Core polarization effects in effective Hamiltonians far from stability

We investigate the neutron rich nuclei which can be described by shell model calculations in the p–sd and sd–pf model spaces. We quantify the effects of the core polarization on the multipole part (pairing and quadrupole) of the effective Hamiltonians. We show that proton core polarization contributions are responsible for the reduction of the neutron–neutron nuclear matrix elements which, in the recent shell model studies, appeared necessary between p–sd carbon and oxygen and sd–pf silicon and calcium nuclei.