Two hypothesizes concerning interaction of neutrons with nanoparticles and having applications in the physics of ultracold neutron (UCN) were recently considered in ref. [Physics of Atomic Nuclei 65(3): 400 (2002)]; they were motivated by the experimental observation of small changes in energy of UCN upon their collisions with surface. The first hypothesis explaines the nature of the observed phenomenon by inelastic coherent scattering of UCN on nanoparticles weakly attached at surface, in a state of permanent thermal motion. It got experimental confirmed in ref. [Physics of Atomic Nuclei 65(11): 1996 (2002)]. The second hypothesis inverts the problem of neutron interaction with nanoparticles in the following sence. In all experiments with UCN, the trap-wall temperature was much higher than a temperature of about 1 mK, which corresponds to the UCN energy. Therefore, UCN preferentially increased their energy. The surface density of weakly attached nanoparticles was low. If, however, the nanoparticles temperature is lower than the neutron temperature and if the nanoparticles density is high, the problem of interaction of neutrons with nanoparticles is inverted. In this case, the neutrons can cool down, under certain conditions, owing tot heir scattering on ultracold-heavy-water, deuterium, and oxigen nanoparticles to their temperature of about 1 mK, with result that the UCN density increases by many orders of magnitude. In the present article we repeat the argumentation given in the first mentioned article and formulate in a very general way the research program in order to verify validity of this hypothesis. Both the theoretical and the experimental investigation of the problem are going to intensify in the near future.
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