Semiclassical approach to the description of collisionally induced optical transitions of diatoms

R. M. Beuc and M. Movre, Institute of Physics, Zagreb, Croatia

In a recent paper by Devdariani et al. [1], a formula was obtained that describes asymptotically forbidden quasimolecular optical transitions in the frame of the semiclassical approach. The main difficulty in the analytical description of asymptotically forbidden transitions is the consequence of the simple fact that the transition moments in this situation cannot be approximated by constant values as in the case of allowed transitions. However, potential energy curves and optical transition probability (or radiation width) usually can be reasonably approximated by exponential functions and a general formula which covers the central part of the spectral line, the extremum vicinity and the far wings, and also takes into account the fast exponential change in the state radiative width, can be obtained with the use of the Morse potential for the potential energy difference.
Our approach is based on a refinement of the theoretical model, based on the uniform Airy approximation as presented by Beuc and Horvatic [2]. The main point is careful treatment of the phases corresponding to the relevant Condon points and the resulting interference effects which in the same time take care of the variable transition moment in the vicinity of an extremum in the curve describing the difference between the electronic energies of the initial and the final states of the optical transition.
Bieniek et al. [3] have analyzed analogous processes of ionizing collisions in complex potentials within uniform JWKB stationary-phase techniques. Their numerical results are in excellent agreement with fully quantal, complex-potential computations. Our new results additionally support conclusions reached in [2] and [3] that the unified Franck-Condon theory is capable to describe asymptotically forbidden but collisionally induced transitions.
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[1] A. Devdariani, E. Bichoutskaia, E. Tchesnokov, T. Bichoutskaia, D. S. F. Crothers, E. Leboucher-Dalimier, P. Sauvan and P. Angelo, J. Phys. B.: At. Mol Opt. Phys. 35 (2002) 2469-2475
[2] R. Beuc and V. Horvatic, J. Phys. B: At. Mol. Opt. Phys. 25 (1992) 1497-1510
[3] R. J. Bieniek, M. W. Müller and M. Movre, J. Phys. B: At. Mol. Opt. Phys. 23 (1990) 4521-4538