Symplectic no-core shell model

Jerry P. Draayer, Louisiana State University
Tomáš Dytrych, Louisiana State University
Kristina D. Sviratcheva, Louisiana State University
Chairul Bahri, Louisiana State University
James P. Vary, Iowa State University


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.