Effects of the Addition of a Neutron on Nuclear Properties ofp−fShell Nuclei

In order to study the effects of the addition of neutrons, one has to study the even as well as odd isotopes of a given nucleus. For this reason, the Hartree-Fock-Bogoliubov formalism which is available for even-even nuclei is extended for the even-odd nuclei. The blocking effect introduced by the odd nucleon is taken into account in the formalism. The numerical calculations are carried out for 22 nuclei of the $p-f$ shell (the isotopes of Ti, Cr, Fe, and Zn) considering ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ as a doubly closed core. By comparing the results of the odd nuclei with the results of the even-even nuclei, the spectra of which are obtained in our earlier work, one understands the effects of the addition of neutrons on the nuclear properties such as the deformation, Fermi surface, saturation properties of the nuclear force, single-particle levels, and the pickup strengths. The calculated binding energies, separation energies, pair separation energies, $B\left(E2\mathrm{}\right)\mathrm{}$ values, quadrupole moments, and the neutron and proton pickup strengths compare very well with the experimental values. The possibility of obtaining the "equivalent deformation" for which the Nilsson levels correspond to the calculated single-particle levels is discussed.