  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 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.
