Brueckner-Hartree-Fock calculations and their density dependence

Brueckner-Hartree-Fock (BHF) calculations are presented taking into account the Pauli operator in the self-consistent basis rather than in the oscillator basis. The definition of the single particle energies includes an on-shell rearrangement diagram (starting energy rearrangement) stemming from the only partial occupation of the occupied states due to the short range correlations. Further, it includes an off-shell diagram (Pauli rearrangement) term which originates from the density dependence of the Pauli operator. The three additional terms, the correction for the self-consistent Pauli operator, the starting energy, and the Pauli rearrangement terms, contribute significantly to the nucleus. It is shown that the definition of the single particle energies is analogous to that in density dependent Hartree-Fock calculations. One obtains all the effects of a density dependent force within the BHF formalism without making a detour to nuclear matter and thus avoids many of the approximations used in the calculations with density dependent forces. The method is applied here for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ using the Reid soft core and the Yale potential.