Investigating the predicted breathing-mode excitation of the Hoyle state

TL;DR

This study investigates the existence of a predicted breathing-mode excitation of the Hoyle state in carbon-12, providing experimental evidence of a collective monopole resonance around 9 MeV that could impact astrophysical models.

Contribution

The paper presents experimental evidence for a collective monopole resonance near 9 MeV in carbon-12, supporting the existence of a breathing mode of the Hoyle state and suggesting a possible $ ext{D}_{3h}$ symmetry.

Findings

Evidence of excess monopole strength at 9 MeV in $^{12}$C.

Identification of a collective monopole resonance consistent with a breathing mode.

Implications for astrophysical models of nucleosynthesis in stars.

Abstract

Knowledge of the low-lying monopole strength in $\mathrm{^{12}C}$ $-$ the Hoyle state in particular $-$ is crucial for our understanding of both the astrophysically important $3\alpha$ reaction and of $\alpha$-particle clustering. Multiple theoretical models have predicted a breathing mode of the Hoyle State at $E_{x} \approx 9$ MeV, corresponding to a radial in-phase oscillation of the underlying $\alpha$ clusters. The $\mathrm{^{12}C}(\alpha, \alpha^{\prime})\mathrm{^{12}C}$ and $\mathrm{^{14}C}(p, t)\mathrm{^{12}C}$ reactions were employed to populate states in $^{12}$C in order to search for this predicted breathing mode. A self-consistent, simultaneous analysis of the inclusive spectra with R-matrix lineshapes, together with angular distributions of charged-particle decay, yielded clear evidence for excess monopole strength at $E_{x} \approx 9$ MeV which is highly collective. Reproduction of the experimentally observed inclusive yields using a fit, with consistent population ratios for the various broad states, required an additional source of monopole strength. The interpretation of this additional monopole resonance as the breathing-mode excitation of the Hoyle state would provide evidence supporting a $\mathcal{D}_{3h}$ symmetry for the Hoyle state itself. The excess monopole strength may complicate analysis of the properties of the Hoyle state, modifying the temperature dependence of the $3\alpha$ rate at $T_{9} \gtrsim 2$ and ultimately, the predicted nucleosynthesis in explosive stars.