An improved and extended examination of the adiabatic distorted-wave infinite-order sudden approximation (ADWIOSA)

Abstract

Eno and Balint-Kurti recently presented an adiabatic distorted-wave formulation of the infinite-order sudden approximation (ADWIOSA) that has a number of appealing qualities for calculating vibrot excitations and de-excitations in atom–diatom collisions. The numerical values they determined for a limited number of He+H2 (nj)→He+H2 (n′j′) cross sections compared favorably to close-coupled results. However, they employed spectroscopic diatomic eigenenergies while the exact calculations were based on harmonic eigenenergies. This paper reports extended ADWIOSA cross sections for (0j)→(1j′), (1j)→(2j′), and (0j)→(2j′) transitions using harmonic eigenenergies, and also gives corrected versions of ADWIOSA formulas. The small change in eigenenergy lowers cross sections to 1/2–1/4 their previous values. The comparison to exact results is then not quite as favorable, which is generally due to limitations in the basic sudden approximation rather than the distorted-wave technique. The extended analysis also reveals clear trends in the sudden approximation. For fixed total energy, the ratio of a sudden approximation cross section and the corresponding exact value is an increasing function of the energy separation between initial and final vibrot states, and is a decreasing function of j0 (the typical diatomic rotational quantum number parameterizing the sudden approximation). Although satisfactory cross sections were often obtained for Δn=1 transitions, very inaccurate values were produced for Δn=2 transitions—probably because the ADWIOSA is only a first-order perturbation technique. Finally, it is shown that the properties of the ADWIOSA that result from choosing harmonic oscillators as the diatomic wave functions not only produce analytic expressions for potentials and coupling elements, but also yield an approximate, useful relationship between (n1, j)→(n1±1, j′) and (n2, j)→(n2±1, j′) transitions for the same collisional kinetic energies: σ(n1, j→n1±1, j′)/σ(n2, j→n2±1, j′) ? [minimum(n1,n1±1)+1]/[minimum(n2,n2±1)+1].