For years she worked for FREE — universities wouldn’t pay a professor’s wife — and still cracked why certain nuclei are unusually stable. Like electrons, protons and neutrons fill SHELLS, and when a shell is exactly full the nucleus is rock-solid. The full-shell counts — 2, 8, 20, 28, 50, 82, 126 — she called MAGIC NUMBERS. Slide the count and find them.
The nuclear SHELL MODEL: nucleons occupy quantised energy levels, and a large gap opens after certain totals — 2, 8, 20, 28, 50, 82, 126 — where a shell is completely filled, making that nucleus tightly bound and abundant. Goeppert Mayer’s insight was the strong SPIN-ORBIT coupling that produces 28, 50, 82, 126 (a plain oscillator gives only 2, 8, 20). A fail-loud self-check throws unless those seven magic numbers register and the doubly-magic nuclei (helium-4, oxygen-16, calcium-40, lead-208) are magic in BOTH proton and neutron count.
A shell picture of a many-body quantum system; the levels shift with deformation and near the drip lines (some ‘magic’ numbers weaken for exotic nuclei). The seven magic numbers and the doubly-magic examples are the established, measured result (Nobel 1963).