Magic Number Nuclei

atomic nuclei containing 2, 8, 20, 28, 50, 82, or 126 protons or neutrons (the numbers 2, 8, and so forth are called magic). Magic number nuclei differ from neighboring nuclei in that they are more stable and are more widespread in nature. The binding energy of a nucleon in a nucleus sharply increases in passing through the magic number. For example, for nuclei containing 124-128 neutrons, the binding energy of the 82nd proton is about 8.5 MeV, and that of the 83rd proton about 4.5 MeV. Nuclei similar to ₈₂Pb²⁰⁸ (82 protons, 126 neutrons), for which both numbers are magic, are called doubly magic.

The existence of magic number nuclei provided one of the arguments in the 1940’s in favor of the shell model of the atomic nucleus. According to the model, nucleons fill up a system of neutron and proton shells in the nucleus with a specified number of places in each. The magic numbers correspond to the filled shells.