The symplectic no-core shell model (Sp-NCSM) is described. The theory is applied to a study of the structure of 12 C and 16 O . Results from a full 6ħΩ NCSM calculation for low-lying states in these nuclei using a realistic nucleon-nucleon interaction are found to project at approximately the 90% level onto a few of the leading 0 p -0 h and 2 p -2 h symplectic representations. The results are nearly independent of the oscillator strength parameter and whether bare or renormalized effective interactions are used in the analysis. The Sp-NCSM model space is typically only a very small fraction (under 1%) of the NCSM space, and grows slowly with increasing ħΩ. The comparisons with NCSM results suggest either the effective nucleon-nucleon interaction possesses a heretofore unappreciated symmetry, namely Sp(3,R) and the complementary (spin-isospin) supermultiplet symmetry, or the nuclear many-body system acts as a filter that allows the symplectic symmetry to propagate in a coherent way into the many-body dynamics while tending to dampen out symplectic symmetry breaking terms. Also, since the Sp-NCSM is a multi-ħΩ generalization of the Elliott SU (3) model, the results obtained to date reaffirm the relevance of SU (3) to atomic nuclei.
Low-momentum nucleon–nucleon interaction and shell-model calculations