Perturbation calculations of nucleon-nucleon effective interactions in the Hartree-Fock basis

We prove that the Hartree-Fock (HF) basis provides good convergences for many-body perturbation calculations with renormalized realistic nuclear forces. Two types of ab initio perturbation calculations of effective interactions have been performed in the HF basis instead of the harmonic oscillator basis. One is called the Brillouin-Wigner (BW) perturbation and another is the Rayleigh-Schrödinger (RS) perturbation. The results show that ab initio perturbation calculations within the HF basis have comparably good convergences as the nonperturbative in-medium similarity renormalization group. In the HF basis some types of perturbation diagrams can be cancelled out, while the cancellation does not happen in the harmonic oscillator basis. We have investigated the sd shell with the chiral N³LO potential softened by . With the low-momentum N³LO potential, we first perform the spherical HF calculation for the ¹⁶O core, and use the perturbations to derive the sd-shelleffective two-body interactions in the HF basis. The calculations give simultaneously single-particle energies and excitation spectra of two-valence-particle systems (i.e. ¹⁸O, ¹⁸F, and ¹⁸Ne in the sd shell). Convergences have been analyzed order by order. We find that the HF RS perturbation gives even better results than the HF BW approximation. The HF effective interactions derived by the perturbations can be used for further many-body calculations.