View source for Neutron temperature

{{Short description|Kinetic energy of an unbound neutron}}
{{Use American English|date = March 2019}}
{{Science with neutrons}}
The '''neutron detection temperature''', also called the '''neutron energy''', indicates a [[free neutron]]'s [[kinetic energy]], usually given in [[electron volt]]s. The term ''temperature'' is used, since hot, thermal and cold neutrons are [[Neutron moderator|moderated]] in a medium with a certain temperature. The neutron energy distribution is then adapted to the [[Maxwell–Boltzmann distribution|Maxwell distribution]] known for thermal motion. Qualitatively, the higher the temperature, the higher the kinetic energy of the free neutrons. The [[momentum]] and [[wavelength]] of the neutron are related through the [[de Broglie relation]]. The long wavelength of slow neutrons allows for the large cross section.<ref name="debroglie">{{cite web |last1=de Broglie |first1=Louis |title=On the Theory of Quanta |url=http://aflb.ensmp.fr/LDB-oeuvres/De_Broglie_Kracklauer.pdf |website=aflb.ensmp.fr |access-date=2 February 2019}}</ref>

== Neutron energy distribution ranges ==

The precise boundaries of neutron energy ranges are not well defined, and differ between sources,<ref>
H. Tomita, C. Shoda, J. Kawarabayashi, T. Matsumoto, J. Hori, S. Uno, M. Shoji, T. Uchida, N. Fukumotoa and T. Iguchia, ''Development of epithermal neutron camera based on resonance-energy-filtered imaging with GEM'', 2012, quote: "Epithermal neutrons have energies between 1 eV and 10 keV and smaller nuclear cross sections than thermal neutrons."</ref> but some common names and limits are given in the following table.

{| class="wikitable"
|+ Neutron energy range names<ref>{{cite book|last=Carron|first=N.J.|title=An Introduction to the Passage of Energetic Particles Through Matter|year=2007|page=308|bibcode=2007ipep.book.....C}}</ref><ref name="neutronenergy">{{cite web |title=Neutron Energy |url=https://www.nuclear-power.net/nuclear-power/reactor-physics/atomic-nuclear-physics/fundamental-particles/neutron/neutron-energy/ |website=www.nuclear-power.net |access-date=27 January 2019}}</ref>
|-
! Neutron energy !! Energy range
|-
| 0.0 – 0.025 eV || Cold (slow) neutrons
|-
| 0.025 eV || Thermal neutrons (at 20&nbsp;°C)
|-
| 0.025–0.4 eV || Epithermal neutrons
|-
| 0.4–0.5 eV || Cadmium neutrons
|-
| 0.5–10 eV || Epicadmium neutrons
|-
| 10–300 eV || Resonance neutrons
|-
| 300 eV–1 MeV || Intermediate neutrons
|-
| 1–20 MeV || Fast neutrons
|-
| > 20 MeV || Ultrafast neutrons
|}

The following is a detailed classification:

=== Thermal ===
A '''thermal neutron''' is a free neutron with a kinetic energy of about 0.025 [[electron volt|eV]] (about 4.0×10<sup>−21</sup> [[Joule|J]] or 2.4 MJ/kg, hence a speed of 2.19&nbsp;km/s), which is the energy corresponding to the most probable speed at a temperature of 290 K (17&nbsp;°C or 62&nbsp;°F), the [[mode (statistics)|mode]] of the [[Maxwell–Boltzmann distribution]] for this temperature, E<sub>peak</sub> = [[Boltzmann constant|k]] T.

After a number of collisions with nuclei ([[scattering]]) in a medium ([[neutron moderator]]) at this temperature, those [[neutron]]s which are not absorbed reach about this energy level.

Thermal neutrons have a different and sometimes much larger effective [[neutron absorption]] [[Neutron cross-section|cross-section]] for a given [[nuclide]] than fast neutrons, and can therefore often be absorbed more easily by an [[atomic nucleus]], creating a heavier, often [[unstable isotope|unstable]] [[isotope]] of the [[chemical element]] as a result. This event is called [[neutron activation]].

===Epithermal===
{{example needed|date=July 2015}}

Epithermal neutrons are those with energies above the thermal energy at room temperature (i.e. 0.025 eV). Depending on the context, this can encompass all energies up to fast neutrons (as in e.g.<ref>W. C. Feldman et al., Fluxes of Fast and Epithermal Neutrons from Lunar Prospector: Evidence for Water Ice at the Lunar Poles.Science281,1496-1500(1998).DOI:10.1126/science.281.5382.1496</ref><ref>Mirfayzi, S.R., Yogo, A., Lan, Z. et al. Proof-of-principle experiment for laser-driven cold neutron source. Sci Rep 10, 20157 (2020). https://doi.org/10.1038/s41598-020-77086-y</ref>).

This includes neutrons produced by conversion of accelerated protons in a pitcher-catcher geometry <ref>Akifumi YOGO, Develompents of Laser-Driven Neutron Sourse based on “Pitcher-Catcher” Method, The Review of Laser Engineering, 2018, Volume 46, Issue 10, Pages 582-, Released on J-STAGE December 18, 2020. https://doi.org/10.2184/lsj.46.10_582</ref>

===Cadmium===
{{example needed|date=July 2015}}
:*Neutrons which are strongly absorbed by [[cadmium]]
:*Less than 0.5 eV.

===Epicadmium===
{{example needed|date=July 2015}}
:*Neutrons which are not strongly absorbed by cadmium
:*Greater than 0.5 eV.

===Cold (slow) neutrons===
{{example needed|date=July 2015}}
:* Neutrons of lower (much lower) energy than thermal neutrons.
:* Less than 5 meV.
:Cold (slow) neutrons are subclassified into cold (CN), very cold (VCN), and ultra-cold (UCN) neutrons, each having particular characteristics in terms of their optical interactions with matter. As the wavelength is made (chosen to be) longer,  lower values of the momentum exchange become accessible. Therefore, it is possible to study larger scales and slower dynamics. Gravity also plays a very significant role in the case of UCN. Nevertheless, UCN reflect at all angles of incidence. This is because their momentum is comparable to the optical potential of materials. This effect is used to store them in bottles and study their fundamental properties<ref>{{Citation |title=Introduction |date=2019-09-23 |url=https://www.worldscientific.com/doi/abs/10.1142/9789811212710_0001 |work=Ultracold Neutrons |pages=1–9 |publisher=WORLD SCIENTIFIC |doi=10.1142/9789811212710_0001 |isbn=978-981-12-1270-3 |s2cid=243745548 |access-date=2022-11-11}}</ref><ref>{{Cite journal |last1=Jenke |first1=Tobias |last2=Bosina |first2=Joachim |last3=Micko |first3=Jakob |last4=Pitschmann |first4=Mario |last5=Sedmik |first5=René |last6=Abele |first6=Hartmut |date=2021-06-01 |title=Gravity resonance spectroscopy and dark energy symmetron fields |journal=The European Physical Journal Special Topics |language=en |volume=230 |issue=4 |pages=1131–1136 |doi=10.1140/epjs/s11734-021-00088-y |s2cid=229156429 |issn=1951-6401|doi-access=free |arxiv=2012.07472 |bibcode=2021EPJST.230.1131J }}</ref> e.g. lifetime, neutron electrical-dipole moment etc... The main limitations of the use of slow neutrons is the low flux and the lack of efficient optical devices (in the case of CN and VCN). Efficient neutron optical components are being developed and optimized to remedy this lack.<ref>{{Cite book |last1=Hadden |first1=Elhoucine |last2=Iso |first2=Yuko |last3=Kume |first3=Atsushi |last4=Umemoto |first4=Koichi |last5=Jenke |first5=Tobias |last6=Fally |first6=Martin |last7=Klepp |first7=Jürgen |last8=Tomita |first8=Yasuo |title=Photosensitive Materials and their Applications II |chapter=Nanodiamond-based nanoparticle-polymer composite gratings with extremely large neutron refractive index modulation |editor-first1=Robert R |editor-first2=Yasuo |editor-first3=John T |editor-first4=Inmaculada |editor-last1=McLeod |editor-last2=Tomita |editor-last3=Sheridan |editor-last4=Pascual Villalobos |date=2022-05-24 |chapter-url=https://www.spiedigitallibrary.org/conference-proceedings-of-spie/12151/1215109/Nanodiamond-based-nanoparticle-polymer-composite-gratings-with-extremely-large-neutron/10.1117/12.2623661.full |publisher=SPIE |volume=12151 |pages=70–76 |doi=10.1117/12.2623661|bibcode=2022SPIE12151E..09H |isbn=9781510651784 |s2cid=249056691 }}</ref>

===Resonance===
{{example needed|date=July 2015}}
:*Refers to neutrons which are strongly susceptible to non-fission capture by [[Uranium-238|U-238]].
:*1 eV to 300 eV

===Intermediate===
{{example needed|date=July 2015}}
:*Neutrons that are between slow and fast
:*Few hundred eV to 0.5 MeV.

===Fast===
: A '''fast neutron''' is a free neutron with a kinetic energy level close to 1&nbsp;[[Mega-|M]][[electronvolt|eV]] (100&nbsp;[[tera-|T]][[Joule|J]]/[[Kilogram|kg]]), hence a speed of 14,000&nbsp;km/[[second|s]] or higher. They are named ''fast'' [[neutron]]s to distinguish them from lower-energy thermal neutrons, and high-energy neutrons produced in cosmic showers or accelerators.

Fast neutrons are produced by nuclear processes:
*[[Nuclear fission]]: thermal fission of {{chem|235|U}} produces neutrons with a mean energy of 2&nbsp;MeV (200&nbsp;TJ/kg, i.e. 20,000&nbsp;km/s),<ref name=Byrne2011>{{cite book |last1=Byrne |first1=James |title=Neutrons, nuclei, and matter: an exploration of the physics of slow neutrons |url=https://books.google.com/books?id=njUjm4Rkg9UC&pg=PA259 |date=2011 |publisher=Dover Publications |location=Mineola, N.Y |isbn=978-0-486-48238-5 |edition=Dover |page=259}}</ref> which qualifies as "fast". However, the energy spectrum of these neutrons approximately follows a [[right-skewed]] Watt distribution <math>N(E) \propto \exp(-aE) \sinh(\sqrt{bE})</math>,<ref>{{cite book |vauthors=Zijp WL, Nolthenius HJ, Baard JH, ((European Commission)) |author-link4=European Commission |title=Nuclear data guide for reactor neutron metrology |date=1989 |url=https://op.europa.eu/en/publication-detail/-/publication/90248cbb-e387-40ac-a02c-d1cdd11c70b2 |page=359 |publisher=Kluwer |location=Dordrecht |isbn=0-7923-0486-1 |id=CD-NA-12-354-EN-C}}</ref><ref>{{cite journal |last1=Watt |first1=B. E. |title=Energy Spectrum of Neutrons from Thermal Fission of U<sup>235</sup> |journal=Physical Review |date=15 September 1952 |volume=87 |issue=6 |pages=1037–1041 |doi=10.1103/PhysRev.87.1037|bibcode=1952PhRv...87.1037W }}</ref> with a range of 0 to about 17&nbsp;MeV,<ref name=Byrne2011/> a [[median]] of 1.6&nbsp;MeV,<ref name=Kauffman2024>{{cite journal |last1=Kauffman |first1=Andrew |last2=Herminghuysen |first2=Kevin |last3=Van Zile |first3=Matthew |last4=White |first4=Susan |last5=Hatch |first5=Joel |last6=Maier |first6=Andrew |last7=Cao |first7=Lei R. |title=Review of research and capabilities of 500 kW research reactor at the Ohio State University |journal=Annals of Nuclear Energy |date=October 2024 |volume=206 |doi=10.1016/j.anucene.2024.110647 |doi-access=free |bibcode=2024AnNuE.20610647K }}</ref> and a [[mode (statistics)|mode]] of 0.75&nbsp;MeV.<ref name=Byrne2011/> A significant proportion of fission neutrons do not qualify as "fast" even by the 1&nbsp;MeV criterion.
*[[Spontaneous fission]] is a mode of radioactive decay for some heavy nuclides. Examples include [[plutonium-240]] and [[californium-252]].
*[[Nuclear fusion#Criteria and candidates for terrestrial reactions|Nuclear fusion]]: [[deuterium]]&ndash;[[tritium]] fusion produces neutrons of 14.1&nbsp;MeV (1400 TJ/kg,&nbsp;i.e. 52,000&nbsp;km/s, 17.3% of the [[speed of light]]) that can easily fission [[uranium-238]] and other non-[[fissile]] [[actinides]].
*[[Neutron emission]] occurs in situations in which a nucleus contains enough excess neutrons that the [[separation energy]] of one or more neutrons becomes negative (i.e. excess neutrons "[[nuclear drip line|drip]]" out of the nucleus). Unstable nuclei of this sort will often decay in less than one second.

Fast neutrons are usually undesirable in a steady-state nuclear reactor because most fissile fuel has a higher reaction rate with thermal neutrons. Fast neutrons can be rapidly changed into thermal neutrons via a process called moderation. This is done through numerous collisions with (in general) slower-moving and thus lower-temperature particles like atomic nuclei and other neutrons. These collisions will generally speed up the other particle and slow down the neutron and scatter it. Ideally, a room temperature [[neutron moderator]] is used for this process. In reactors, [[heavy water]], [[Deuterium-depleted water|light water]], or [[graphite]] are typically used to moderate neutrons.
[[File:MaxwellBoltzmann-en.svg|right|thumb|upright=1.2|alt=See caption for explanation. Lighter noble gases (helium and neon depicted) have a much higher probability density peak at low speeds than heavier noble gases, but have a probability density of 0 at most higher speeds. Heavier noble gases (argon and xenon depicted) have lower probability density peaks, but have non-zero densities over much larger ranges of speeds.|A chart displaying the speed probability density functions of the speeds of a few [[noble gas]]es at a temperature of 298.15 K (25 C). An explanation of the vertical axis label appears on the image page. Similar speed distributions are obtained for [[neutron radiation|neutrons]] upon [[Neutron moderator|moderation]].]]

===Ultrafast===
{{example needed|date=July 2015}}
:*Relativistic
:*Greater than 20 MeV

===Other classifications===
;Pile
:*Neutrons of all energies present in nuclear reactors
:*0.001 eV to 15 MeV.
;[[Ultracold neutrons|Ultracold]]
:*Neutrons with sufficiently low energy to be reflected and trapped
:*Upper bound of 335 neV

==Fast-neutron reactor and thermal-neutron reactor compared==
Most [[nuclear reactor|fission reactor]]s are [[thermal-neutron reactor]]s that use a [[neutron moderator]] to slow down ("''thermalize''") the neutrons produced by [[nuclear fission]]. Moderation substantially increases the fission [[Nuclear cross section|cross section]] for [[fissile]] nuclei such as [[uranium-235]] or [[plutonium-239]]. In addition, [[uranium-238]] has a much lower capture cross section for thermal neutrons, allowing more neutrons to cause fission of fissile nuclei and propagate the chain reaction, rather than being captured by <sup>238</sup>U. The combination of these effects allows [[light water reactor]]s to use [[low-enriched uranium]]. [[Heavy water reactor]]s and [[graphite-moderated reactor]]s can even use [[natural uranium]] as these moderators have much lower [[neutron capture]] [[Neutron cross-section|cross section]]s than light water.<ref>[http://www.world-nuclear.org/education/phys.htm Some Physics of Uranium. Accessed March 7, 2009]</ref>

An increase in fuel temperature also raises uranium-238's thermal neutron absorption by [[Doppler broadening]], providing [[negative feedback]] to help control the reactor. When the coolant is a liquid that also contributes to moderation and absorption (light water or heavy water), boiling of the coolant will reduce the moderator density, which can provide positive or negative feedback (a positive or negative [[void coefficient]]), depending on whether the reactor is under- or over-moderated.

Intermediate-energy neutrons have poorer fission/capture ratios than either fast or thermal neutrons for most fuels. An exception is the [[uranium-233]] of the [[thorium cycle]], which has a good fission/capture ratio at all neutron energies.

[[Fast-neutron reactor]]s use unmoderated [[fast neutron]]s to sustain the reaction, and require the fuel to contain a higher concentration of [[fissile material]] relative to [[fertile material]] (uranium-238). However, fast neutrons have a better fission/capture ratio for many nuclides, and each fast fission releases a larger number of neutrons, so a [[fast breeder reactor]] can potentially "breed" more fissile fuel than it consumes.

Fast reactor control cannot depend solely on Doppler broadening or on negative void coefficient from a moderator. However, thermal expansion of the fuel itself can provide quick negative feedback. Perennially expected to be the wave of the future, fast reactor development has been nearly dormant with only a handful of reactors built in the decades since the [[Chernobyl accident]] due to low prices in the [[uranium market]], although there is now a revival with several Asian countries planning to complete larger prototype fast reactors in the next few years.{{when|date=December 2021}}

== See also ==
{{columns-list|colwidth=30em|
* [[Absorption hardening]]
* [[List of particles]]
* [[Neutron detection]]
* [[Neutron source]]
* [[Nuclear reaction]]
* [[Scintillator]]
}}

==References==
{{Reflist|2}}

==External links==
*[http://www.nuclearglossary.com/suites/nuclearglossary_neutrons.html Language of the Nucleus]

[[Category:Neutron|Temperature]]
[[Category:Temperature|Neutron]]