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

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

2007-10-04

arxiv.org/abs/0710.0959v2

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, no figures. Title changed, some sentences refined, refereces updated

Scientific paper

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.

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