Stueckelberg close-curve-crossing phases

Abstract
A discussion of the semiclassical two-channel close-'curve-crossing' S matrix is given, with special reference to Stueckelberg phases as calculated within the non-adiabatic parabolic model. It is shown that the phase Gamma 1, normally associated with elastic adiabatic evolution through the 'curve crossing', is considerably in error when calculated within the Landau-Zener approximation, but shows favourable agreement with earlier numerical evaluations from coupled equations, provided the full Zwaan-Stueckelberg phase-integral interpretation is effected.