Assuming the existence of a spherical ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ core, self-consistent Hartree-Fock, Hartree-Fock-Bogoliubov, and spherical BCS calculations for the even oxygen isotopes are carried out for Kuo-Brown and a number of other effective interactions. In agreement with the finding of Chandra and Rustgi for the even Ca and Ni isotopes, the spherical BCS approximation is found to yield the actual minimum-energy solution for the even oxygen isotopes as well. The present calculation thus adds credibility to the general inferences made by Chandra and Rustgi that for single-closed-shell structures, the self-consistent shape will always be spherical BCS.

• Received 26 December 1972

DOI:https://doi.org/10.1103/PhysRevC.8.1152