Semiclassical calculation of the harmonic oscillator transition probability for a collinear hard sphere collision

Closed form expressions are obtained for the vibrational transition probabilities in a semiclassical formulation for the inelastic hard sphere collision of an atom with a harmonic oscillator. The uniform semiclassical expression is found to be in excellent agreement with the numerically computed quantum mechanical transition probabilities. Expressions are also obtained for the average energy transfer in this collision and for the scattering of atoms from a hard cube model surface.