Semi-classical scattering theory and total cross sections for systems with many crossing points

A semi-classical theory for systems of potential curves with more than one crossing point is developed for cases where a two-state approximation is valid at each crossing point. Total excitation and quenching cross sections are computed for model systems and compared with those calculated using the Landau-Zener treatment which ignores the phases of the wavefunctions. It is found that in cases where flux may be reflected between two classical turning points of two or more potentials (either adiabatic or non-adiabatic), interference effects may change the distribution of outgoing flux in the open channels.