Quantum Vibrational Transition Probabilities in Atom–Diatomic Molecule Collisions

Abstract

A generalization of the method of Shuler and Zwanzig is shown to permit the calculation of the scattering matrix for collinear atom–diatomic molecule systems having rather general intermolecular potentials. The procedure is related to the method of invariant imbedding. It is then applied to the calculation of transition probabilities for a harmonic oscillator molecule interacting with the bombarding atom via a hard-sphere potential with a “step”—i.e., V(y) = ∞, y < σ0; V(y) = V1, σ0 ≤ y < σ1; V(y) = 0, σ1 ≤ y, where y is the distance between the bombarding atom and the nearest end of the molecule. The dependence of the transition probabilities on the height (depth) and width of the potential step is studied. Resonance effects on the transition probabilities were observed; these involve the De Broglie wavelength of the collisional motion and the width of the potential step. Application of this approach to diatomic–diatomic collisions is out-lined.