Rotationally inelastic scattering with effective potentials

Abstract

Appropriate close‐coupled equations and cross‐section expressions are derived starting with a previously developed effective intermolecular potential between an atom and a diatomic molecule. A comparison is made between the effective equations and those arising from the use of conventional potentials in close coupling. The effective expressions are algebraically simpler, and fewer effective coupled equations must be solved. Rotationally inelastic cross‐section calculations on the ${\mathrm{He–H}}_2$ system are carried out to illustrate the simplifications and also to present a more detailed study of this system. The effective total and differential cross sections agree quite well with previous conventional calculations. In addition, more extensive calculations are presented which include several transitions $\mathrm{J\; \to \; J\prime }$ not previously studied: $\text{0 → 2, 0 → 4, 0 → 6, 2 → 4, 2 → 6, 4 → 6}$ for parahydrogen and $\text{1 → 3, 1 → 5, 1 → 7\hspace{0.17em}, 3 → 5, 3 → 7, 5 → 7}$ for orthohydrogen at total energies up to E = 0.86 eV. The important role of rotation‐translation energy transfer is illustrated in these results. Finally, the expected region of validity and realm of usefulness of effective potentials is discussed.