Elastic scattering and rotational excitation in ion-molecule collisions. II. Li+–H2 and H+–H2 collisions

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Abstract
A general semiclassical treatment of elastic scattering and of rotational excitation in ion–molecule collisions is presented. When the orbits associated with the different channels corresponding to the internal modes do not differ significantly, simplification occurs and the internal degrees of freedom can then be coupled to the relative motion via the introduction of an optical potential (which in turn depends on the transition amplitudes). Total energy is consequently conserved. An expression is derived for the inelastic scattering amplitude which acknowledges various interference effects and possible rainbow scattering. With all phase-information supressed, the procedure, when compared with the full quantum-mechanical results, reproduces the background elastic and inelastic scattering in Li+–H2 and in H+–H2 collisions. Restoration of the phases, particularly of the eikonal or action phases associated with the different classical paths that contribute to a specified scattering angle, produces the interference oscillations present in the differential cross section for scattering angles less than the rainbow angle. The method, when compared with the full quantal procedure, is remarkably efficient and accurate.