Nuclear shell model and 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.