Self-Consistent Treatment of the Pauli Operator in the Brueckner-Hartree-Fock Approach

Brueckner-Hartree-Fock (BHF) equations are derived including the correction due to treating the Pauli operator in the HF basis instead of the single oscillator basis, both for standard BHF and for a variational calculation. Calculations were done with an approximate energy denominator. The correction effects for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ are significant: about a 10% decrease in total binding energy, 12-30% decreases in single-particle energies, and up to 20% decrease in the peak of the charge-density distribution.