Quantum Vibrational Transition Probabilities in Atom–Diatomic Molecule Collisions. III. Reactive Scattering

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Abstract
The methods of Diestler and McKoy and Cheung and Wilson are combined to yield a procedure for calculating vibrational transition probabilities for inelastic reactive and nonreactive collisions. The model treated is that of a collinear collision between an atom and a diatomic molecule. The procedure should result in marked reductions in the computer time and core requirements for such calculations. An alternative method based solely on the approach of Cheung and Wilson is also developed; this method requires that the potential‐energy surface in the vicinity of the transition state be approximated by a quadratic form and should permit extremely rapid computation of reactive‐scattering transition probabilities. A second alternative method based on the use of the Born approximation in the vicinity of the transition state is also discussed.