Symplectic no-core shell model
The symplectic no-core shell model (Sp-NCSM) is described. The theory is applied to a study of the structure of 12C and 16O. Results from a full 6Latin small letter h with strokeΩ 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 0p-0h and 2p-2h 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 Latin small letter h with strokeΩ. 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-Latin small letter h with strokeΩ generalization of the Elliott SU(3) model, the results obtained to date reaffirm the relevance of SU(3) to atomic nuclei. © 2008 World Scientific Publishing Company.