Collinear Collisions of an Atom and Harmonic Oscillator

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Abstract
A comparison is made between quantum, semiclassical, and classical treatments of collinear collisions, with exponential repulsive potential, between an atom and a harmonic oscillator. The quantum calculations used for comparison are those of Secrest and Johnson. The semiclassical treatment, which we call ITFITS, gives analytic transition probabilities in the form of a quantum forced oscillator whose energy transfer is determined separately for each combination of initial and final states by a “refined impulsive” classical approximation symmetrized over initial and final states. Detailed balance is obeyed. The classical treatment is phase averaged, the energy transfer, calculated by numerical integration of the equations of motion, being averaged over the initial phase of the oscillator. The quantum transition probabilities are very well matched for both single and multiple quantum jumps by the semiclassical ITFITS approximation. The quantum average energy transfer is closely approximated both by the semiclassical and classical treatments. We conclude that, over the range of the quantum data, a semiclassical analysis is quite reasonable for transition probabilities and that both semiclassical and classical treatments give an essentially accurate description of average energy partitioning.