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.
Categories: nucl-th