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American Journal of Physics

Semiclassical treatment of above-barrier scattering

Barry R. Holstein

Published Apr 1, 1984• 8 citations
Publisher

Abstract

We show how the semiclassical approach to barrier penetration based on path integral methods may be generalized to handle the case that the energy of the scattered particle is greater than the height of the potential barrier.
DOI
10.1119/1.13882

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The interaction between incident and target particles is inferred from the numbers and angular distribution of scattered particles and from their energy distribution. It is important to recognize that a scattering region, as represented for example by a rectangular barrier, is a region where, in classical terms, forces are applied to the incident particles. A full analysis of scattering events must, in principle, embody the description of a localized free particle that travels toward a center of force and is scattered by it. Quantum-mechanically, that implies a theoretical analysis in terms of packet states, with an explicit account of their change of position with time. One of the most striking effects described by quantum mechanics is the transmission of incident particles across a potential barrier whose height is greater than the particle energy. Classically, these particles lack the energy to get over the barrier, yet for quantum-mechanical systems some fraction of incident particles are transmitted.