Self-Consistent Study of Even Nickel Isotopes with Central Yukawa and Hamada-Johnston Interactions

Employing Hartree-Fock (HF), spherical BCS, and Hartree-Fock-Bogoliubov approximations and using central Yukawa (CY) and Kuo-Brown renormalized matrix elements for the Hamada-Johnston (HJ) interaction, a study of the behavior of nuclear shapes for the even Ni isotopes is carried out. Nuclear properties such as binding energy with respect to the ${\mathrm{Ca}}^{40}$ core, intrinsic quadrupole and hexadecapole moments, spectroscopic pickup strengths with special emphasis on the pickup strength for the $j=\frac{7}{2}$ state are calculated for different shapes and compared. It is found that the theoretical values of binding energy corresponding to shapes with minimum energy compare well with the experimental values. Addition of more neutrons to ${\mathrm{Ni}}^{56}$ decreases considerably the occupation probability for the protons in the $j=\frac{7}{2}$ state for all the shapes and approximations for the HJ interaction. With the CY interaction, the pickup strength in the $j=\frac{7}{2}$ state is not much affected for the BCS solution but it decreases in other approximations. It is found that the self-consistent solution for ${\mathrm{Ni}}^{56}$ corresponding to the HJ interaction does not converge to a spherical shape; instead it gives an oblate HF solution.