Reaction Matrix Method for Computing Probabilities of Vibration—Translation Energy Transfer; Range of Applicability for the Collinear Collision of an Atom and a Diatomic

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Abstract
Transition probabilities for the case of a collinear collision of an atom and a harmonic oscillator are computed using both the distorted wave and K‐matrix approximations. Results are shown as a function of a new parameter β which incorporates the parameters E, m, and α of Secrest and Johnson and which is proportional to the ratio of the oscillator period divided by the collision time. Ranges of applicability for the above approximate methods are discussed in terms of β for one‐ and two‐quanta transitions. The K‐matrix approach is seen to extend the range of β for which the distorted wave approximation maintains a given degree of accuracy for one‐quantum transitions. Also the K‐matrix method yields vastly improved results for two‐quanta transitions which exhibit the same type of dependence on β as the one‐quantum‐transition probabilities.