Dominant role of symplectic symmetry in<i>ab initio</i>no-core shell model results for light nuclei

Abstract

The symplectic Sp$(3,\mathbb{R})$ symmetry of eigenstates for the $^{16}\mathrm{O}$ ground state and the ${0}_{\mathrm{gs}}^{+}$ and lowest ${2}^{+}$ and ${4}^{+}$ configurations of $^{12}\mathrm{C}$ that are determined within the framework of the no-core shell model with the JISP16 realistic interaction is examined. These states are found to project at the 80--85% level onto a few 0-particle-0-hole symplectic representations, including the most deformed configuration. The corresponding symplectic space spans 0-particle-0-hole nuclear configurations together with single- and multiparticle excitations. The results are nearly independent of the harmonic oscillator strength and whether the bare or renormalized effective interactions are used in the analysis. The outcome points to the relevance of a symplectic no-core shell model and reaffirms the Elliott SU(3) model on which the symplectic scheme is built.