Anomalous behavior of the dispersion of a neutron transmitting through a crystal at nearly Bragg energies

The features of the propagation of a neutron through a crystal at nearly Bragg energies has been studied within the framework of the preparation of an experiment on the search for the electric dipole moment of a neutron by the crystal diffraction method. The time of passage of the neutron through the crystal has been studied as a function of the deviation from the Bragg condition. The anomalous behavior of the dispersion of the neutron, i.e., the energy dependence of its average velocity, has been observed. It has been shown that the derivative $dv/dE$ for the diffracting neutron at nearly Bragg energies can be three or four orders of magnitude larger than this derivative for a free neutron. This opens new possibilities in precision neutron spectroscopy.