Symplectic Symmetry and the Ab Initio No-Core Shell Model

Abstract

The symplectic symmetry of eigenstates for the $0_{gs}^{+}$ in ${}^{16}$O and the $0_{gs}^{+}$ and lowest $2^{+}$ and $4^{+}$ configurations of ${}^{12}$C that are well-converged within the framework of the no-core shell model with the JISP16 realistic interaction is examined. These states are found to project at the 85-90% level onto very few symplectic representations including the most deformed configuration, which confirms the importance of a symplectic no-core shell model and reaffirms the relevance of the Elliott $\mathrm{SU}(3)$ model upon which the symplectic scheme is built.

6 pages, 4 figures, Proceedings of the XXX Symposium on Nuclear Physics, January 3-6, 2007, Cocoyoc, Mexico. to be published in Revista Mexicana de Fisica