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Isotope abundance, nuclear separation energies, spin and nuclear magnetic moments supply complementary tests: abundance concerns which atomic nuclei survive and accumulate, removal energy concerns binding, and magnetic properties test the angular momentum assignments. Agreement across these observables is more informative than fitting one list of numbers.

In her 1963 lecture, Maria Goeppert Mayer recalled excess abundances at $N=50$ and $82$. She contrasted the strong binding of the last neutron in oxygen isotope ${}^{16}\mathrm{O}$ with the weaker extra neutron in oxygen isotope ${}^{17}\mathrm{O}$, and displayed beta decay energies near $N=20$ and $50$. These are compiled empirical patterns, rather than readings from an apparatus she built.^[ref]

Her 1949 letter compared observed spins and nuclear magnetic moments with orbital assignments. For example, lead isotope ${}^{207}\mathrm{Pb}$ was assigned a $p_{1/2}$ neutron hole near $N=126$, whereas bismuth's odd proton began the next shell as $h_{9/2}$. The moments tested orbital character as well as spin.^[ref]

A useful comparison holds $Z$ fixed when comparing neighboring isotopes, and examines odd-even staggering separately from a shell discontinuity. Abundance additionally depends on production and decay history. Neither the abundance pattern nor a successful spin assignment directly images orbiting particles; neither fixes a unique nuclear mean field. The experimental techniques themselves include mass spectrometry and nuclear magnetic resonance, whose preparation and readout differ. The Hofstadter nuclear electron scattering experiment separately constrains nuclear size and nuclear charge distributions, rather than measuring these occupancies.

The 1948 empirical synthesis preceded the 1949 strong spin-orbit interaction proposals. Johannes Hans Daniel Jensen recalled developing that idea in a discussion with colleagues, independently of Maria Goeppert Mayer's work; their shared problem was to account for the observed magic numbers and spins.^[ref]

Johannes Hans Daniel Jensen emphasized that even nuclear ground states retain correlations and that independent-particle motion becomes less adequate at higher excitation. This helps explain why the nuclear shell model needs residual interactions and complementary collective descriptions.^[ref]

The 1963 Nobel Prize in Physics recognized Maria Goeppert Mayer and Johannes Hans Daniel Jensen for nuclear shell structure. Eugene Paul Wigner's share recognized his contributions to nuclear and elementary-particle theory, especially fundamental symmetry principles, a distinct award motivation.^[ref]

One half went to Eugene Paul Wigner for theories of atomic nuclei and elementary particles, particularly symmetry principles; the other half jointly to Maria Goeppert Mayer and Johannes Hans Daniel Jensen for discoveries about the nuclear shell model.^[ref]