Applications of Effective Operators within the NCSM

The no-core shell model (NCSM) is a powerful many-body method which provides the solution to the Schr\"odinger equation for $A$ interacting nucleons in a restricted space. Starting from realistic nucleon-nucleon interactions that accurately fit the experimental phaseshifts, we use a unitary transformation approach to obtain an effective interaction in the model space (realistic three-nucleon forces can be also implemented, but we restrict the discussion to two-body forces). The same renormalization procedure can be applied to other operators, obtaining results consistent with the NCSM wave functions. In our presentation we will discuss renormalization of short- and long-range operators, as well as the latest applications of the NCSM to the description of ground- and excited-state properties. I.S. and B.R.B acknowledge partial support by NFS grants PHY0070858 and PHY0244389. The work was performed in part under the auspices of the U. S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. P.N. received support from LDRD contract 04-ERD-058. J.P.V. acknowledges partial support by USDOE grant No DE-FG-02-87ER-40371, and C.W.J. acknowledges USDOE grant No.DE-FG02-03ER41272 .