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This article describes the classification of neutrons freed from the atomic nucleus according to kinetic energy with Ultra Cold Neutrons (UCN) being the slowest. This very interesting article overviews how UCNs could be contained and kinds of material to be used in the UCN trap.

It describes briefly about storage of UCNs in a material bottle covered with Fomblin oil. However it gives no details on the material bottle and wikipedia has no links to Fomblin oil, which is some kind of compressor oil. I don't believe it matters what kind of oil is used as I don't understand what properties of any kind of oil make them suitable for confining UCNs.

How the UCNs are stored doesn't make sense to me. Is this really possible? If so, what is the capacity of storage or maximum storage density in a defined container? I already exhausted Wikipedia on this topic. Since I am asking a question about applied physics, I assumed SE Engineering was the place to post this, but their feedback said Physics SE would be better since it is cutting edge research phase physics.

rob
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The Fermi pseudopotential associated with most materials is about $10^{-7}\rm\,eV = 100\rm\,neV$. This potential is present and uniform inside of a material and absent outside, so you can mathematically treat a neutron moving across a smooth surface between some material and a vacuum using the formalism for a one-dimensional step function potential, complete with partial transmission and partial reflection. For neutrons with kinetic energies smaller than the step potential, you get complete reflection: the neutrons exponentially penetrate the material, but unless they are absorbed they find themselves eventually in the reflected wave.

There's a completely equivalent explanation in terms of wave optics: a neutron interacting with a smooth surface can undergo total external reflection (compare) if the angle of incidence is grazing enough. For sufficiently long-wavelength neutrons, the critical angle for some materials can be larger than $90^o$: any neutron interacting with the surface is reflected. Those long-wavelength neutrons get the label "ultra-cold."

Fomblin oil is nice for several reasons. First, it's fluorinated rather than hydrogenated, so it's a terrible neutron absorber: a neutron may reflect from the oil many times without being captured. Second, Fomblin has good mechanical and vacuum properties at low temperature. I think that the first UCN experiment to use Fomblin was Serberov's "Gravitrap," which was an open-topped bucket. (A fun problem is to show that a $100\rm\,neV$ neutron near Earth's surface can't bounce any higher than about two meters. Serberov's neutron bucket didn't have a lid.) Other traps have solid walls, but then the surface quality becomes more important; since Fomblin oil remains liquid even in vacuum, it always forms smooth surfaces.

Ten years ago the world record UCN density was $10^3$ or $10^4\rm\,cm^{-3}$; I haven't been paying attention to the state of the art lately.

rob
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Ultracold neutrons can be stored because their magnetic moments allow them to scatter off of atomic electron clouds. If their kinetic energy (temperature) is high enough to allow them to kick electrons into higher orbitals, they will scatter inelastically and perhaps be absorbed by an atomic nucleus. Below this temperature they will elastically scatter off of the entire atom. The oil is what determines the value of this critical temperature.

As for your question about the density of storage, I'll leave that for someone other than myself to answer, but neutrons are fermions so the Pauli principle will provide an upper limit. Other factors will probably force a much lower density value.

Edit: Until I did some serious study of UCN research in response to the exchange of comments between @rob and myself (see below), I had not followed this field since the latter-1970s. The answer that I gave above was prevalent among some nuclear theorists at that time (I am quite sure that I did not make it up on my own). That was referred to as "magnetic scattering" and it does provide the explanation for UCN confined in magnetic traps (where a static magnetic field interacts with the neutron magnetic moment). In materials, however, magnetic scattering is not an adequate explanation of the phenomenon. Rob's answer is the currently accepted explanation. It is easy to demonstrate the failure of my answer by looking at the experimental neutron scattering lengths of different isotopes of the same element (see here. If magnetic scattering off of the electron cloud were the explanation then there would be no variation among isotopes.

Lewis Miller
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  • This answer is flawed. It's the strong interaction that repels neutrons from materials, not magnetism. The Pauli density limit occurs in neutron stars and is not experimentally accessible outside of a nucleus. – rob Sep 29 '17 at 00:20
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    @rob You are right about the significance of the Pauli density limit. As for the role of the strong interaction in confinement of ultracold neutrons, you are mistaken. It is the electromagnetic force that allows confinement. – Lewis Miller Sep 29 '17 at 14:32
  • For a derivation of the Fermi pseudopotential from the neutron-nucleus scattering length, with UCN confinement as an application, see Golub, Richardson, and Lamoreaux (1991). – rob Sep 29 '17 at 15:03
  • @rob Here is a link (https://www.aps.org/units/dnp/research/harvarducn.cfm) that demonstrates trapping of ultracold neutrons via static magnetic fields. That trapping is due to the interaction between the static field and the anomalous magnetic moment of the neutron. What makes the confinement by materials different? – Lewis Miller Sep 29 '17 at 15:03
  • That's the NIST magnetic bottle --- I considered that experiment as a PhD project. In that trap, one neutron polarization state is confined in the weak-magnetic-field region. (The superfluid helium is invisible to the neutrons for complicated reasons.) Any UCNs that interact with the material walls of the NIST magnetic trap are lost. But the questioner here asks about material bottles for UCNs. A neutron interacting with a neutral atom sees, to excellent approximation, only the nucleus. – rob Sep 29 '17 at 15:14
  • @rob I was once involved (1970s) in generating theoretical optical model porentials for neutrons scattering off nuclei. Those models all yielded attractive potentials for low energy neutrons (but not this low energy). That conflicts with the repulsion seen experimentally. How does the potential switch from attractive to repulsive a UCN energies? – Lewis Miller Sep 29 '17 at 15:27
  • I can't fit an explanation in the comments, but that would make a good follow-up question. – rob Sep 29 '17 at 17:36