Nuclear separation energy

The energy needed to remove specified nucleons from a bound atomic nucleus in its ground state. It compares neighboring nuclear masses, and so can reveal a nuclear shell closure more clearly than a smoothly varying total nuclear binding energy.

With bare nuclear masses, the proton separation energy is the energy needed to remove a proton. A negative value means the daughter plus proton has lower rest energy. Proton emission can still have a finite lifetime because of a Coulomb or centrifugal barrier.

A nuclear drip line marks a boundary beyond which one- or few-nucleon emission becomes energetically allowed. One- and two-particle nuclear separation energies can give distinct boundaries because of nuclear pairing.

The neutron drip line is the neutron-rich boundary at which one- or two-neutron emission becomes energetically possible. Neutrons beyond that boundary are not stably bound; the absence of a Coulomb barrier often makes their emission prompt, subject to angular-momentum barriers.

The proton drip line is the proton-rich boundary at which one- or two-proton emission becomes energetically possible. It is governed by proton separation energies, rather than the energetics of beta decay alone.

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.