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 the magic pdf free 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 isotopes having magic numbers means that transuranium elements can be created with extremely large nuclei and yet not be subject to the extremely rapid radioactive decay normally associated with high atomic numbers.
Large isotopes with magic numbers of nucleons are said to exist in an island of stability. 126, which are realized in spherical nuclei, theoretical calculations predict that nuclei in the island of stability are deformed.
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. Eugene Wigner: “Wigner, too, believed in the liquid drop model, but he recognized, from the work of Maria Mayer, the very strong evidence for the closed shells. It seemed a little like magic to him, and that is how the words ‘Magic Numbers’ were coined.
Examples of double magic isotopes include helium-4, oxygen-16, calcium-40, calcium-48, nickel-48, nickel-78, and lead-208. Double-magic effects may allow existence of stable isotopes which otherwise would not have been expected.