Abstract
The previous one-dimensional calculations of Shuler and Zwanzig for the vibrational transition probabilities for harmonic oscillators undergoing impulsive hard-sphere collisions with an incident atom have been extended to three dimensions. By the use of the modified wave number approximation, the three-dimensional scattering problem is related to the one-dimensional solution and the three-dimensional transition probabilities are obtained through numerical integration over the previously calculated one-dimensional probabilities. It is shown that vibrational transitions with | Δv | >1 are strongly allowed (in addition to the | Δv | = 1 transitions) in good agreement with the one dimensional impulsive collision results. The implication of this result on the mode and rate of the dissociation of diatomic molecules is discussed briefly.
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