Study of even calcium and nickel isotopes with self-consistent approximations

Employing the central Yukawa interaction, and renormalized matrix elements for the Hamada-Johnston and Tabakin potentials, self-consistent Hartree-Fock, Hartree-Fock-Bogoliubov (HFB), and spherical BCS calculations for even calcium and nickel isotopes are carried out. The existence of spherical ⁴⁰Ca and ⁵⁶Ni cores is assumed and the calcium and nickel isotopes are treated within the framework of single-closed-shell structure. It is found that for a given isotope and interaction the HFB and spherical BCS approximations always correspond to the same actual minimum energy solution. This feature is observed for all the isotopes and interactions considered here, though the quasiparticle energies and the occupation numbers are found to differ. For Ca isotopes the BCS results are also compared with the shell-model calculations of McGrory, Wildenthal, and Halbert, and are found to approximate the ground-state properties of all the even isotopes rather well.