## Magic number (physics) |

in

, anuclear physics **magic number**is a number of (eithernucleons orprotons , separately) such that they are arranged into completeneutrons within theshells . the seven most widely recognized magic numbers as of 2019 areatomic nucleus **2, 8, 20, 28, 50, 82, and 126**(sequencea018226 in the ). for protons, this corresponds to the elementsoeis ,helium ,oxygen ,calcium ,nickel ,tin and the hypotheticallead , 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 averageunbihexium perbinding energy than one would expect based upon predictions such as thenucleon and are hence more stable against nuclear decay.semi-empirical mass formula the unusual stability of

having magic numbers means thatisotopes could theoretically be created with extremely large nuclei and yet not be subject to the extremely rapidtransuranium elements normally associated with highradioactive decay . large isotopes with magic numbers of nucleons are said to exist in anatomic numbers . unlike the magic numbers 2–126, which are realized in spherical nuclei, theoretical calculations predict that nuclei in the island of stability are deformed. before this was realized, higher magic numbers, such as 184, 258, 350, and 462 (sequenceisland of stability a033547 in the ), were predicted based on simple calculations that assumed spherical shapes: these are generated by the formula (seeoeis ). 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.binomial coefficient ^{[1]}^{[2]}^{[3]}- origin of the term
- doubly magic
- derivation
- see also
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In **magic number** is a number of **2, 8, 20, 28, 50, 82, and 126** (sequence A018226 in the

The unusual stability of ^{[1]}^{[2]}^{[3]}