronic transitions are induced by the nonadiabatic coupling matrix elements between the initial and final adiabatic electronic states (potential coupling).…”