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The nuclear shell model is a model of the nucleus in nuclear physics. It is analogous to the atomic shell model that is more familiar to those who have studied basic physics. Recall that in the atomic shell model, the electrons populate shells, and once a shell is filled, there is a significant drop in the binding energy for the next electron added.
It is similar for the nuclear shell model. When adding nucleons (protons or neutrons) to a nucleus, there are certain points where the binding energy of the next nucleon is significantly less than the last one. This observation, that there are certain "magic numbers" of nucleons: 2, 8, 20, 28, 50, 82, 126 which are more tightly bound than the next higher number, that are the origin of the shell model.
Note that the shells exist for both protons and neutrons individually, so that we can speak of "magic nuclei" where one nucleon type is at a magic number, and "doubly magic nuclei", where both are.
