Effective Shell-Model interactions for the p-shell from the No-Core Shell Model

The {\em ab initio} no-core shell model (NCSM) is a powerful many-body technique to perform fundamental microscopic studies of the structure of light nuclei. However, it becomes rather challenging to produce converged results for nuclei with A $\geq$ 12. In this contribution, following the idea of Ref. [2] we derive effective p-shell Hamiltonians from $N_{\rm max} \hbar \Omega$ NCSM calculations for $^6$Li with $N_{\rm max} =2,4,...,14$. We show how the averaged many-body correlations modify the p-shell two-body Hamiltonian and explore the dependence of the effective one-body and two-body matrix elements on $N_{\rm max}$. We present the results of the standard shell model calculations using derived effective Hamiltonian for p-shell nuclei with $A>6$ and compare it to the exact NCSM results. \newline [2] P.Navratil, M.Thoresen, and B.R.Barrett, Phys.Rev.C. {\bf 55}, R573 (1997).