Generalized Pairing in Light Nuclei. I. Solutions of Hartree-Fock-Bogoliubov Equations inN=ZEven-Even Nuclei

Abstract

The Hartree-Fock-Bogoliubov (HFB) equations are solved for the $N=Z$ even-even nuclei in the $s-d$ shell. The possibility of generalized pairing correlations (e.g. both $T=0\mathrm{}$ and $T=1\mathrm{}$ pairing) is studied in detail. It is found that the two kinds of pairing are mutually exclusive and that the lowest HFB solution for the even-even $N=Z$ nuclei has $T=0\mathrm{}$ independent pairs. The validity and the extent of these correlations is further examined by projecting the solutions onto eigenstates of the total number operator. These $T=0\mathrm{}$ pairing correlations occur for the axially symmetric prolate ${\mathrm{Mg}}^{24}$, oblate ${\mathrm{S}}^{32}$, and prolate ${\mathrm{Ar}}^{36}$ HFB solutions. In studying the relevance of these HFB solutions to the experimental spectra, it is found that the HFB field gives a more consistent description of the structure of $N=Z$ even-even nuclei and that it can resolve the discrepancies and also the failures of the HF field in the upper half of the $s-d$ shell.