  Ultracold and very cold neutrons (UCN and VCN) interact strongly with
nanoparticles due to the similarity of their wavelengths and nanoparticles
sizes. We analyze the hypothesis that this interaction can provide efficient
cooling of neutrons by ultracold nanoparticles at certain experimental
conditions, thus increasing the density of UCN by many orders of magnitude. The
present analytical and numerical description of the problem is limited to the
model of independent nanoparticles at zero temperature. Constraints of
application of this model are discussed.
