Optical theorem for Aharonov-Bohm scattering

TL;DR

This paper derives the optical theorem for Aharonov-Bohm scattering, accounting for a finite vortex core and boundary conditions, and analyzes the diffraction effects crucial for the theorem's validity.

Contribution

It provides a derivation of the optical theorem for Aharonov-Bohm scattering considering finite vortex size and boundary conditions, highlighting the role of diffraction.

Findings

Optical theorem holds regardless of Robin boundary conditions.

Diffraction effects persist in the short-wavelength limit.

Scattering amplitude behavior is analyzed in the forward direction.

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.