Strong-Coupling Semiclassical Methods. The Average Approximation for Atom-Atom Collisions

Calculations on the $2p{\sigma }_u-2p{\pi }_u$ excitation in proton-hydrogen collisions demonstrate that strongly coupled radial equations may be solved using simple semiclassical approximations at the turning points. A theoretical justification of the best of these methods is based on an extension of the large-mass high-energy approximation into the turning-point region. Other model problems are solved to illustrate properties of this new average approximation.