  Quantum-mechanical theory for scattering of nonrelativistic charged particles
with spin by a penetrable magnetic vortex is elaborated. The scattering
differential cross section is shown to consist of two terms, one describing
diffraction on the vortex in the forward direction and another one describing
penetration through the vortex. The Aharonov-Bohm effect is manifested as a
fringe shift in the diffraction pattern. The penetration effect is analyzed for
the case of the uniform distribution of the magnetic field strength inside the
vortex. We find that the penetrability of the magnetic vortex does not affect
the diffraction pattern, and, hence, the Aharonov-Bohm effect is the same for a
penetrable vortex as for an impenetrable one.
