Background: Recent advances in nuclear structure theory have led to the availability of several complementary ab initio many-body techniques applicable to light and medium-mass nuclei as well as nuclear matter. After successful benchmarks of different approaches, the focus is moving to the development of improved models of nuclear Hamiltonians, currently representing the largest source of uncertainty in ab initio calculations of nuclear systems. In particular, none of the existing two- plus three-body interactions is capable of satisfactorily reproducing all the observables of interest in medium-mass nuclei.

Purpose: A novel parametrization of a Hamiltonian based on chiral effective field theory is introduced. Specifically, three-nucleon operators at next-to-next-to-leading order are combined with an existing (and successful) two-body interaction containing terms up to next-to-next-to-next-to-leading order. The resulting potential is labeled $NN+3N\text{(lnl)}$. The objective of the present work is to investigate the performance of this new Hamiltonian across light and medium-mass nuclei.

Methods: Binding energies, nuclear radii, and excitation spectra are computed using state-of-the-art no-core shell model and self-consistent Green's function approaches. Calculations with $NN+3N\text{(lnl)}$ are compared to two other representative Hamiltonians currently in use, namely ${\mathrm{NNLO}}_{\text{sat}}$ and the older $NN+3N\left(400\right)$.

Results: Overall, the performance of the novel $NN+3N\text{(lnl)}$ interaction is very encouraging. In light nuclei, total energies are generally in good agreement with experimental data. Known spectra are also well reproduced with a few notable exceptions. The good description of ground-state energies carries on to heavier nuclei, all the way from oxygen to nickel isotopes. Except for those involving excitation processes across the $N=20$ gap, which is overestimated by the new interaction, spectra are of very good quality, in general superior to those obtained with ${\mathrm{NNLO}}_{\text{sat}}$. Although largely improving on $NN+3N\left(400\right)$ results, charge radii calculated with $NN+3N\text{(lnl)}$ still underestimate experimental values, as opposed to the ones computed with ${\mathrm{NNLO}}_{\text{sat}}$ that successfully reproduce available data on nickel.

Conclusions: The new two- plus three-nucleon Hamiltonian introduced in the present work represents a promising alternative to existing nuclear interactions. In particular, it has the favorable features of (i) being adjusted solely on $A=2,3,4$ systems, thus complying with the ab initio strategy, (ii) yielding an excellent reproduction of experimental energies all the way from light to medium-heavy nuclei, and (iii) behaving well under similarity renormalization group transformations, with negligible four-nucleon forces being induced, thus allowing large-scale calculations up to medium-heavy systems. The problem of the underestimation of nuclear radii persists and will necessitate novel developments.

• Received 23 July 2019
• Revised 6 November 2019

DOI:https://doi.org/10.1103/PhysRevC.101.014318