  The scattering of electrons by an Aharonov--Bohm field is considered from the
viewpoint of quantum-mechanical problem of constructing a self-adjoint
Hamiltonian for the Pauli equation. The correct domain for the self-adjoint
Hamiltonian, which takes into account explicitly the electron spin is found. A
one-parameter self-adjoint extension of the Hamiltonian for spin-polarized
electrons in the Aharonov--Bohm field is selected. The correct domain of the
self-adjoint Hamiltonian can contain regular and singular (at the point ${\bf
r}=0$) square-integrable functions on the half-line with measure $rdr$. We
argue that the physical reason of the existence of singular functions is the
additional attractive potential, which appear due to the interaction between
the spin magnetic moment of fermion and Aharonov--Bohm magnetic field. The
scattering amplitude and cross section are obtained for spin-polarized
electrons scattered by the Aharonov--Bohm field. It is shown that in some range
of the extension parameter there appears a bound state. Since the Hamiltonian
of the nonrelativistic Dirac--Pauli equation for a massive neutral fermion with
the anomalous magnetic moment (AMM) in the electric field of a linear charge
aligned perpendicularly to the fermion motion has the form of the Hamiltonian
for the Pauli equation in the Aharonov--Bohm flux tube, we also calculate the
scattering amplitude and cross section for the neutral fermion.
