The effective three-body monopole interaction and ground-state energies in the $0p$-shell*

Following Refs. [1,2], we have earlier developed a valence cluster expansion to construct effective 2- and 3-body Hamiltonians for the $0p$-shell by performing No Core Shell Model (NCSM) calculations for $A=6$ and 7 nuclei and explicitly projecting the many-body Hamiltonians onto the $0\hbar\Omega$ space. These effective Hamiltonians can be separated into 0-, 1- and 2-body contributions(also 3-body for $A=7$), which can be used in standard shell model (SSM) calculations. In new studies we have derived the effective 3-body monopole Hamiltonian for the 0p-shell by performing $6\hbar\Omega$ NCSM calculations for $A=7-16$ nuclei and used it to investigate how the ground-state energies of these nuclei are affected, when it is included in the SSM calculations. \\[4pt] [1] P. Navr\'atil, M. Thoresen and B.R. Barrett, Phys. Rev. C {\bf 55}, R573 (1997). \\[0pt] [2] A. Lisetskiy, {\bf et al.}, Phys. Rev. C {\bf 78}, 044302 (2008).