  The planar non-relativistic quantum dynamics of a neutral massive fermion
with an anomalous magnetic moment (AMM) in the presence of the electric field
of infinitely long and thin thread with a charge density distributed uniformly
along it (an Aharonov--Casher field) is examined. The relevant Hamiltonian is
singular and requires additional specification of a one-parameter self-adjoint
extension, which can be given in terms of physically acceptable (self-adjoint)
boundary conditions. We find all possible self-adjoint Hamiltonians with an
Aharonov--Casher field (ACF) by constructing the corresponding Hilbert space of
square-integrable functions, including the $r = 0$ region, for all their
Hamiltoniahs. We determine the most relevant physical quantities, such as
energy spectrum and wave functions and discuss their correspondence with those
obtained by the physical regularization procedure. We show that energy levels
of bound states are simple poles of the scattering amplitude. Expressions for
the scattering amplitude and cross section depending on the fermion spin are
reexamined.
