Highly deformed modes in the ab initio symplectic no-core shell model

We show that highly deformed modes essential for nuclear dynamics modeling can readily be included in the symplectic no-core shell model (Sp-NCSM) space. In particular, a prescription for constructing general deformed k-particle-k-hole (kp-kh) translationally invariant symplectic Sp(3, R) starting state configurations and symplectic excitations thereof in a fermion-based spherical harmonic oscillator basis is presented. This prescription is used to build the symplectic excitations over all possible 2h Omega 2p-2h as well as the most deformed 4h Omega 4p-4h Sp(3,R) configurations in C-12 and O-16. The extent to which these configurations enter into low-lying states for these nuclei calculated within the framework of the no-core shell model with a realistic microscopic interaction is then determined. Typically, the addition of these 2p-2h and 4p-4h representations to the leading 0p-0h results grow the overall overlap with the no-core-shell-model eigenstates by 5-10% for a total of 85-90%. And most importantly, even with the addition of these higher-order particle - hole configurations, the dimensionality of the symplectic subspace constitutes a very small fraction of the conventional full no-core shell model space, which reaffirms the relevance of the Sp-NCSM scheme.