 Neutron separation energy

Writing positive nuclear binding energy as $B(Z,N)$ and nuclear mass as $M(Z,N)$,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 ${ϵ}_{-}=-8u$ and the next empty level ${ϵ}_{+}=-3u$, 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.