  The scattering of spin-polarized electrons in an Aharonov--Bohm vector
potential is considered. We solve the Pauli equation in 3+1 dimensions taking
into account explicitly the interaction between the three-dimensional spin
magnetic moment of electron and magnetic field. Expressions for the scattering
amplitude and the cross section are obtained for spin-polarized electron
scattered off a flux tube of small radius. It is also shown that bound electron
states cannot occur in this quantum system. The scattering problem for the
model of a flux tube of zero radius in the Born approximation is briefly
discussed.
