Dynamical diffraction of thermal neutrons by absorbing magnetic crystals

Dynamical diffraction of thermal neutrons is treated for a plane single-crystal plate of magnetic neutron-absorbing material. It is shown that the results of the theory of dynamical X-ray diffraction can be used in the case of neutron diffraction, when the Fourier transforms of the polarizability are replaced by the Fourier transforms of the interaction potential divided by the kinetic energy of the neutrons. The Fourier transforms of the magnetic part of the interaction potential are calculated expicitly. In order to take the nuclear part of the interaction into account the method of the Fermi pseudopotential is used. The results are applied to the case of symmetrical Bragg reflection. There are two solutions for the intensity of the reflected beam as a function of the angle of neutron incidence, corresponding to the two possible directions of the neutron spin, parallel or antiparallel to the magnetic field in the crystal. It is shown that the positions of the maxima and the widths of the curves illustrating the intensity dependence on the angle of neutron incidence are different for the two possible spin directions and depend on the direction of the magnetization in the crystal. The total intensity of the reflected beam for the diffraction of unpolarized neutrons is obtained by averaging the intensities for the two possible spin directions.