Abstract
The semiclassical theory of potential scattering leads naturally to an inclusion of complex-value classical paths which describe classically forbidden processes. However, only a few of the existing complex trajectories contribute. The authors discuss which of these forbidden paths should be retained and a detailed investigation of the complex contributions is given for the special class of repulsive inverse-power potentials. The oscillatory structure of the quantum-mechanical differential cross section is resolved as an interference pattern of classically allowed and forbidden trajectories. The region of validity of the complex-trajectory approximation is investigated. For potentials with a minimum the forbidden trajectories contribute to scattering angles larger than the rainbow angle. This is demonstrated for a superposition of inverse-power potentials.
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