Editing Magic number (physics) (section)

{{short description|Number of protons or neutrons that make a nucleus particularly stable}}
[[File:Table isotopes en.svg|300px|right|thumb|A graph of isotope stability, with some of the magic numbers]]
In [[nuclear physics]], a '''magic number''' is a number of [[nucleon]]s (either [[proton]]s or [[neutron]]s, separately) such that they are arranged into complete [[Nuclear shell model|shells]] within the [[atomic nucleus]]. As a result, atomic nuclei with a "magic" number of protons or neutrons are much more stable than other nuclei. The seven most widely recognized magic numbers as of 2019 are '''2, 8, 20, 28, 50, 82,''' and '''126'''.

For protons, this corresponds to the elements [[helium]], [[oxygen]], [[calcium]], [[nickel]], [[tin]], [[lead]], and the hypothetical [[unbihexium]], although 126 is so far only known to be a magic number for neutrons. Atomic nuclei consisting of such a magic number of nucleons have a higher average [[binding energy]] per [[nucleon]] than one would expect based upon predictions such as the [[semi-empirical mass formula]] and are hence more stable against nuclear decay. 

The unusual stability of [[isotope]]s having magic numbers means that [[transuranium element]]s could theoretically be created with extremely large nuclei and yet not be subject to the extremely rapid [[radioactive decay]] normally associated with high [[atomic number]]s. Large isotopes with magic numbers of nucleons are said to exist in an [[island of stability]]. Unlike the magic numbers 2–126, which are realized in spherical nuclei, theoretical calculations predict that nuclei in the island of stability are deformed.<ref name=Kratz>
{{cite conference
 |last1=Kratz |first1=J. V.
 |date=5 September 2011
 |title=The Impact of Superheavy Elements on the Chemical and Physical Sciences
 |url=http://tan11.jinr.ru/pdf/06_Sep/S_1/02_Kratz.pdf
 |conference=4th International Conference on the Chemistry and Physics of the Transactinide Elements
 |access-date=27 August 2013
}}</ref><ref>{{cite web|url=http://www.eurekalert.org/pub_releases/2008-04/acs-nse031108.php|title=Nuclear scientists eye future landfall on a second 'island of stability'}}</ref><ref>{{cite journal |doi=10.1007/BF01406719 | volume=228 | issue=5 | title=Investigation of the stability of superheavy nuclei aroundZ=114 andZ=164 | journal=Zeitschrift für Physik | pages=371–386| bibcode=1969ZPhy..228..371G|last1 = Grumann|first1 = Jens| last2=Mosel | first2=Ulrich | last3=Fink | first3=Bernd | last4=Greiner | first4=Walter | year=1969 | s2cid=120251297 }}</ref>
[[File:Semi-empirical_mass_formula_discrepancy.png|thumb|302x302px|The difference between known [[Binding energy|binding energies]] of isotopes and the binding energy as predicted from the [[semi-empirical mass formula]]. Distinct sharp peaks in the contours appear only at magic numbers.]]
Before this was realized, higher magic numbers, such as 184, 258, 350, and 462, were predicted based on simple calculations that assumed spherical shapes: these are generated by the formula <math>2(\tbinom n1+ \tbinom n2+\tbinom n3)</math> {{xref|(see [[Binomial coefficient]])}}. It is now believed that the sequence of spherical magic numbers cannot be extended in this way. Further predicted magic numbers are 114, 122, 124, and 164 for protons as well as 184, 196, 236, and 318 for neutrons.<ref name="Kratz">
{{cite conference
 |last1=Kratz |first1=J. V.
 |date=5 September 2011
 |title=The Impact of Superheavy Elements on the Chemical and Physical Sciences
 |url=http://tan11.jinr.ru/pdf/06_Sep/S_1/02_Kratz.pdf
 |conference=4th International Conference on the Chemistry and Physics of the Transactinide Elements
 |access-date=27 August 2013
}}</ref><ref>{{cite web|url=http://www.eurekalert.org/pub_releases/2008-04/acs-nse031108.php|title=Nuclear scientists eye future landfall on a second 'island of stability'}}</ref><ref>{{cite journal |doi=10.1007/BF01406719 | volume=228 | issue=5 | title=Investigation of the stability of superheavy nuclei aroundZ=114 andZ=164 | journal=Zeitschrift für Physik | pages=371–386| bibcode=1969ZPhy..228..371G|last1 = Grumann|first1 = Jens| last2=Mosel | first2=Ulrich | last3=Fink | first3=Bernd | last4=Greiner | first4=Walter | year=1969 | s2cid=120251297 }}</ref> However, more modern calculations predict 228 and 308 for neutrons, along with 184 and 196.<ref name="SHlimit">{{cite conference|last=Koura|first=H.|date=2011|title=Decay modes and a limit of existence of nuclei in the superheavy mass region|url=http://tan11.jinr.ru/pdf/10_Sep/S_2/05_Koura.pdf|conference=4th International Conference on the Chemistry and Physics of the Transactinide Elements|access-date=18 November 2018}}</ref>