A theoretical study of the vibrational excitation of diatomic molecules

Abstract

Exact quantum mechanical-vibrational transition probabilities are calculated for a collinear atom-diatomic molecule collision, using the real reactance matrix K. Both the Morse and harmonic binding potentials are considered. It is found that the discrepancy between the transition probabilities for these binding potentials may be large, depending on the collision parameters m and α; the discrepancy increases as m becomes large and decreases as α becomes large. Large Morse well depths (characterised by large values Of De) do not necessarily imply agreement between the transition probabilities of the two oscillators. Anharmonicity will be important in most collisions. The validity of several approximate theories when applied to this problem is investigated, It is found that the revised first order distorted wave approximation of Mies (1964a), and hence the revised first order perturbation theory approximation (Mies 1964b), are valid providing the reduced mass m is not too large or the collision too strong. Based on these investigations the one-dimensional form of the correspondence principle for strongly coupled states (Percival and Richards 1970a) is modified to include, approximately, the perturbation of the bound system. The modified theory is tested on the system of a harmonic oscillator, perturbed by a potential q2F(t) and excellent agreement with the exact quantum mechanical solution is obtained. The theory is then applied to the collinear atom-diatomic molecule collision, with a Morse molecular binding potential. For a large range of collision parameters, the results are in good agreement with the exact quantum mechanical transition probabilities, even for low order transitions. The modified correspondence principle is shown to have a larger range of validity than the revised first order perturbation theory approximation of Mies (1964b)to which it reduces in the weak perturbation limit.