Ultracold neutrons
Encyclopedia
Ultracold neutrons 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.
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 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 in order 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 is transformed 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.
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 . 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
.
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 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 magnetized
, the neutron optical potential is different for the two polarizations, caused by
where
is the magnetic moment of the neutron
and
the magnetic field created on the surface by the magnetization.
Each material has a specific loss probability per reflection,
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 10−4 to 10−3.
, to which the experiment of Arzumanov et al. contributes strongest. Ref. measured 
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., who found 
. Thus, the two most presicely measured values deviate by 5.6σ
(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).
Properties
The reflection is caused by the coherent strong interactionStrong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
of the neutron with atomic nuclei. It can be quantum-mechanically described by an effective potential which is commonly referred to as the Fermi
Enrico Fermi
Enrico Fermi was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics...
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
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
of incident neutrons must not be higher than this value in order to be reflected under any angle of incidence
Angle of incidence
Angle of incidence is a measure of deviation of something from "straight on", for example:* in the approach of a ray to a surface, or* the angle at which the wing or horizontal tail of an airplane is installed on the fuselage, measured relative to the axis of the fuselage.-Optics:In geometric...
, especially for normal incidence. The kinetic energy of 300 neV corresponds to a maximum velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
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
Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...
with a temperature of 3.5 mK.
Due to the small kinetic energy of an UCN, the influence of gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
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
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
of the neutron, produced by its spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
, interacts with magnetic fields. The total energy changes with ~60 neV/T.
History
It was Enrico FermiEnrico Fermi
Enrico Fermi was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics...
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 . 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
Walter Henry Zinn
Walter Henry Zinn was a nuclear physicist at the University of Chicago Metallurgical Laboratory.- Life and work :...
and Fermi and Leona Marshall . The storage of neutrons with very low kinetic energies was predicted by Yakov Borisovich Zel'dovich
Yakov Borisovich Zel'dovich
Yakov Borisovich Zel'dovich was a prolific Soviet physicist born in Belarus. He played an important role in the development of Soviet nuclear and thermonuclear weapons, and made important contributions to the fields of adsorption and catalysis, shock waves, nuclear physics, particle physics,...
and experimentally realized simultaneously by groups at Dubna
Joint Institute for Nuclear Research
The Joint Institute for Nuclear Research, JINR , in Dubna, Moscow Oblast , Russia, is an international research centre for nuclear sciences, with 5500 staff members, 1200 researchers including 1000 Ph.D.s from eighteen member states The Joint Institute for Nuclear Research, JINR , in Dubna, Moscow...
and Munich
Technical University of Munich
The Technische Universität München is a research university with campuses in Munich, Garching, and Weihenstephan...
.
Reflecting materials
| Material: | VF | vC | η (10−4) |
| Beryllium Beryllium Beryllium is the chemical element with the symbol Be and atomic number 4. It is a divalent element which occurs naturally only in combination with other elements in minerals. Notable gemstones which contain beryllium include beryl and chrysoberyl... |
252 neV | 6.89 m/s | 2.0-8.5 |
| BeO BEO BEO may refer to:* Banquet event order* Belmont Airport IATA code* Book entry onlyBeo is a variant of the name of the Anglo-Saxon god Beowa.BeO is the chemical formula for beryllium oxide.... |
261 neV | 6.99 m/s | |
| Nickel Nickel Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile... |
252 neV | 6.84 m/s | 5.1 |
| Diamond Diamond In mineralogy, diamond is an allotrope of carbon, where the carbon atoms are arranged in a variation of the face-centered cubic crystal structure called a diamond lattice. Diamond is less stable than graphite, but the conversion rate from diamond to graphite is negligible at ambient conditions... |
304 neV | 7.65 m/s | |
| Graphite Graphite The mineral graphite is one of the allotropes of carbon. It was named by Abraham Gottlob Werner in 1789 from the Ancient Greek γράφω , "to draw/write", for its use in pencils, where it is commonly called lead . Unlike diamond , graphite is an electrical conductor, a semimetal... |
180 neV | 5.47 m/s | |
| Iron Iron Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust... |
210 neV | 6.10 m/s | 1.7-28 |
| Copper Copper Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish... |
168 neV | 5.66 m/s | 2.1-16 |
| Aluminium Aluminium Aluminium or aluminum is a silvery white member of the boron group of chemical elements. It has the symbol Al, and its atomic number is 13. It is not soluble in water under normal circumstances.... |
54 neV | 3.24 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 (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
Beryllium is the chemical element with the symbol Be and atomic number 4. It is a divalent element which occurs naturally only in combination with other elements in minerals. Notable gemstones which contain beryllium include beryl and chrysoberyl...
, Beryllium oxide
Beryllium oxide
Beryllium oxide , also known as beryllia, is an inorganic compound with the formula BeO. This colourless solid is a notable electrical insulator with a higher thermal conductivity than any other non-metal except diamond, and actually exceeds that of some metals. As an amorphous solid, beryllium...
, Nickel
Nickel
Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...
(including 58Ni) and more recently also diamond-like carbon
Diamond-like carbon
Diamond-like carbon exists in seven different forms of amorphous carbon materials that display some of the typical properties of diamond. They are usually applied as coatings to other materials that could benefit from some of those properties. All seven contain significant amounts of sp3...
(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
Magnetization
In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material...
, the neutron optical potential is different for the two polarizations, caused by
where
is the magnetic moment of the neutronNeutron magnetic moment
The neutron magnetic moment is the magnetic moment of the neutron. It is of particular interest, as magnetic moments are created by the movement of electric charges. Since the neutron is a neutral particle, the magnetic moment is an indication of substructure, i.e...
and
the magnetic field created on the surface by the magnetization.Each material has a specific loss probability per reflection,
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 10−4 to 10−3.
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 , to which the experiment of Arzumanov et al. contributes strongest. Ref. measured 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., who found . Thus, the two most presicely measured values deviate by 5.6σMeasurement of the neutron electric dipole moment
The neutron electric dipole momentNeutron electric dipole moment
The neutron electric dipole moment is a measure for the distribution of positive and negative charge inside the neutron. A finite electric dipole moment can only exist if the centers of the negative and positive charge distribution inside the particle do not coincide. So far, no neutron EDM has...
(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).