An atomic nucleus is a clump of protons and neutrons, collectively called nucleons. Around 1950, Goeppert-Mayer and Jensen proposed the independent-particle “shell model,” where each nucleon moves in a common potential. Just like electron closed shells in the periodic table, nuclei show extra stability at "magic numbers" 2, 8, 20, 28, 50, 82, and 126. By adding spin–orbit coupling to the potential, they resolved discrepancies between theory and experiment. The model matches many data on nuclear sizes and decay. It is indispensable for nuclear-power reactors and the design of medical isotopes.

In the shell model, one sets an approximate three-dimensional mean potential—often a harmonic oscillator plus a spin–orbit term or the Woods–Saxon form—and places nucleons independently as fermions. Because Pauli’s exclusion principle limits occupancy to 2j+1 nucleons per orbital, energy levels fill sequentially, with closed shells at magic numbers. Goeppert-Mayer and Jensen introduced a strong spin–orbit interaction to fit experimental data and resolve level inversion issues of earlier models. Their theory reproduces many-body observables such as electromagnetic transition rates, β-decay selection rules, and magnetic moments, forming the basis for R-matrix methods and reaction calculations in nuclear astrophysics.

Goeppert-Mayer and Jensen analyzed independent-particle equations in a mean-field approximation, showing that enhancing the ℓ·s coupling by a factor of 1.5–2 accounts for the a1g–d5/2 level inversion. This allowed rescaling of the Nilsson diagram’s vertical axis and quantitative description of level ordering in deformed nuclei. They further discussed inter-shell interactions via BCS pairing, linking the picture to collective dipole giant resonances. Their work remains a benchmark for modern energy-density functional calculations (Skyrme, Gogny) and ab initio approaches.