Exact analytic solutions are found for the Dirac equation in 2+1 dimensions for a spinone- 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 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 found that the presence of the Ahanorov-Bohm flux tends to stabilize the system.
Relation:
Chinese Journal of Physics=中華民國物理學刊 47(3), pp.294-304
