Ultracold neutrons (UCN) are free neutrons which can be stored in traps made from certain materials. The storage is based on the reflection of UCN by such materials under any angle of incidence.
Properties The reflection is caused by the coherent strong interaction of the neutron with atomic nuclei. It can be quantum-mechanically described by an effective potential which is commonly referred to as the Fermi pseudo potential or the neutron optical potential. The corresponding velocity is called the critical velocity of a material. Neutrons are reflected from a surface if the velocity component normal to the reflecting surface is less than or equal to the critical velocity. As the neutron optical potential of most materials is below 300 neV, the kinetic energy of incident neutrons must not be higher than this value to be reflected under any angle of incidence, especially for normal incidence. The kinetic energy of 300 neV corresponds to a maximum velocity of 7.6 m/s (or a minimum wavelength of 52 nm). As their density is usually very small, UCN can also be described as a very thin ideal gas with a temperature of 3.5 mK. Due to the small kinetic energy of an UCN, the influence of gravitation is significant. Thus, the trajectories are parabolic. Kinetic energy of an UCN transforms into potential (height) energy with ~102 neV/m. The magnetic moment of the neutron, produced by its spin, interacts with magnetic fields. The total energy changes with ~60 neV/T. UCN can lose polarization during their storage in material traps. The neutron spin-flip probability for the materials studied amounts to ~ (1–2)×10−5 per collision and does not depend on the temperature.
History Enrico Fermi first realized that the coherent scattering of slow neutrons would result in an effective interaction potential for neutrons traveling through matter, which would be positive for most materials. The consequence of such a potential would be the total reflection of neutrons slow enough and incident on a surface at a glancing angle. This effect was experimentally demonstrated by Fermi and Walter Henry Zinn and Fermi and Leona Marshall. The storage of neutrons with very low kinetic energies was predicted by Yakov Borisovich Zel'dovich and experimentally realized simultaneously by groups at Dubna and Munich.
UCN production There are various methods for the production of UCN. Such facilities have been built and are in operation:
The use of a horizontal evacuated tube from the reactor, curved so all but UCN would be absorbed by the walls of the tube before reaching the detector. Neutrons transported from the reactor though a vertical evacuated guide about 11 meters long are slowed down by gravity, so only those that happened to have ultracold energies can reach the detector at the top of the tube. A neutron turbine in which neutrons at 50 m/s are directed against the blades of a turbine wheel with receding tangential velocity 25 m/s, from which neutrons emerge after multiple reflections with a speed of about 5 m/s. Protons are accelerated to around 600 MeV and impinge on a lead target, producing neutrons via spallation. These neutrons are thermalized in e.g. heavy water and then moderated e.g. in liquid or solid deuterium to be cold. The final production of UCN occurs via downscattering in solid deuterium. Such a UCN source was realized at the Paul Scherrer Institute, Switzerland and at the Los Alamos National Laboratory, USA. Superfluid helium at low temperature can convert cold neutrons into ultracold ones. With a source of this type it is possible to achieve a UCN density of 1.3·104 n/cm3.
Reflecting materials
Any material with a positive neutron optical potential can reflect UCN. The table on the right gives an (incomplete) list of UCN reflecting materials including the height of the neutron optical potential (VF) and the corresponding critical velocity (vC). The height of the neutron optical potential is isotope-specific. The highest known value of VF is measured for 58Ni: 335 neV (vC = 8.14 m/s). It defines the upper limit of the kinetic energy range of UCN. The most widely used materials for UCN wall coatings are beryllium, beryllium oxide, nickel (including 58Ni), and, more recently, diamond-like carbon (DLC). Non-magnetic materials such as DLC are usually preferred for the use with polarized neutrons. Magnetic centers in e.g. Ni can lead to de-polarization of such neutrons upon reflection. If a material is magnetized, the neutron optical potential is different for the two polarizations, caused by
V F ( p o l . ) = V F ( u n p o l . ) ± μ N ⋅ B {\displaystyle V_{F}(pol.)=V_{F}(unpol.)\pm \mu _{N}\cdot B}
where μ N {\displaystyle \mu _{N}} is the magnetic moment of the neutron and B = μ 0 ⋅ M {\displaystyle B=\mu _{0}\cdot M} the magnetic field created on the surface by the magnetization. Each material has a specific loss probability per reflection,
μ ( E , θ ) = 2 η E cos 2 θ V F − E cos 2 θ {\displaystyle \mu (E,\theta )=2\eta {\sqrt {\frac {E\cos ^{2}\theta }{V_{F}-E\cos ^{2}\theta }}}}
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