Effective interactions for sd-shell space from {\em ab-initio} approach

Insight gained from projected No Core Shell Model calculations in the p-shell [1] can now be utilized to obtain information about and to derive effective Standard Shell Model (SSM) single particle energies (SPEs) and two-body matrix elements (TBMEs) for heavier nuclei. Here we report on a NCSM investigation in $2 \hbar \Omega$, $4 \hbar \Omega$ and $6 \hbar \Omega$ model spaces for $A=17,18$ in order to determine effective interactions for the sd-shell employing valence cluster expansion method. The validity range of the two-body valence cluster truncation is demonstrated by SSM results for binding energies and spectra of $A \ge 19$ nuclei. [1]~A.~F.~Lisetskiy, B.~R.~Barrett, M.~K.~G.~Kruse, P.~Navr\'atil, I.~Stetcu, and J.~P.~Vary, Phys. Rev. C 78, 044302 (2008). $^{\dagger}$Supported in part by NSF grant PHY-0555396; $^{\ddagger}$ Prepared by LLNL under contract No. DE-AC52-07NA27344; $^{*}$ Supported in part by DOE No. DE-AC52-06NA25396; $^{**}$ Supported in part by DOE grant DE-FG02-87ER40371.