Effective potential formulation of molecule-molecule collisions with application to H2–H2

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Abstract
Coupled equations and cross section expressions are derived for the collision of two distinguishable and two identical molecules. A previously developed effective potential (Hamiltonian) formulation of molecular collisions is used throughout this paper. A semiclassical analysis of the total and differential cross sections is presented as an extension of previous elastic scattering studies. The semiclassical analysis is used to discuss conditions for significant quantum statistical oscillations in the elastic and inelastic identical molecule cross sections. Close coupling calculations for collisions of para‐para, ortho‐ortho, and ortho‐para hydrogen up to E = 0.725 eV are presented as an illustration of the general formulation. Various aspects of the H2–H2 potential are investigated. In particular, the different roles of the long‐ and short‐range anisotropies are illustrated. Both total and differential cross sections are presented for a number of transitions. The identical molecule inelastic differential cross sections show considerable quantum statistical oscillations, particularly in para‐para hydrogen. The degree of quantum statistical interference is shown to depend on the specific transition considered. The nature and desirability of certain experimental measurements is discussed with regard to determining the energy and angular dependent behavior of the cross sections.