In this paper we present an evolution of our derivation of the shell-model effective Hamiltonian, namely introducing effects of three-body contributions. More precisely, we consider a three-body potential at next-to-next-to-leading order in chiral perturbation theory, and the induced three-body forces that arise from many-body correlations among valence nucleons. The first one is included, in the derivation of the effective Hamiltonian for one- and two-valence nucleon-systems, at first order in the many-body perturbation theory. Namely, we include only the three-body interaction between one or two valence nucleons and those belonging to the core. For nuclei with more than two valence particles, both induced—turned on by the two-body potential—and genuine three-body forces come into play. Since it is difficult to perform shell-model calculations with three-body forces, these contributions are estimated for the ground-state energy only. To establish the reliability of our approximations, we focus attention on nuclei belonging to the $p$ shell, aiming to benchmark our calculations against those performed with the ab initio no-core shell model. The obtained results are satisfactory, and pave the way to the application of our approach to nuclear systems with heavier masses.

• Received 5 June 2018

DOI:https://doi.org/10.1103/PhysRevC.98.044305