Hartree-Fock-Bogoliubov Calculations for Even-Even Nuclei inp−fShell

Hartree-Fock-Bogoliubov (HFB) calculations are done for some even-even nuclei in the $p-f$ shell taking ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ as a doubly closed core. It is observed that the nuclear shape changes from a prolate to oblate shape, and the pairing correlations increase in the neutron states and decrease in the proton states as one goes from the Ti to the Zn and Ge isotopes. Whether the $f_{\frac{7}{2}}$ shell-closure approximation in which ${}_{}{}^{56}{}_{}{}^{}\mathrm{Ni}$ is taken as a closed core is valid or not is discussed by comparing the calculated occupation probabilities of the $f_{\frac{7}{2}}$ shell and the break in the pair separation energy at ${}_{}{}^{56}{}_{}{}^{}\mathrm{Ni}$ with the experimental values. Projected HFB spectra have been obtained for ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$, and ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$. Reasonable agreement with the experimental spectra is obtained for ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$ and ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$. The reasons for the failure of the present method in ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$ are discussed.