Fermion pair production in planar Coulomb and Aharonov--Bohm potentials
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.
Keywords
Cite
@article{arxiv.0710.0959,
title = {Fermion pair production in planar Coulomb and Aharonov--Bohm potentials},
author = {V. R. Khalilov and Choon-Lin Ho},
journal= {arXiv preprint arXiv:0710.0959},
year = {2008}
}
Comments
8 pages, no figures. Title changed, some sentences refined, refereces updated