Brueckner-Hartree-Fock Calculations of Spherical Nuclei in an Harmonic-Oscillator Basis

A method is developed for performing Brueckner-Hartree-Fock (BHF) calculations of spherical nuclei in the harmonic-oscillator representation. Both the Brueckner and the HF self-consistencies are satisfied. The method is applied to the calculation of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ with a $G$ matrix derived from the Hamada-Johnston potential. The nuclei are too small and underbound. Various kinds of convergence are studied. It is concluded that the calculations are essentially as easy and as reliable as, though a little longer than, pure Hartree-Fock calculations.