Effects of nongauge potentials on the spin-1/2 Aharonov-Bohm problem

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 one-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