Upper bounds on many-channel scattering phase shifts by an adiabatic-type approximation

An approximate equation for the treatment of atom-atom collision problems is proposed, based on the assumption that in the closed channels nuclear kinetic energy is negligible compared with the electronic energy. It is shown that this approximation yields upper bounds on the exact scattering phase shifts when the collision energy lies below the lowest nonadiabatic resonance level. To test the quality of this approximation, three model problems, all of them involving two coupled channels one of which is closed, are introduced. Each of these models is solvable exactly, solvable in the ordinary adiabatic approximation (which provides lower bounds on the phase shifts) and solvable within the new approximation. The accuracy of the results obtained is discussed with special reference to its dependence upon the form and strength of the interactions involved.