n-p Pairing, Wigner Energy, and Shell Gaps

The diagonal correlation energy due to n-n, p-p, and n-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.