One can adopt two-step $G$-matrix approximations for the Brueckner-Hartree-Fock (BHF) calculations. The first $G$ matrix is to soften the bare force, and the second one is to include the high-order correlations of the interaction in medium. The first $G$-matrix calculation for two-nucleon interaction should be done in the center-of-mass coordinate. As another alternative BHF approach, we have adopted the $V_{\text{low-}k}$ technique to soften the interaction and used the $G$ matrix to include high-order correlations. The $V_{\text{low-}k}$ renormalization leads to high-momentum and low-momentum components of the interaction decoupled. With the $V_{\text{low-}k}$ potential, we have performed the BHF calculations for finite nuclei. The $G$-matrix elements with exact Pauli exclusions are calculated in the self-consistent BHF basis. To see effects from further possible correlations beyond BHF, we have simultaneously performed renormalized BHF (RBHF) calculations with the same potential. In RBHF, the mean field derived from realistic forces is modified by introducing the particle-occupation depletion resulting from many-body correlations. The ground-state energies and radii of the closed-shell nuclei, ${}^4\mathrm{He}$, ${}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$, have been investigated. The convergences of the BHF and RBHF calculations have been discussed and compared with other ab initio calculations with the same potential.

• Received 13 January 2017
• Revised 4 March 2017

DOI:https://doi.org/10.1103/PhysRevC.95.034321