SELF-CONSISTENT STUDY OF NUCLEAR SHAPES

Self-consistent Hartree-Fock (HF) and Hartree-Fock-Bogoliubov (HFB) calculations have been performed for the even Ti, Cr, and Fe isotopes. The residual two-body interaction is assumed to be a central potential with a Yukawa radial dependence and an exchange mixture which has been adjusted to fit the low-lying shell-model states of O1018 and F918. It is found that the HF minima occur for prolate shapes, and hence the HFB calculations are done only for prolate deformations. The HFB calculation yields normal solutions for N=Z nuclei and spherical shapes for Z<N=28 nuclei. The effect of pairing on the ground-state properties is also studied. The value of the mass quadrupole moment for the HFB solution is smaller than that for the HF solutions for all the nuclei under consideration. A spherical BCS calculation has been performed to estimate the effect of deformation on pairing energy in the HFB calculation. We construct the excited states for the Z<N=28 nuclei from the spherical BCS ground-state solutions in the random-phase approximation. This gives the values for the 0+2+ energy separation and the B(E2) rates which are in good agreement with experiment. © 1969 The American Physical Society.