Chiral three-body force and monopole properties of shell-model Hamiltonian

So far, the nature of three-nucleon forces (3NFs) derived by the chiral effective field theory has been intensively investigated by various theoretical approaches. In this work, to address the chiral 3NF within the shell-model framework, three-body matrix elements are formulated in terms of the harmonic oscillator basis functions, by adopting the nonlocal regulator. We perform a benchmark test for p-shell nuclei inorder to confirm our framework. Then we show that the contribution of the 3NF to the monopole component of the effective shell model Hamiltonian plays an essential role to account for the shell evolution of f p-shell nuclei