The theory of inelastic scattering of neutrons in ferromagnetic crystals containing impurities

On the basis of the theory developed by the author in the previous paper the cross section of one-magnon neutron scattering in a crystal containing a low concentration of impurities is calculated. When the energy transfer is less than the widths of the band of the quasi-continuous spectrum of spin excitations the one-magnon scattering consists of two parts, coherent and incoherent, with effective scattering amplitudes depending on the energy transfer. The widths of the peaks in the energy distribution of neutrons coherently scattered by spin waves are calculated and it is shown that the widths have a resonance character near an energy transfer corresponding to the levels of quasi-localized states of s, p or d type. The cross section of the incoherent scattering shows a resonance only near the level of a quasi-localized s state. When the energy transfer is larger than the width of the band, neutrons are scattered by localized modes of s, p and d type. This scattering is incoherent and the amplitudes of scattering by localized modes of different types have a different angular dependence, the observation of which should allow the determination of the degree of localization of the corresponding states in the crystal.