Is semi-classical scattering theory accurate for transitions from low-lying vibrational states?

Abstract

Various semi-classical approximations are compared with exact transition probabilities from the lowest vibrational state for the forced harmonic oscillator. The primitive semi-classical transition probability is shown to be seriously inaccurate except, paradoxically, for the most strongly forbidden classical transitions. Bessel and Airy uniformizations lead to substantial and equivalent improvements for the 0 →n transitions. For the 0 →0 transition, the Bessel uniformization is correct in near elastic situations but the Airy uniformization is required for cases of strong interaction.

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Notes on contributors

P. Pechukas

On leave from Department of Chemistry, University of Columbia, New York, U.S.A.