= Nuclear shell closure
Filling the accessible one-species <nuclear shell model> states below a substantial <energy> gap. A closed spherical $j$ level has all $m_j$ values occupied, so their sum is zero. In the independent-particle picture, a closed core therefore contributes zero total <angular momentum>; a single particle outside it, or a single missing particle inside it, supplies the leading <spin> assignment. Residual interactions can change this simple picture.
The <three-dimensional isotropic harmonic oscillator> alone has one-species shell capacities $(q+1)(q+2)$ for oscillator index $q=0,1,\ldots$, including <spin>. Summing gives closures $2,8,20,40,70,112,\ldots$, rather than the complete traditional <magic number> sequence. Strong <nuclear spin-orbit splitting> can separate a high-$j$ level from its former neighbors. Realistic radial <potential energies> and residual interactions also matter: a chosen oscillator plus an arbitrary single constant is not a demonstrated explanation of every real nuclear gap.
Traditional <nuclear shell closures> can weaken along <isotope> chains far from stability, as in neutron-rich <magnesium>.<Magic numbers disappear and expand area of nuclear deformation by RIKEN>[20 November 2013, magnesium shell weakening]{ref}
The relevant test is the actual <energy> gap and the correlated nuclear <quantum states>, rather than membership in an immutable numerical list.
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