= Empirical evidence for nuclear shells
<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.<The Shell Model by Maria Goeppert Mayer>[§2, p. 21; Figs. 2–3, p. 23]{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>.<On Closed Shells in Nuclei. II by Maria Goeppert Mayer>[p. 1970, discussion and Table II]{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.
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