Perturbed symmetric resonance: the parabolic model

Abstract

An exact parabolic model for perturbed symmetric resonance is developed and solved. To supplement the Zwaan-Stueckelberg theory (1932) a comparison-equation method is adopted. It reduces the problem to parabolic cylinder function factors for which the corres ponding diabatic crossing is classically inaccessible. Appeal to the author's previous strong-coupling expansions for parabolic cylinder functions of large order (1972) and argument is made to reinforce the view that the adiabatic treatment gives the more precise picture. Both semiclassical and impact-parameter derivations are given. Previous formulae as reported by the author are proven (1971).