Collinear collision between a particle and a harmonic oscillator with a Morse potential interaction

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Abstract
The model problem of a collinear collision between a particle and a harmonic oscillator interacting via a Morse Potential is considered. The Devonshire formula, or the distorted wave formula, for the transition probabilities is corrected and a new formula is obtained which yields improved results. The origin of the correction is the improved treatment of the matrix elements of the interaction potential, and the correction is analogous to that made in the corresponding model problem in which the interaction potential is a repulsive exponential. The differences in scattering from the Morse potential and a purely exponential potential are discussed. A new correction factor to account for attractive forces is given; the result is similar to one given previously in simplicity, but yields a more accurate correction.