Effective three-body monopole interaction in the valence cluster approximation for the p-shell

No-core shell model calculations of binding energies using the two-body cluster approximation can omit higher-body correlations in small model spaces. To try and remedy this, we include higher-body correlations up to six nucleons in a two-body effective hamiltonian suitable for standard shell model (SSM) calculations, by performing two successive unitary transformations. The obtained effective hamiltonian contains a core, one-body and two-body pieces (due respectively to interactions among the core nucleons, between a valence and core nucleons and between two valence nucleons). We investigated the size of these interactions as a function of isospin for nuclei with A = 8 to 16 and compared the ab-initio results with the SSM results. The differences grow larger with A, indicating the need for three- and higher-body terms in the effective hamiltonian with increasing A. Taking the effective three-body monopole interaction into account for A$>$7, we found greatly improved results.