  The perturbation theory expansion of the Aharonov-Bohm scattering amplitude
has previously been studied in the context of quantum mechanics for spin zero
and spin-1/2 particles as well in Galilean covariant field theory. This problem
is reconsidered in the framework of the model in which the flux line is
considered to have a finite radius which is shrunk to zero at the end of the
calculation. General agreement with earlier results is obtained but with the
advantage of a treatment which unifies all the various subcases.
