Renormalized Brueckner-Hartree-Fock and density dependent Hartree-Fock theories of finite nuclei

Renormalized Brueckner-Hartree-Fock and density dependent Hartree-Fock calculations in the literature have been difficult to compare because they involve both different physical approximations and also technical computational differences. Hence, results obtained in both calculations for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ are corrected for technical differences and compared in detail. It is shown that comparable Brueckner-Hartree-Fock calculations using an oscillator basis and using the local density approximation are in good numerical agreement, and that three mechanisms are of roughly equal importance in obtaining the proper interior density: occupation probabilities, the potential arising from the variation of the pauli operator, and the phenomenological parametrization of higher order corrections to the effective nuclear interaction. The renormalized oscillator basis calculations include only the effect of occupation probability diagrams. The "bare" local density approximation results are an improvement over the renormalized results since the former includes the effects of both occupation probabilities and the variation of the Pauli operator. The adjusted local density approximation calculations then give further improvement due to the phenomenological parametrization of the force, simulating the effect of higher-order diagrams.