Fermion pair production in planar Coulomb and Aharonov--Bohm potentials

TL;DR

This paper derives exact solutions for the Dirac equation in 2+1 dimensions with Coulomb and Aharonov--Bohm potentials, analyzing fermion pair production and the system's stability.

Contribution

It provides new analytic solutions for the Dirac equation with combined potentials and explores the impact of Aharonov--Bohm flux on system stability and pair production.

Findings

Aharonov--Bohm flux stabilizes the system.

Derived transcendental equations for energy spectrum and critical charges.

Analyzed fermion pair production near the negative-energy continuum boundary.

Abstract

Exact analytic solutions are found for the Dirac equation in 2+1 dimensions for a spin-one-half particle in a combination of the Lorentz 3-vector and scalar Coulomb as well as Aharonov--Bohm potentials. We employ the two-component Dirac equation which contains a new parameter introduced by Hagen to describe the spin of the spin-1/2 particle. We derive a transcendental equations that implicitly determine the energy spectrum of an electron near the negative-energy continuum boundary and the critical charges for some electron states. Fermion pair production from a vacuum by a strong Coulomb field in the presence of the magnetic flux tube of zero radius is considered. It is shown that the presence of the Ahanorov--Bohm flux tends to stabilize the system.