$n\mathrm{\text{−}}p$ Pairing, Wigner Energy, and Shell Gaps

The diagonal correlation energy due to $n\mathrm{\text{−}}n$, $p\mathrm{\text{−}}p$, and $n\mathrm{\text{−}}p$ pairing is shown to resolve the discrepancies between shell gaps determined from binding energy differences and the gaps calculated with Woods-Saxon potentials or with other mean-field models. The difference in diagonal correlation energy between an $N=Z$ nucleus with filled shells and the nucleus with one less nucleon resolves this problem in lowest order. A previously derived result, that the diagonal correlation energy in the last occupied orbital for the latter nuclei is $1/2$ of the equivalent correlation energy for closed shell nuclei, is tested against observed binding energies and found to be fairly accurate.

Figure 1

Correlation energy ratios as a function of mass. The $x$ axis is the mass of the nuclide ($A/2$, $A/2$). Open circles are for ($A/2$, $A/2-1$); open squares for ($A/2-1$, $A/2$).

Figure 2

Comparison of gaps. For each nuclide, the ordering is observed gap, extracted gap, and calculated WS spacing.