Test of the quantum mechanical sudden vibrational approximation for collinear inelastic collisions

Numerical results for collinear vibrationally inelastic transition probabilities based on a quantum mechanical sudden vibrational approximation are presented. The results are compared with those obtained by replacing the vibrational wave functions by a semiclassical formula. For the exponentially repulsive potential employed, the quantal and semiclassical transition probabilities are given analytically. To test both theories transition probabilities are compared with exact results for three collision systems with different mass ratios as a function of energy. As the relative mass of the atom decreases the quantal approximation becomes quantitatively accurate whereas the semiclassical does not, independent of the energy