We present a study of the role played by realistic three-body forces in providing a reliable monopole component of the effective shell-model Hamiltonian. To this end, starting from a nuclear potential built up within the chiral perturbation theory, we derive effective shell-model Hamiltonians with and without the contribution of the three-body potential and compare the results of shell-model calculations with a set of observables that evidence shell-evolution properties. The testing ground of our investigation is nuclei belonging to the $fp$ shell, since the shell-evolution towards shell closures in ${}^{48}\mathrm{Ca}$ and ${}^{56}\mathrm{Ni}$ provides a paradigm for shell-model Hamiltonians. Our analysis shows that only by including contributions of the three-body force is the monopole component of the effective shell-model Hamiltonian then able to reproduce the experimental shell evolution towards and beyond the closure at $N=28$.

• Received 7 December 2018
• Revised 13 June 2019

DOI:https://doi.org/10.1103/PhysRevC.100.034324