By using only a fraction of the model space extended beyond current no-core shell-model limits and a many-nucleon interaction with a single parameter, we gain additional insight within a symmetryguided shell-model framework, into the many-body dynamics that gives rise to the ground state rotational band together with phenomena tied to alpha-clustering substructures in the low-lying states in 12 C, and in particular, the challenging Hoyle state and its first 2 + and 4 + excitations. For these states, we offer a novel perspective emerging out of no-core shell-model considerations, including a discussion of associated nuclear deformation and matter radii. This, in turn, provides guidance for ab initio shell models by informing key features of nuclear structure and the interaction.

We present a microscopic description of nuclei in an intermediate-mass region, including the proximity to the proton drip line, based on a no-core shell model with a schematic many-nucleon long-range interaction with no parameter adjustments. The outcome confirms the essential role played by the symplectic symmetry to inform the interaction and the winnowing of shell-model spaces. We show that it is imperative that model spaces be expanded well beyond the current limits up through fifteen major shells to accommodate particle excitations that appear critical to highly-deformed spatial structures and the convergence of associated observables.

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We present a detailed discussion of the structure of the low-lying positive-parity energy spectrum of 12 C from a no-core shell-model perspective. The approach utilizes a fraction of the usual shellmodel space and extends its multi-shell reach via the symmetry-based no-core symplectic shell model (NCSpM) with a simple, physically-informed effective interaction. We focus on the ground-state rotational band, the Hoyle state and its 2 + and 4 + excitations, as well as the giant monopole 0 + resonance, which is a vibrational breathing mode of the ground state. This, in turn, allows us to address the open question about the structure of the Hoyle state and its rotational band. In particular, we find that the Hoyle state is best described through deformed prolate collective modes rather than vibrational modes, while we show that the higher-lying giant monopole 0 + resonance resembles the oblate deformation of the 12 C ground state. In addition, we identify the giant monopole 0 + and quadrupole 2 + resonances of selected light and intermediate-mass nuclei, along with other observables of 12 C, including matter rms radii, electric quadrupole moments, as well as E2 and E0 transition rates.

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