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The development of ideas about the optical phenomenon called the accelerating matter effect led to the hypothesis of the existence of a very general acceleration effect. Its formulation is that the result of the particle interaction with any object moving with acceleration should be a change in its energy and frequency. The validity of the acceleration effect hypothesis in quantum mechanics has recently been confirmed by numerically solving a number of problems related to the interaction of a wave packet with potential structures moving with acceleration. If these ideas are true, they can be fully attributed to the case of neutron scattering on the atomic nuclei of accelerating matter. Since the time of neutron interaction with the nucleus is very short, the observation of the acceleration effect during scattering by nuclei requires them to move with a very high acceleration. This goal can be achieved if centripetal acceleration is used., Comment: We realized that this approach is not quite correct

Spectra of ultracold neutrons that appeared in experiments on neutron diffraction by a moving grating were measured using the time-of-flight Fourier spectrometer. Diffraction lines of five orders were observed simultaneously. The obtained data are in good agreement with the theoretical predictions based on the multiwave dynamical theory of neutron diffraction by a moving grating., Comment: Submitted to Phys. Rev. A

We describe a new time-of-flight Fourier spectrometer for investigation of UCN diffraction by a moving grating. The device operates in the regime of a discrete set of modulation frequencies. The results of the first experiments show that the spectrometer may be used for obtaining UCN energy spectra in the energy range of 60$\div$200 neV with a resolution of about 5 neV. The accuracy of determination of the line position was estimated to be several units of $10^{-10}$ eV, Comment: Submitted to NIMA

A new approach to the free fall experiment with UCN is proposed. The idea is that the experiment is performed with neutrons from different equidistant lines of a discrete energy spectrum with a precisely known distance between the lines. Such a spectrum may be formed by neutron diffraction from a moving phase grating. Time-of-flight values of neutrons from different lines of the spectrum must be measured. Neither the initial neutron energy, nor the geometry parameters of the installation are required to be known in this method., Comment: Submitted to proceedings of the 6th European Conference on Neutron Scattering (ECNS 2015)

We describe an experimental installation for a new test of the weak equivalence principle for neutron. The device is a sensitive gravitational spectrometer for ultra-cold neutrons allowing to precisely compare the gain in kinetic energy of free falling neutrons to quanta of energy ${\hbar}{\Omega}$ transferred to the neutron via a non stationary device, i.e. a quantum modulator. The results of first test experiments indicate a collection rate allowing measurements of the factor of equivalence $ { \gamma}$ with a statistical uncertainty in the order of $5{\times}10^{-3}$ per day. A number of systematic effects were found, which partially can be easily corrected. For the elimination of others more detailed investigations and analysis are needed. Some possibilities to improve the device are also discussed., Comment: Submitted to NIMA