Resource Letter NSM-1: New insights into the nuclear shell model

This Resource Letter provides a guide to the literature on the spherical shell model as applied to nuclei. The nuclear shell model describes the structure of nuclei starting with a nuclear core developed by the classical neutron and proton magic numbers $N,Z=2,8,20,28,50,82,126$⁠, where gaps occur in the single-particle energies as a shell is filled, and the interactions of valence nucleons that reside beyond that core. Various modern extensions of this model for spherical nuclei are likewise described. Significant extensions of the nuclear shell model include new magic numbers for spherical nuclei and now for deformed nuclei as well. When both protons and neutrons have shell gaps at the same spherical or deformed shapes, they can reinforce each other to give added stability to that shape and lead to new magic numbers. The vanishings of the classical spherical shell model energy gaps and magic numbers in new neutron-rich nuclei are described. Spherical and deformed shell gaps are seen to be critical for the existence of elements with $Z>100$⁠.