Semiclassical multistate curve-crossing models: Reduction of the transition amplitudes to diabatic and adiabatic phase integrals

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Abstract
A systematic procedure for deriving semiclassical transition amplitudes in multistate curve-crossing situations is used to prove that, apart from a phase factor, this amplitude can be expressed entirely with the action angles defining the diabatic and adiabatic levels. This formulation is useful in intermediate coupling regimes where coincidences between diabatic and adiabatic levels are responsible for the structure in cross sections. The way to use this transition amplitude when the initial or final (or both) channels are closed is indicated. A numerical example concerning resonance Raman scattering is worked out.