Effect of the potential well on vibrational scattering and the validity of SSH theory

The vibrational de‐excitation probability, P ₁₀, is calculated quantum mechanically over a large energy range for models of three collision systems: $O2–O2, Cl2–Cl2$⁠, and $Br2–Br2$⁠. The vibrational de‐excitation cross section, $σ10$⁠, is similarly calculated for the $Cl2–Cl2$ model. P ₁₀ and $σ10$ are obtained for the Lennard‐Jones intermolecular potential and three other ``well‐less'' potentials designed to duplicate the scattering of the Lennard‐Jones potential. The results emphasize the adiabatic nature of potentials with wells and indicate that the acceleration approximation for the effect of the well is not valid. The curves of P ₁₀ and $σ10$ as a function of initial translational energy are used to obtain exact collision numbers. These numbers are compared to the results of SSH theory. SSH theory is found to predict collision numbers with reasonable accuracy except at low temperatures. SSH theory is also not suitable for analyzing experimental collision numbers for the well depth potential parameter.