On the Energy Dependence of Inelastic Molecular Collision Probabilities

It is pointed out that because of the uncertainty principle, cross sections for inelastic molecular collisions vanish at the threshold, in sharp distinction to their classical behavior. The dependence of the inelastic collision probability on the energy is deduced and found to be of the form k2l+1(a0+a2k2+a4k4+···),where k and l are the wave number and the total angular momentum quantum number, respectively, which describe the incident wave in case of de-excitation or the emergent wave in case of excitation. It is shown that because of this property of inelastic collisions, the pre-exponential factor in the collision theory of bimolecular kinetics contains only non-negative integral powers of the temperature.