Self-Consistent Calculations for Even Ti, Cr, and Fe Isotopes

Results of self-consistent calculations with Hartree-Fock (HF), Hartree-Fock-Bogoliubov (HFB), and spherical BCS approximations obtained with the central Yukawa (CY) interaction and with renormalized Kuo and Brown matrix elements for the Hamada-Johnston (HJ) interaction are reported for even Ti, Cr, and Fe isotopes. The calculated ground-state energies, corrected for Coulomb interaction amongst the extracore protons, are compared with the experimental values, and a better agreement for the HJ interaction is obtained than for the CY although they do not differ much with respect to each other. It is found that in the HFB approximation, the HJ interaction favors prolate solutions over oblate or spherical ones. Unlike the CY, the HFB approximation for $Z<N=28\mathrm{}$ nuclei with the HJ interaction does not converge to spherical minima with lowest energy. It is also seen that the pairing contribution to the spherical BCS energy minimum is considerably larger for the HJ interaction as compared to the CY. The desirability of spherical solutions for $Z<N=28\mathrm{}$ nuclei for the HJ interaction is discussed, and it is argued that it cannot be obtained by including $n-p$ pairing in the $T=1\mathrm{}$ state. Modification of the Kuo and Brown renormalized matrix elements is suggested. Results for the oblate and prolate HFB solutions for ${\mathrm{Fe}}^{58}$ with HJ interaction are discussed, as these solutions have very close energy minima.