= Neutron separation energy
{title2=$S_n(Z,N)=B(Z,N)-B(Z,N-1)$}
Writing positive <nuclear binding energy> as $B(Z,N)$ and nuclear <mass> as $M(Z,N)$,
$$
S_n(Z,N)=\left[M(Z,N-1)+m_n-M(Z,N)\right]c^2
=B(Z,N)-B(Z,N-1).
$$
The two-<neutron> <nuclear separation energy> is $S_{2n}(Z,N)=B(Z,N)-B(Z,N-2)$. In an independent-particle example, let the last occupied <energy level> have $\epsilon_-=-8u$ and the next empty level $\epsilon_+=-3u$, for a chosen positive <energy> unit $u$. With an unchanged core and no residual interactions, removal from the filled level costs $8u$, whereas removing the first particle added above it costs $3u$: the drop $5u$ equals the one-particle gap. These are invented model inputs, not measured nuclear values. <Nuclear pairing>, rearrangement of the <nuclear mean field>, and correlations complicate that identification in real <masses>; a finite difference of <nuclear binding energies> is not automatically a bare one-particle gap.
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