The discrete quantum properties of matter are manifest in a variety of phenomena. Any particle that is trapped in a sufficiently deep and wide potential well is settled in quantum bound states. For example, the existence of quantum states of electrons in an electromagnetic field is responsible for the structure of atoms, and quantum states of nucleons in a strong nuclear field give rise to the structure of atomic nuclei. In an analogous way, the gravitational field should lead to the formation of quantum states. But the gravitational force is extremely weak compared to the electromagnetic and nuclear force, so the observation of quantum states of matter in a gravitational field is extremely challenging. Because of their charge neutrality and long lifetime, neutrons are promising candidates with which to observe such an effect. Here we report experimental evidence for gravitational quantum bound states of neutrons. The particles are allowed to fall towards a horizontal mirror which, together with the Earth's gravitational field, provides the necessary confining potential well. Under such conditions, the falling neutrons do not move continuously along the vertical direction, but rather jump from one height to another, as predicted by quantum theory.

The lowest stationary quantum state of neutrons in the Earth's gravitational field is identified in the measurement of neutron transmission between a horizontal mirror on the bottom and an absorber/scatterer on top. Such an assembly is not transparent for neutrons if the absorber height is smaller than the ''height'' of the lowest quantum state.

We study possibility of efficient reflection of very cold neutrons (VCN) from powders of nanoparticles. In particular, we measured the scattering of VCN at a powder of diamond nanoparticles as a function of powder sample thickness, neutron velocity and scattering angle. We observed extremely intense scattering of VCN even off thin powder samples. This agrees qualitatively with the model of independent nanoparticles at rest. We show that this intense scattering would allow us to use nanoparticle powders very efficiently as the very first reflectors for neutrons with energies within a complete VCN range up to $10^{-4}$ eV

We studied the phenomenon of relatively small changes in the energy of ultracold neutrons (UCN) (when compared to thermal motion energy) when these are reflected on a surface. The changes observed involved both increases in UCN energy (their heating) and decreases (cooling) of the order of ~ 10-7 eV. The probability values of this process on various surfaces ranged between 10-8 and 10-5 per one collision; the probability of such a small heating was many times larger than that of such a small cooling. We measured the spectra of such heated neutrons and the dependence of small heating probability on the temperature of sample out-gazing. We found that out-gazing of samples in vacuum at a temperature of 500–600 K could increase the small heating probability on stainless steel surface by a factor of ~ 100; and on copper surface by a factor of ~ 10. We observed, for the first time, extremely intensive small heating of UCN on powder of diamond nanoparticles. Neither small heating of UCN, nor nanoparticles could be found on a sapphire single crystal surface. This set of experimental data indicates that the inelastic scattering of UCN on weakly bound nanoparticles at a surface in a state of thermal motion is responsible for the process investigated.

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