= Magic number
{wiki=Magic_number_(physics)}
= Nuclear magic number
{synonym}
A <proton> number $Z$ or <neutron> number $N$ associated with a pronounced <nuclear shell closure>. The traditional sequence is
$$
2,\quad8,\quad20,\quad28,\quad50,\quad82,\quad126.
$$
These count either species separately, rather than their sum $A=Z+N$. Calling a number magic summarizes a structural pattern; it does not promise that every <isotope> at that number is equally stable.
\Image[/nuclear-magic-shell-capacities.png]
{title=Counting states between traditional nuclear shell closures}
{description=Original capacity diagram for a chosen spherical level scheme. Each orbital contributes $2j+1$ states for one species. Rows show groups and cumulative totals, not measured energies or a universal ordering within each group.}
For example, in the chosen scheme the $20$-particle core plus the eight substates of $1f_{7/2}$ gives $28$. The next group contributes $4+6+2+10=22$, giving $50$. The following two groups contribute $8+6+4+2+12=32$ and $10+8+6+4+2+14=44$, giving $82$ and $126$. Counting verifies the capacities once the grouping has been chosen; it does not establish the physical <energy> gaps that justify that grouping.
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