The Aharonov-Bohm effect in scattering of nonrelativistic electrons by a penetrable magnetic vortex

TL;DR

This paper develops a quantum-mechanical scattering theory for nonrelativistic electrons interacting with a penetrable magnetic vortex, demonstrating that the Aharonov-Bohm effect persists regardless of vortex penetrability.

Contribution

It provides a detailed analysis showing that the Aharonov-Bohm effect remains unchanged for penetrable vortices, extending previous understanding to more realistic vortex models.

Findings

The diffraction pattern is unaffected by vortex penetrability.

The Aharonov-Bohm fringe shift is consistent for both penetrable and impenetrable vortices.

Penetrability does not alter the fundamental quantum interference effect.

Abstract

Quantum-mechanical theory for scattering of nonrelativistic charged particles with spin by a penetrable magnetic vortex is elaborated. The scattering differential cross section is shown to consist of two terms, one describing diffraction on the vortex in the forward direction and another one describing penetration through the vortex. The Aharonov-Bohm effect is manifested as a fringe shift in the diffraction pattern. The penetration effect is analyzed for the case of the uniform distribution of the magnetic field strength inside the vortex. We find that the penetrability of the magnetic vortex does not affect the diffraction pattern, and, hence, the Aharonov-Bohm effect is the same for a penetrable vortex as for an impenetrable one.