Energy-modified adiabatic approximation for scattering theory

The adiabatic approximation in scattering theory is modified by allowing for the splitting and shifts of perturbed target-state energy levels. This energy-modified adiabatic approximation, derived from operator equations formally equivalent to close-coupling equations in the basis of perturbed target states, is shown to be qualitatively correct for threshold and resonance structures, for which the usual adiabatic theory is inadequate. In the case of electron-molecule vibrational excitation, it is shown that electronic threshold scattering structures should be associated with each vibrational threshold. A single electronic resonance becomes a manifold of multichannel vibrational excitation resonances. Vibrational excitation structures in $e^{-}-N_2$ scattering are computed as an example of the method.