Magic number

A magic number is a specific number of protons or neutrons for which an atomic nucleus is particularly stable, exhibiting binding energy that is noticeably higher than neighboring nuclei with similar numbers. They are

More formally, the magic numbers refer to specific values of the atomic number $Z$ or neutron number $N$ of a nucleus. According to the nuclear shell model, these magic numbers correspond to closed protonic or neutronic shells in the nucleus, much like how closed electron shells in the atom lead to highly stable noble gases. Since proton and neutron shells are independent of each other, its possible for a nucleus to be magic in one or even both shells. In the latter case, the nucleus is said to be doubly magic and these are even more stable than their singly magic counterparts.

Magic nuclei possess many stable or very long-lived isotopes and isotones. The energy required to remove a nucleon from a magic nucleus is high, as is the energy needed to promote one to an excited state. Examples of particularly stable doubly magic nuclei are $\ce{_{2}^{4}He_{2}}$, $\ce{_{8}^{16}O_{8}}$, $\ce{_{20}^{40}Ca_{20}}$, $\ce{_{20}^{48}Ca_{28}}$ and $\ce{_{82}^{208}Pb_{128}}$.