Appendix C: Magic Numbers

In chemistry, atoms with filled outer shells are most unreactive, making the atoms with atomic number$\displaystyle Z=2,10,18,36,54,86$ (the noble gases) the most stable elements. It turns out that in the nucleus, protons and neutrons are also arranged in shells and subshells, just that the magic numbers are different. When the number of the protons (Z) or the number of neutrons (N) is 2, 8, 20, 28, 50, 82 or 126, the resulting nucleus tends to be more stable. This “explains” why doubly magic nuclides (nuclides whose Z and N are both magic) such as

$\displaystyle \displaystyle {}_{2}^{4}He$

$\displaystyle \displaystyle {}_{8}^{{16}}O$

$\displaystyle {}_{{20}}^{{40}}Ca$

$\displaystyle {}_{{20}}^{{48}}Ca$

$\displaystyle {}_{{82}}^{{208}}Pb$

are substantially more stable compared to their neighboring nuclei of similar sizes.