The available data on neutron scattering were reviewed to constrain a hypothetical new short-range interaction. We show that these constraints are several orders of magnitude better than those usually cited in the range between 1 pm and 5 nm. This distance range occupies an intermediate space between collider searches for strongly coupled heavy bosons and searches for new weak macroscopic forces. We emphasize the reliability of the neutron constraints insofar as they provide several independent strategies. We have identified a promising way to improve them.

Diamond, with its exceptionally high optical nuclear potential and low absorption cross-section, is a unique material for a series of applications in VCN (very cold neutron) physics and techniques. In particular, powder of diamond nanoparticles provides the best reflector for neutrons in the complete VCN energy range. It allowed also the first observation of quasi-specular reflection of cold neutrons (CN) from disordered medium. Effective critical velocity for such a quasi-specular reflection is higher than that for the best super-mirror. Nano-diamonds survive in high radiation fluxes; therefore they could be used, under certain conditions, in the vicinity of intense neutron sources.

The values of the antineutron-nucleus scattering lengths, and, in particular, their imaginary parts, are needed to evaluate the feasibility of using neutron mirrors in laboratory experiments to search for neutron-antineutron oscillations. We analyze existing experimental and theoretical constraints on these values with emphasis on low-$A$ nuclei and use the results to suggest materials for the neutron-antineutron guide and to evaluate the systematic uncertainties in estimating the neutron-antineutron oscillation time. As an example, we discuss a scenario for a future neutron-antineutron oscillation experiment proposed for the European Spallation Source. We also suggest future experiments which can provide a better determination of the values of antineutron-nuclei scattering lengths.