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{{Science with neutrons}}
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'''Ultracold neutrons''' (UCN) are [[free neutron]]s 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 ''[[Enrico Fermi|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 or equal 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&nbsp;m/s or a minimum [[Wavelength#De Broglie wavelength of particles|wavelength]] of 52&nbsp;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 is transformed into potential (height) energy with ~102 neV/m.
 
The [[magnetic moment]] of the neutron, produced by its [[Spin (physics)|spin]], interacts with magnetic fields. The total energy changes with ~60 neV/T.
 
== History ==
It was [[Enrico Fermi]] who realized first 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.<ref>E. Fermi, Ricerca Scientifica '''7''' (1936) 13</ref> 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]] <ref>E. Fermi, W.H. Zinn, Phys. Rev. '''70''' (1946) 103</ref><!--10.1103/PhysRev.70.99--> and Fermi and Leona Marshall.<ref>E. Fermi, L. Marshall, Phys. Rev. '''71''' (1947) 666</ref> The storage of neutrons with very low kinetic energies was predicted by [[Yakov Borisovich Zel'dovich]]<ref>Ya.B. Zeldovich, Sov. Phys. JETP-'''9''' (1959) 1389</ref> and experimentally realized simultaneously by groups at [[Joint Institute for Nuclear Research|Dubna]] <ref>V.I. Lushikov ''et al.'', Sov. Phys. JETP Lett. '''9''' (1969) 23</ref> and [[Technical University of Munich|Munich]].<ref>A. Steyerl, Phys. Lett. '''B29''' (1969) 33</ref><!--10.1016/0370-2693(69)90127-0-->
 
== UCN production ==
{{Empty section|Production|date=May 2008}}
 
== Reflecting materials ==
{| class="wikitable" align=right
|- style="background:#CCCCCC"
| Material:||V<sub>F</sub><ref name="golub">R. Golub, D. Richardson, S.K. Lamoreaux, ''Ultra-Cold Neutrons'', Adam Hilger (1991), Bristol</ref>||v<sub>C</sub><ref name="ignatovich">V.K. Ignatovich, ''The Physics of Ultracold Neutrons'', Clarendon Press (1990), Oxford, UK</ref>||η (10<sup>−4</sup>)<ref name="ignatovich"/>
|-
| style="background:#DDDDDD"| [[Beryllium]]||252 neV ||6.89&nbsp;m/s || 2.0-8.5
|-
| style="background:#DDDDDD"| [[BeO]]||261 neV ||6.99&nbsp;m/s ||
|-
| style="background:#DDDDDD"| [[Nickel]]  ||252 neV ||6.84&nbsp;m/s || 5.1
|-
| style="background:#DDDDDD"| [[Diamond]]  ||304 neV ||7.65&nbsp;m/s ||
|-
| style="background:#DDDDDD"| [[Graphite]]  ||180 neV ||5.47&nbsp;m/s ||
|-
| style="background:#DDDDDD"| [[Iron]]    ||210 neV ||6.10&nbsp;m/s || 1.7-28
|-
| style="background:#DDDDDD"| [[Copper]]  ||168 neV ||5.66&nbsp;m/s || 2.1-16
|-
| style="background:#DDDDDD"| [[Aluminium]]  ||54 neV ||3.24&nbsp;m/s|| 2.9-10
|}
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 (''V<sub>F</sub>'') and the corresponding critical velocity (''v<sub>C</sub>''). The height of the neutron optical potential is isotope-specific. The highest known value of V<sub>F</sub> is measured for <sup>58</sup>Ni: 335 neV (v<sub>C</sub>=8.14&nbsp;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 <sup>58</sup>Ni) and more recently also [[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 [[Magnetization|magnetized]], the neutron optical potential is different for the two polarizations, caused by
 
<math>V_F(pol.)=V_F(unpol.)\pm\mu_N\cdot B</math>
 
where <math>\mu_N</math> is the [[neutron magnetic moment|magnetic moment of the neutron]] and <math>B=\mu_0\cdot M</math> the magnetic field created on the surface by the magnetization.
 
Each material has a specific '''loss probability'''  per reflection,
 
<math>\mu(E,\theta)=2\eta\sqrt{\frac{E\cos^2\theta}{V_F-E\cos^2\theta}}</math>
 
which depends on the kinetic energy of the incident UCN (''E'') and the angle of incidence (''θ''). It is caused by absorption and thermal upscattering. The '''loss coefficient''' η is energy-independent and typically of the order of 10<sup>−4</sup> to 10<sup>−3</sup>.
 
== Experiments with UCN ==
The production, transportation and storage of UCN is currently motivated by their usefulness as a tool to determine properties of the neutron and to study fundamental physical interactions. Storage experiments have improved the accuracy or the upper limit of some neutron related physical values.
 
=== Measurement of the neutron lifetime ===
Today's world average value for the neutron lifetime is <math>885.7\pm0.8~s</math>,<ref name="PDG">W.-M. Yao ''et al.'' (Particle Data Group), J. Phys. G '''33''', 1 (2006) and 2007 partial update for edition 2008 (URL: http://pdg.lbl.gov)</ref> to which the experiment of Arzumanov et al.<ref name="arzumanov"/> contributes strongest. Ref.<ref name="arzumanov">S. Arzumanov, L. Bondarenko, S. Chernyavsky, W. Drexel ''et al.'', Phys. Lett. B '''483''' (2000) 15</ref> measured <math>\tau_n=885.4\pm0.9_{\mathrm{stat}}\pm0.4_{\mathrm{syst}}~s</math> by storage of UCN in a material bottle covered with [[Fomblin oil]]. Using traps with different surface to volume ratios allowed them to separate storage decay time and neutron lifetime from each other. There is another result, with even smaller uncertainty, but which is not included in the World average. It was obtained by Serebrov et al.,<ref>A. Serebrov, V. Varlamov, A. Kharitonov, A. Fomin ''et al.'', Phys. Lett. B '''605''' (2005) 72</ref> who found <math>878.5~\pm0.7_{\mathrm{stat}}\pm0.4_{\mathrm{syst}}~s</math>. Thus, the two most precisely measured values deviate by 5.
 
=== Measurement of the neutron electric dipole moment ===
{{main|Neutron electric dipole moment}}
The [[neutron electric dipole moment]] (nEDM) is a measure for the distribution of positive and negative charge inside the neutron. No nEDM has been found until now (May 2008). Today's lowest value for the upper limit of the nEDM was measured with stored UCN (see main article).
 
=== Observation of the gravitational interactions of the neutron ===
 
Physicists have observed quantized states of matter under the influence of gravity for the first time. Valery Nesvizhevsky of the Institute Laue-Langevin and colleagues found that cold neutrons moving in a gravitational field do not move smoothly but jump from one height to another, as predicted by quantum theory. The finding could be used to probe fundamental physics such as the equivalence principle, which states that different masses accelerate at the same rate in a gravitational field (V Nesvizhevsky ''et al.'' 2001 Nature 415 297).
 
=== Measurement of the neutron-anti-neutron oscillation time ===
 
=== Measurement of the A-coefficient of the neutron beta decay correlation ===
The only reported measurement of the beta-asymmety is from the Los Alamos group. Here's the first paper using UCN to complete a measurement of A using UCN was a 4.5% measurement reported in http://prl.aps.org/abstract/PRL/v102/i1/e012301 the next result from the LANSCE group is also a PRL first authored by Jianglai Liu in 2010 which was roughly 1.5%  and a new result will be out in the coming year.
 
== References ==
<div class="references-1column">
<references/>
</div>
 
{{DEFAULTSORT:Ultracold Neutrons}}
[[Category:Neutron]]

Latest revision as of 21:30, 2 November 2014

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