Molecular Collisions. XV. Classical Limit of the Generalized Phase Shift Treatment of Rotational Excitation: Atom—Rigid Rotor

Abstract

The generalized phase shift (GPS) approach to the problem of rotationally inelastic molecular collisions is extended from the level of the first‐order (semiclassical) approximation of Paper XIV to the essentially infinite order level, but specialized to the full classical limit. The limitations and assumptions are that (i) the de Boer reduced wavelength parameter be small (i.e., ${\Lambda }^{*}\text{≪ 1}$ ), (ii) the relative translational motion takes place under the influence of the orientation‐averaged (spherical) part of the anisotropic interaction potential (i.e., curved but planar trajectories), and (iii) the rotational energy, E_rot, may be well approximated by its classical expression (i.e., rotational quantum numbers $\text{≫ 1}$ ). The procedure is applied numerically to a model problem involving an anisotropic L‐J (12,6) potential (as in XIV), taking advantage of the previously computed generalized action integrals. The program yields directly an arbitrarily chosen specified number of moments of the inelasticity probability density function $P{\mathrm{(\Delta \; E}}_{\mathrm{rot}})$ at various impact parameters b. Inversion of the set of moments leads to $P{\mathrm{(\Delta \; E}}_{\mathrm{rot}})$ . For the examples chosen, the lowest eight moments suffice to obtain practical accuracy of convergence on the inversion. For large b, i.e., in the weak‐coupling regime, the first moment vanishes and the second moment (which can be well‐approximated using the first‐order results of XIV) dominates, governing the breadth of the inelasticity density function.