the nuclear shell model
/ Goeppert Mayer: GUP-ert MY-er /
The liquid-drop picture treats the nucleus as a structureless blob, yet certain nuclei are conspicuously more stable than their neighbours, in a pattern that looks eerily like the noble-gas stability of atoms. The shell model takes that hint seriously: it treats each nucleon as an independent particle moving in an average potential well created by all the others, and it fills quantized energy levels with protons and neutrons much as electrons fill atomic orbitals.
Concretely, one replaces the intractable many-body problem by a single-particle Hamiltonian with a mean-field potential (often a harmonic oscillator or Woods-Saxon well). Solving it gives discrete energy levels labelled by quantum numbers; protons and neutrons, each being spin-1/2 fermions, fill these levels separately in obedience to the Pauli exclusion principle. The decisive ingredient, introduced by Maria Goeppert Mayer and independently by Jensen, is a strong spin-orbit coupling: an interaction proportional to l dot s that splits each level by total angular momentum j and reshuffles the ordering. Only with this spin-orbit term do the shell closures land at the observed magic numbers.
The payoff is real predictive power. Nuclei with completely filled proton or neutron shells (magic numbers 2, 8, 20, 28, 50, 82, 126) are extra tightly bound; the model also predicts ground-state spins and parities, magnetic moments, and the pattern of low-lying excited states. Its honesty clause is that it is an independent-particle approximation: nucleons are strongly interacting, so the smooth mean field is an idealization, and collective phenomena (rotations, vibrations, large deformations) need the drop-like or collective models to complement it.
Oxygen-16 has 8 protons and 8 neutrons, both magic; the model predicts a spin-parity of 0+ and unusual stability, both confirmed. It also correctly gives the 1/2- ground state of many nuclei with an odd nucleon in a p_1/2 orbital.
Doubly magic oxygen-16 is a textbook shell-model success.
Without the strong spin-orbit coupling the naive shell model predicts the wrong magic numbers. It was Goeppert Mayer and Jensen's spin-orbit term (Nobel Prize 1963) that made the model work.