Neutron diffraction by perfect crystals

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Abstract
The dynamical theory of neutron diffraction has been formulated to include the reflected waves from the boundaries of a crystal. This formulation allows a unified treatment of the neutron optical and diffraction phenomena in crystals. It is shown that the neutron propagation in the crystal is determined by two structure factors characterizing the lattice: the total structure factor and the structure factor of the neutron-spin-neutron-orbit interaction. Diffraction by a parallel crystal plate has been studied in considerable detail. It has been found that for a definite neutron-spin orientation, the diffracted and transmitted beams are modulated by six terms periodic in the thickness of the crystal. The period of the dominant term, in this Pendellösung fringe structure, has been calculated in several cases of experimental importance. If the glancing angle of incidence substantially exceeds the critical angle for total reflection, the results are identical with those obtained by a simple extension, to the neutron case, of the x-ray dynamical theory. The diffraction by a magnetized crystal has been examined in some detail and it is shown that measurement of the Pendellösung periods for the two neutron-spin orientations may be used to determine both the nuclear and magnetic neutron scattering amplitude.