Semiclassical theory of molecular collisions: collinear atom harmonic oscillator collisions with attractive interactions

Semiclassical transition probabilities have been calculated for the collinear collision of an atom with a harmonic oscillator interacting via a Lennard-Jones (12, 6) or Morse interaction. Calculations have been made for both classically allowed and classically forbidden transitions. The uniform Airy and Bessel semiclassical approximations agree well with exact quantum results, although care is necessary for elastic transitions. The Airy approximation breaks down for near elastic collisions whilst the Bessel approximation breaks down for low quantum numbers at high collision energies (especially for 0 →0 transitions). The primitive semiclassical approximation is generally less accurate than either the Airy or Bessel approximations.