Small angle magnetic inelastic neutron scattering as a criterion for the correctness of the existing Bose-representations of spin operators

The fourth order terms in Bose-operators of the spin deviations at low temperatures are taken into account in order to evaluate the corrective contribution to the spin-wave dispersion law and the corresponding differential cross section of the magnetic neutron scattering in ferromagnets with S = 12. The calculations are done for the case when the change in neutron scattering energy is comparable to the energy of dipolar interaction between atomic spins or between the spins and external magnetic field. The obtained theoretical results enable one to test directly the correctness of the existing Bose-representations of spin operators by analyzing the experimental intensities of the neutron magnetic scattering at small angles and the accompanying effects of neutron polarization.