Effects of Nongauge Potentials on the Spin-1/2 Aharonov-Bohm Problem

TL;DR

This paper investigates how nongauge potentials influence the spin-1/2 Aharonov-Bohm problem, demonstrating that energy-dependent potentials can eliminate singular solutions and analyzing the effects of Coulomb interactions on the system.

Contribution

It introduces a Galilean spin-1/2 wave equation approach to avoid Klein's paradox and shows how energy-dependent nongauge potentials can remove singular solutions.

Findings

Singular solutions are eliminated with energy-dependent nongauge potentials.

The flux parameter range for singular solutions is halved with Coulomb potential.

Expressions for binding energies in the combined system are derived.

Abstract

Some recent work has attempted to show that the singular solutions which are known to occur in the Dirac description of spin-1/2 Aharonov-Bohm scattering can be eliminated by the inclusion of strongly repulsive potentials inside the flux tube. It is shown here that these calculations are generally unreliable since they necessarily require potentials which lead to the occurrence of Klein's paradox. To avoid that difficulty the problem is solved within the framework of the Galilean spin-1/2 wave equation which is free of that particular complication. It is then found that the singular solutions can be eliminated provided that the nongauge potential is made energy dependent. The effect of the inclusion of a Coulomb potential is also considered with the result being that the range of flux parameter for which singular solutions are allowed is only half as great as in the pure Aharonov-Bohm limit. Expressions are also obtained for the binding energies which can occur in the combined Aharonov-Bohm-Coulomb system.