Generalized Impact-Parameter Method for Low-Energy Molecular Collisions

A generalized impact-parameter method (not based upon perturbation theory) which is capable of describing the evolution of a collision system throughout the entire interaction region is developed. The method is then applied to the collision of a proton and a hydrogen atom at low (chemical) energies. The results obtained suggest that static calculations such as those using molecular potential-energy surfaces do not represent a very real picture of a dynamic process like a collision. Furthermore, the model does not assume linear trajectories for the atoms. This is shown from the calculations to be of importance in such low-energy collisions, the trajectories being far from linear. The model is capable of generalization to collisions in which more than two atoms are involved, such as the three-body reaction $A+BC\to AB+C$.