Neutron determination of magnon dispersion relations for isotropic disordered magnets

To determine the neutron inelastic coherent scattering (NIS) cross-section for disordered magnets a system of equations of motion for the Green functions (GF) related to the localized-spin correlation-functions S _R⁺S _R′^-, S _R^-S _R′^-, S _R^zS _R′^- has been exploited. The formula for the magnon dispersion relations derived here covers a number of spin structures and depends on the configuration averages of the local fields. It should be emphasized that in particular it works for transverse antiferromagnets.