Two-neutron separation energies and Fermi energies

 

A particular thrust of our analysis will be to identify the location of the two-neutron drip line. The self-consistent HFB variational procedure produces two quantities that provide information of relevance. One is the two-neutron separation energy, S_2n, defined as the difference between the HFB energy for the N-2 and N neutron systems (with the same proton number) and the other is the Fermi energy, $\lambda_{n}$.

The two-neutron separation energy provides ``global'' information on the total Q-value corresponding to a hypothetical simultaneous transfer of two neutrons into the N-2 ground state, leading to the ground state of the nucleus with N neutrons. The Q-value includes information on all differences in the ground-state properties of both nuclei, like pairing, deformation, configuration, etc. Whenever this Q-value becomes negative, the window for the spontaneous and simultaneous emission of two neutrons opens up, and the nucleus with N neutrons is formally beyond the two-neutron drip line.

The Fermi energy, on the other hand, gives ``local'' information on the stability of the given nucleus at a given pairing intensity, deformation, and configuration. Within the HFB theory, the sign of the Fermi energy dictates the localization properties of the HFB wave function; it is localized if $\lambda_{n}$<0 and unlocalized (i.e., behaves asymptotically as a plane wave) if $\lambda_{n}$>0. Thus, within the HFB approach, nuclei with $\lambda_{n}$>0 spontaneously emit neutrons, while those with $\lambda_{n}$<0 do not emit neutrons, irrespective of the available Q-values for the real emission. As such, we must take into account all solutions with $\lambda_{n}$<0 in discussing our self-consistent HFB results.

We will indeed see examples in Sec. 4 in which the nucleus has a negative two-neutron separation energy, so that it is formally beyond the two-neutron drip line, but nevertheless is localized and does not spontaneously spill off neutrons.