Even with the strong nuclear force, a shell model describes important features of nuclei. Nuclei
have tightly bound closed shells for both protons and neutrons. Tightly bound nuclei
correspond to the most abundant elements. What elements exist isgoverned by nuclear physics and
we can get a good idea from a simple shell model.Nuclear magic numbersoccur for neutron or
proton number of 2, 8, 20, 28, 50, 82, and 126, as indicated in the figure below. Nuclei where the
number of protons or neutrons is magic are more tightly bound and often more abundant. Heavier
nuclei tend to havemore neutrons than protons because of the coulomb repulsionof the
protons (and the otherwise symmetric strong interactions). Nuclei which aredoubly magicare
very tightly bound compared to neighboring nuclei. 82 Pb^208 is a good example of a doubly magic
nucleus with many more neutrons than protons.
Remember, its only hydrogen states which are labeled with a principle quantum numbern=nr+
ℓ+ 1. In the nuclear shell model,nrefers only to the radial excitationso states like the 1h (^92)
show up in real nuclei and on the following chart. The other featureof note in the nuclear shell
model is that the nuclearspin orbit interaction is strongand of the opposite sign to that in
atoms. The splitting between states of differentjis smaller than that but of the same order as
splitting between radial or angular excitations. It is this effect and the shell model for which Maria
Mayer got her Nobel prize.