Symmetry-adapted Ab Initio Theory for Many-body Correlations in Nuclei

We demonstrate that no-core shell-model results for low-lying states of light and medium mass nuclei, whether they are dilute or dense systems, reveal a strong dominance of low-spin and high-deformation configurations. This result is independent of whether the system Hamiltonian is phenomenological in nature or derived from a realistic interaction. It implies that only a small fraction of the complete model space is required for a description of such states, and this in turn points to the importance of using a symmetry-adapted, no-core shell-model framework for describing such nuclei, one based on an LS coupling scheme with the associated spatial configurations organized according to deformation. These results confirm that the pioneering work of early developers of the field, J. P. Elliott with his SU(3) model and M. Moshinsky with his U(3) many-body oscillator work, extends to more open, multi-shell environments. Specifically, algebraic methods are both relevant in such an environment and they can be used to quell the combinatorial growth in dimensionality that comes with the addition of oscillator shells to a model space. Indeed, our findings demonstrate the utility of a symmetry-adapted, no-core shell-model approach, one that takes advantage of group theoretical as well as advanced computational methods. And importantly, what at first glance appear to be a daunting task – casting complex algebraic expressions of a symmetry-adapted scheme into a user-friendly and efficient shell-mode code, turns out to be not only doable, but a logical framework that embraces constructs that can be made to execute efficiently on massively parallel, multi-processor (and core) systems. Early results for some light p-shell nuclei are presented. In addition, we will show that the method can be extended to heavier nuclei of the sd-shell and beyond, including some cases of special astrophysical interest in the upper fp- and lower gds-shells, like isotopes of Ge, Se, and even Kr.