Editing Nuclear fission (section)

====Input====
[[File:Stdef2.png|150px|right|thumb|The stages of binary fission in a liquid drop model. Energy input deforms the nucleus into a fat "cigar" shape, then a "peanut" shape, followed by binary fission as the two lobes exceed the short-range [[nuclear force]] attraction distance, and are then pushed apart and away by their electrical charge. In the liquid drop model, the two fission fragments are predicted to be the same size. The nuclear shell model allows for them to differ in size, as usually experimentally observed.]]

Fission [[Nuclear cross section|cross sections]] are a measurable property related to the probability that fission will occur in a nuclear reaction. Cross sections are a function of incident neutron energy, and those for {{chem|235|U}} and {{chem|239|Pu}} are a million times higher than {{chem|238|U}} at lower neutron energy levels. Absorption of any neutron makes available to the nucleus binding energy of about 5.3&nbsp;MeV. {{chem|238|U}} needs a fast neutron to supply the additional 1&nbsp;MeV needed to cross the critical energy barrier for fission. In the case of {{chem|235|U}} however, that extra energy is provided when {{chem|235|U}} adjusts from an odd to an even mass. In the words of Younes and Lovelace, "...the neutron absorption on a {{chem|235|U}} target forms a {{chem|236|U}} nucleus with excitation energy greater than the critical fission energy, whereas in the case of ''n'' + {{chem|238|U}}, the resulting {{chem|239|U}} nucleus has an excitation energy below the critical fission energy."<ref name=ww/>{{rp|25–28}}<ref name=rr/>{{rp|282–287}}<ref>{{cite journal |last1=Bohr |first1=N. |title=Resonance in Uranium and Thorium Disintegrations and the Phenomenon of Nuclear Fission |url=https://journals.aps.org/pr/abstract/10.1103/PhysRev.55.418.2 |journal=Physical Review |publisher=American Physical Society |access-date=9 October 2023 |date=1939|volume=55 |issue=4 |pages=418–419 |doi=10.1103/PhysRev.55.418.2 |bibcode=1939PhRv...55..418B }}</ref><ref>{{cite web |title=Essential cross sections |url=https://eng.libretexts.org/Sandboxes/jhalpern/Energy_Alternatives/04%3A_Nuclear_Power/4.06%3A_Controlling_the_Fission_Chain_Reaction-_Nuclear_Reactors/4.6.01%3A_Essential_Cross_Sections |website=LibreTexts Library |date=July 2022 |access-date=9 October 2023}}</ref>

About 6&nbsp;MeV of the fission-input energy is supplied by the simple binding of an extra neutron to the heavy nucleus via the strong force; however, in many fissionable isotopes, this amount of energy is not enough for fission. Uranium-238, for example, has a near-zero fission cross section for neutrons of less than 1&nbsp;MeV energy. If no additional energy is supplied by any other mechanism, the nucleus will not fission, but will merely absorb the neutron, as happens when {{chem|238|U}} absorbs slow and even some fraction of fast neutrons, to become {{chem|239|U}}. The remaining energy to initiate fission can be supplied by two other mechanisms: one of these is more kinetic energy of the incoming neutron, which is increasingly able to fission a [[fissionable]] heavy nucleus as it exceeds a kinetic energy of 1&nbsp;MeV or more (so-called fast neutrons). Such high energy neutrons are able to fission {{chem|238|U}} directly (see [[thermonuclear weapon]] for application, where the fast neutrons are supplied by nuclear fusion). However, this process cannot happen to a great extent in a nuclear reactor, as too small a fraction of the fission neutrons produced by any type of fission have enough energy to efficiently fission {{chem|238|U}}. (For example, neutrons from thermal fission of {{chem|235|U}} have a [[mean]] energy of 2&nbsp;MeV, a [[median]] energy of 1.6&nbsp;MeV, and a [[mode (statistics)|mode]] of 0.75&nbsp;MeV,<ref>{{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><ref>{{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 |quote=Consequently, the fast neutron energy spectrum of FBF is at above 0.4 eV, with an average of 2.0 MeV and the median energy of 1.6 MeV.|doi-access=free |bibcode=2024AnNuE.20610647K }}</ref> and the energy spectrum for fast fission is similar.{{citation needed|date=November 2024}})

Among the heavy [[actinide]] elements, however, those isotopes that have an odd number of neutrons (such as <sup>235</sup>U with 143 neutrons) bind an extra neutron with an additional 1 to 2&nbsp;MeV of energy over an isotope of the same element with an even number of neutrons (such as <sup>238</sup>U with 146 neutrons). This extra binding energy is made available as a result of the mechanism of [[Semi-empirical mass formula#Pairing term|neutron pairing effects]], which itself is caused by the [[Pauli exclusion principle]], allowing an extra neutron to occupy the same nuclear orbital as the last neutron in the nucleus. In such isotopes, therefore, no neutron kinetic energy is needed, for all the necessary energy is supplied by absorption of any neutron, either of the slow or fast variety (the former are used in moderated nuclear reactors, and the latter are used in [[fast-neutron reactor]]s, and in weapons).

According to Younes and Loveland, "Actinides like {{chem|235|U}} that fission easily following the absorption of a thermal (0.25 meV) neutron are called ''fissile'', whereas those like {{chem|238|U}} that do not easily fission when they absorb a thermal neutron are called ''fissionable''."<ref name=ww/>{{rp|25}}