"Skew" scattering of cold unpolarized neutrons in ferromagnetic crystal

The problem of neutron scattering by the single magnetic atom is theoretically considered in the second order perturbation theory. It is demonstrated that elastic scattering of unpolarized neutron by magnetic atom is skewed, i.e. contains the term with the symmetry of mixed product of the atom magnetic moment and wave vectors of incident and scattered neutrons. The problem of dynamical diffraction of unpolarized neutrons by the perfect ferromagnetic crystal is investigated. The case is considered when the Bragg condition is satisfied for two reciprocal lattice vectors. In this case neutron skew scattering manifests itself as the dependence of the diffracted beam intensity on the sign of the crystal magnetization. The calculations have been done for the diffraction of unpolarized neutrons by Dy crystal. In case of the diffraction by Dy the change of the intensity under the magnetization reversal achieves 50%.