Evidence for symplectic symmetry in ab initio no-core shell model results

Abstract

Advances in the construction of realistic internucleon interactions together with the advent of massively parallel computers have resulted in a successful utilization of the ab initio approaches to the investigation of properties of light nuclei. The no-core shell model is a prominent ab initio method that yields a good description of the low-lying states in few-nucleon systems as well as in more complex p-shell nuclei. Nevertheless, its applicability is limited by the rapid growth of the many-body basis with larger model spaces and increasing number of nucleons. To extend the scope of the ab initio no-core shell model to heavier nuclei and larger model spaces, we analyze the possibility of augmenting the spherical harmonic oscillator basis with symplectic Sp(3,R) symmetry-adapted configurations of the symplectic shell model which describe naturally the monopole-quadrupole vibrational and rotational modes, and also partially incorporate α-cluster correlations. In our study we project low-lying states of 12C and 16O determined by the no-core shell model with the JISP16 realistic interaction onto Sp(3,R)-symmetric model space that is free of spurious center-of-mass excitations. The eigenstates under investigation are found to project at the 85-90% level onto a few of the most deformed symplectic basis states that span only a small fraction (≈0.001%) of the full model space. The results are nearly independent of whether the bare or renormalized effective interactions are used in the analysis. The outcome of this study points to the relevance of the symplectic extension of the ab initio no-core shell model. Further, it serves to reaffirm the Elliott SU(3) model upon which the symplectic scheme is built. While extensions of this work are clearly going to be required if the theory is to become a model of choice for nuclear structure calculations, these early results seem to suggest that there may be simplicity within the complexity of nuclear structure that has heretofore not been fully appreciated. As follow-on work to what is reported in this thesis, we expect to develop a stand alone shell-model code that builds upon the underlying symmetries of the symplectic model.