Semiclassical analytical approach to the description of quasimolecular optical transitions

Abstract

A formula was obtained that describes asymptotically forbidden quasimolecular optical transitions in the frame of the semiclassical approach. It is particularly relevant for the weak extrema in the difference between the ground-and excitedstate interaction potentials. When averaged over impact parameters and velocity distribution the formula agreed reasonably well with the recent experimental data for the Ca(4 1 S → 3 1 D) + He transition.

Semiclassical description of collisionally induced rainbow satellites: a model study

“…one needs to know only the amplitude for the zero impact parameter. Devdariani et al [5] obtained a formula that describes asymptotically forbidden quasimolecular optical transitions in the frame of the semiclassical approach. They pointed out the difficulties in the analytical description of asymptotically forbidden transitions, for example due to the fact that the transition moments in this situation cannot be approximated by constant values as in the case of allowed transitions.…”

“…In this work, a detailed analysis was performed of the applicability of various asymptotic approaches to the analytically solvable Devdariani model [5]. The analyticity of the model enables both obtaining the approximate asymptotic results in the closed (analytic) form and checking them against the exact solution.…”

“…Our approach to the model case [5] is based on the application of the uniform Airy approximation [6,7] to the integral in equation (4). This approximation was originally applied to the asymptotically allowed transitions [8][9][10].…”

“…With the model functions (13) and (14), x min → −∞, and for 0 < ρ < 2 the integral in equation (10) can be calculated in the closed form [5], and the final formula reads…”

“…This contribution is negligible for ≈ 0 whenever (ρ − 1 2 ) 2 1.88 λ 2/3 . We note in passing that Devdariani et al [5] used ρ = 0.54, the value chosen to describe the specific experimental example they discussed.…”