Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Magic Numbers

Certain nuclei exhibit enhanced stability with specific numbers of protons and neutrons (2, 8, 20, 28, 50, 82, 126), reflecting shell closure.
📜

The statement of the theorem

The enhanced stability of nuclei with specific proton (ZZ) or neutron (NN) numbers (magic numbers) is explained by the closure of major energy shells in the single-particle spectrum. The single-particle energy levels En,l,jE_{n, l, j} are calculated using a mean-field potential. The magic numbers correspond to the cumulative number of nucleons required to fill the first KK energy shells, Nmagic=⨁k=1K(2jk+1)N_{magic} = \bigoplus_{k=1}^{K} (2j_k + 1), where jkj_k are the angular momentum quantum numbers of the kk-th shell. The stability enhancement is quantified by the binding energy per nucleon, B/AB/A, which exhibits local maxima when ZZ or NN equals a magic number.
Source: Wikipedia