Abstract
It is proven that the model transition probability sin2( tau x)sech2( tau y) for perturbed symmetric resonance, where tau is the collision time and x+iy is the complex adiabatic action difference integrated along a line joining the point of closest approach to a complex adiabatic degeneracy, is exact not only for (unperturbed) symmetric resonance but also for the Rosen-Zener and the Callaway-Bartling model potential problems. The theories of Stueckelberg (1932), Demkov (1964) and Nikitin (1968) are reconciled in that all provide good approximations to the new formula under various different restrictions. Further model potential problems are presented as illustrations of the efficacy of the model formula.