Effective Interactions for pf Shell from the No Core Shell Model

Following the ideas of the Tucson nuclear theory group for the extension of the No-Core Shell Model (NCSM) approach to sd-shell nuclei [1], we show how a NCSM calculation for $^{42}$Ca in a 2$\hbar\Omega$ model space can yield two-body effective interactions for the pf-shell. We demonstrate how the effective Hamiltonian derived in the 2$\hbar\Omega$ NCSM at the 2-body cluster level should be modified to properly account for the many-body correlations produced by truncating to a single major shell. The pf-shell two-body effective interactions for $^{42}$Ca, obtained by direct projection, are used to reproduce the results of large scale NCSM for other Ca isotopes.\\ 1. B.R. Barrett et al, DNP 2007 abstract.