Ab-initioshell model with a core

We construct effective two- and three-body Hamiltonians for the p-shell by performing 12Ω ab initio no-core shell model (NCSM) calculations for $A=6$ and 7 nuclei and explicitly projecting the many-body Hamiltonians onto the 0Ω space. We then separate these effective Hamiltonians into inert core, one- and two-body contributions (also three-body for $A=7$) and analyze the systematic behavior of these different parts as a function of the mass number A and size of the NCSM basis space. The role of effective three- and higher-body interactions for $A>6$ is investigated and discussed.