A $G$ matrix derived from the Reid soft-core potential is used in a series of Brueckner-Hartree-Fock calculations of spherical nuclei. The $G$ matrix is calculated using an intermediate-state spectrum and Pauli operator appropriate to pure oscillator orbitals, with options to shift the entire spectrum or the low-lying levels from unperturbed oscillator energies. The Pauli operator takes into account the filling of different neutron and proton subshells in $N\ne Z$ nuclei. Self-consistent occupation probabilities are included in the calculations and results are presented for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. Various systematics and convergences are studied. Good results can be obtained for the binding energies, but the experimental binding energy and charge radius cannot be fitted simultaneously. It is shown that renormalization with occupation probabilities is crucial for calculating a reasonable single-particle spectrum. The difficulty of comparing single-particle energies with experiment is discussed with particular emphasis on heavy and superheavy nuclei. The nuclei ${}_{}{}^{298}{}_{}{}^{}114$ and ${}_{}{}^{310}{}_{}{}^{}126$ are calculated for a simple force.

• Received 7 April 1971

DOI:https://doi.org/10.1103/PhysRevC.4.81