The role of vibrational excitations in collision-induced dissociation using Faddeev–AGS theory

Abstract

This paper examines the role of vibrational (and rotational) excitations in collision-induced dissociation in atom–diatom reactions. We treat a model system of identical, bosonic hydrogen atoms and investigate the total H+H2→H+H+H cross section as functions of total center-of-mass (c.m.) energy and vibrational–rotational quantum numbers v, j. The investigations are based on Faddeev–AGS theory and both three-dimensional (3D) and collinear (one-dimensional, 1D) geometries are considered. We derive both low- and high-energy relations between the total dissociation cross section, c.m. energy, and the vibrational–rotational wave functions, employing the single-scattering approximation of Faddeev theory. We apply these relations to the spectrum of the Kolos–Wolniewicz potential, both in three dimensions and one dimension. For collisions with a fixed total c.m. energy, our investigations predict considerable vibrational enhancement of the total cross section in the low-energy limit, with this enhancement much more pronounced in the true 3D dynamics than in the artificial collinear geometry, indicating that translational energy is less effective than vibrational in CID. As the c.m. (or translational) energy increases, approaching infinity, a transition occurs to either no enhancement or inhibition, or to slight vibrational inhibition, depending on the nature of the underlying interaction. This property mainly results from how the momentum distributions of the diatomic wave functions sense the available phase space of the dissociation reaction. In light of the anticipated failure of the single-scattering approximation at low collision energies, the predicted trends for vibrational enhancement are tested by calculating dissociation cross sections with exact Faddeev theory for weakened H–H potentials. While the single-scattering approximation does indeed break down badly, the ratio of cross sections for different vibrational states is largely unchanged from the exact. An explanation of this fact, using a modified single-scattering argument with radially cut-off diatomic wave functions, is discussed and developed physically.