Scattering of a neutral fermion with anomalous magnetic moment by a charged straight thin thread

We consider the scattering of a massive neutral fermion with an anomalous magnetic moment in the electric field of a homogeneously charged straight thin thread from the standpoint of the quantum mechanical problem of constructing a self-adjoint Hamiltonian for the nonrelativistic Dirac–Pauli equation. Using the solutions obtained for the self-adjoint Hamiltonian, we investigate the scattering of the neutral fermion in the electric field of a thread oriented perpendicular to the plane of fermion motion (the Aharonov–Casher effect). We find expressions for the scattering amplitude and cross section of neutral fermions in the electric field of the thread. We show that the scattering amplitude and cross section depend both on the direct interaction between the fermion anomalous magnetic moment and the electric field and on the polarization of the fermionic beam in the initial state.