Ab initioshell model with a genuine three-nucleon force for thep-shell nuclei

Abstract

The ab initio no-core shell model (NCSM) is extended to include a realistic three-body interaction in calculations for p-shell nuclei. The NCSM formalism is reviewed and new features needed in calculations with three-body forces are discussed in detail. We present results of first applications to ${}^{6,7}\mathrm{Li},$ ${}^6\mathrm{He},$ ${}^{7,8,10}\mathrm{Be},$ ${}^{10,11,12}\mathrm{B},$ ${}^{12}\mathrm{N},$ and ${}^{10,11,12,13}\mathrm{C}$ using the Argonne ${\mathrm{V}8\mathrm{}}^{\prime }$ nucleon-nucleon (NN) potential and the Tucson-Melbourne ${\mathrm{TM}}^{\prime }\mathrm{}\left(99\right)\mathrm{}$ three-nucleon interaction (TNI). In addition to increasing the total binding energy, we observe a substantial sensitivity in the low-lying spectra to the presence of the realistic three-body force and an overall improvement in level ordering and level spacing in comparison to experiment. The greatest sensitivity occurs for states where the spin-orbit interaction strength is known to play a role. In particular, with the TNI we obtain the correct ground-state spin for ${}^{10,11,12}\mathrm{B}$ and ${}^{12}\mathrm{N},$ contrary to calculations with NN potentials only.