Investigation of Asymmetric Shapes for the Even-Even2p−1fShell Nuclei

An investigation for the existence of asymmetric shapes having symmetry about the $X-Y$, $Y-Z$, and $Z-X$ planes, is carried out for the even-even $2p-1f$ shell nuclei by using the self-consistent Hartree-Fock (HF) and Hartree-Fock-Bogoliubov (HFB) procedures. The results for a central Yukawa interaction and core-polarized Kuo-Brown matrix elements for the Hamada-Johnston interaction are reported. It is found that for those $N=Z$ nuclei which favor triaxial shape, the HF gap is increased considerably as compared to their corresponding HF gap for the axially symmetric shape. For $N\ne Z$ nuclei, though the HF approach may yield triaxial solutions with somewhat lower energies as compared to the axial HF results, these solutions converge to their respective HFB shapes having axis of symmetry in the presence of pairing. For those cases where the HFB approximation yields triaxial solution with minimum energy, the gain in binding energy due to pairing correlations is found to be compensated by the decrease in the HF contribution to the HFB energy, resulting in no over-all gain in binding over the corresponding triaxial HF solution. The pairing energy, intrinsic quadrupole moments, and pickup strengths of those nuclei which favor triaxial solutions are compared with the corresponding axially symmetric results.