Optical theorem for Aharonov-Bohm scattering

Abstract

Quantum-mechanical scattering off a magnetic vortex is considered, and the optical theorem is derived. The vortex core is assumed to be impermeable to scattered particles, and its transverse size is taken into account. We show that the scattering Aharonov-Bohm effect is independent of the choice of boundary conditions from the variety of the Robin ones. The behaviour of the scattering amplitude in the forward direction is analyzed, and the persistence of the Fraunhofer diffraction in the short-wavelength limit is shown to be crucial for maintaining the optical theorem in the quasiclassical limit.