A critique of Zwaan-Stueckelberg phase integral techniques

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Abstract
The Zwaan-Stueckelberg technique, based on semi-classical J.W.K.B. phase integrals and their analytic continuation in the complex plane, is reviewed. Stueckelberg's derivation of Jeffreys' connection formula is discussed, as are his connection formulae for strongly coupled, non-adiabatic collisions involving adiabatic crossings or diabatic non-crossings. His choice of branch cut is clarified. Avoided adiabatic crossings are described using both physical and non-physical branch cuts. Other limitations and defects of the Stueckelberg treatment are examined in detail and most are eliminated. New formulae for the general non-crossing case are presented. They describe perturbed symmetric resonance, reducing in an exactly correct manner for the Rosen-Zener model and also for exact resonance. Within a dynamical adiabatic treatment they also describe perturbed united-atom degeneracy, giving rise to strong rotational coupling in σ-π transitions. The limitation of the Landau-Zener theory to σ-σ transitions is thus avoided.

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