Abstract
We construct effective two- and three-body Hamiltonians for the $p$-shell by performing $12\ensuremath{\hbar}\ensuremath{\Omega}$ ab initio no-core shell model (NCSM) calculations for $A=6$ and 7 nuclei and explicitly projecting the many-body Hamiltonians onto the $0\ensuremath{\hbar}\ensuremath{\Omega}$ 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 $Ag6$ is investigated and discussed.
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