Understanding emergent collectivity and clustering in nuclei from a symmetry-based no-core shell-model perspective

TL;DR

This paper investigates the structure of low-lying states in carbon-12 using a symmetry-based no-core shell model, revealing insights into the nature of the Hoyle state and giant monopole resonances with a focus on collective deformation modes.

Contribution

It introduces a symmetry-based no-core shell model approach that efficiently describes collective phenomena and cluster structures in nuclei, specifically applied to $^{12}$C.

Findings

The Hoyle state is best described as a deformed prolate collective mode.

The giant monopole $0^+$ resonance resembles oblate deformation of the ground state.

Identification of giant monopole and quadrupole resonances in light and intermediate-mass nuclei.

Abstract

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 shell-model 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.