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We present a detailed discussion of the structure of the low-lying positive-parity energy spectrum of C12 from a no-core shell-model perspective. The approach utilizes a fraction of the usual shell-model space and extends its multishell 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 C12 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 C12, including matter rms radii, electric quadrupole moments, and E2 and E0 transition rates.

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Physical Review C