We investigate the influence of phenomenological three-nucleon interactions on the systematics of ground-state energies and charge radii throughout the whole nuclear mass range from ${}^4\mathrm{He}$ to ${}^{208}\mathrm{Pb}$. The three-nucleon interactions supplement unitarily transformed two-body interactions constructed within the unitary correlation operator method or the similarity renormalization group approach. To be able to address heavy nuclei as well, we treat the many-body problem in Hartree-Fock plus many-body perturbation theory, which is sufficient to assess the systematics of energies and radii, and limit ourselves to regularized three-body contact interactions. We show that even with such a simplistic three-nucleon interaction a simultaneous reproduction of the experimental ground-state energies and charge radii can be achieved, which is not possible with unitarily transformed two-body interactions alone.

• Received 10 May 2010

DOI:https://doi.org/10.1103/PhysRevC.82.024319