Nuclear Shell Model Magic Numbers

What you are seeing: the single-particle shell structure of nucleons in a harmonic-oscillator-plus-spin-orbit potential. With the spin-orbit term included, the closed-shell gaps fall exactly at the observed magic numbers $2, 8, 20, 28, 50, 82, 126$ . Pour nucleons in (slider $N$ ) and watch the levels fill bottom-up; the readout flags magic numbers.

Without the spin-orbit term, only $2, 8, 20$ would be magic (the pure HO closures); the appearance of $28, 50, 82, 126$ as observed magic numbers is one of the historic confirmations of the spin-orbit nuclear force.

Figure 1. Nuclear shell-model level diagram with magic-number gaps.

N28

WHAT TO TRY

Pour nucleons in with the N slider: levels fill bottom-up, and the readout flags each closed shell. The large gaps land exactly at the magic numbers 2, 8, 20, 28, 50, 82, 126.
Stop at a magic number: the next level sits across a wide energy gap, so the nucleus is extra bound and spherical. This is why magic nuclei are the most stable isotopes.
Note that the gaps come from the spin-orbit term: without it the harmonic-oscillator shells would close at the wrong numbers. The 1f7/2 closure at 28 is the textbook example.