Systematics of binding energies and radii based on realistic two-nucleon plus phenomenological three-nucleon interactions

Nuclear structure theory is approaching an era of systemati c many-body calculations using nuclear Hamiltonians based on Quantum Chromodynamics (QCD). An important step along these lines is the formulation of nuclear interactions with in chiral effective field theory [1‐3], leading to a consistent hierarchy of two-, three- and many-nucleon interactions starti ng from the relevant degrees of freedom and symmetries for the low-energy nuclear structure regime. The use of these two-, three- and many-nucleon interactions in nuclear structure calculations is a formidable task. In addition to few-body calculations the most promising nuclear structure calculations using the chiral two- plus thr eenucleon interaction consistently have been performed in th e no-core shell model (NCSM) for mid p-shell nuclei [4]. An immense numerical effort is needed to compute and manage the three-body matrix elements in these calculations, which limits the range of applicability of these calculatio ns at present. Recently, the use of consistent two- plus threenucleon interactions resulting from a Similarity Renormal ization Group evolution of the chiral two- plus three-nucleon i nteraction was demonstrated also in the context of the NCSM [5]. This approach, a unitary transformation of the chiral Hamiltonian aiming at a pre-diagonalization that improves the convergence properties of NCSM substantially, holds great potential also for the use in other many-body schemes and will play a significant role in the future. However, the computational effort for including those two- plus three-nucleon interactions into many-body calculations, be it exact or ap proximate, is still the limiting factor for many applicatio ns. In this paper we follow a more pragmatic route to explore the impact of three-body forces in connection with unitaril y transformed two-nucleon interactions. We start from the Ar