Investigating the predicted breathing-mode excitation of the Hoyle state

Abstract

Knowledge of the low-lying monopole strength in ${}^{12}\mathrm{C}$ $-$ the Hoyle state in particular $-$ is crucial for our understanding of both the astrophysically important $3\hat{I}\pm$ reaction and of $\hat{I}\pm$-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 $\hat{I}\pm$ clusters. The ${}^{12}\mathrm{C}(\hat{I}\pm ,\hat{I}{\pm }^{\prime }){}^{12}\mathrm{C}$ and ${}^{14}\mathrm{C}(p,t){}^{12}\mathrm{C}$ 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 $3\hat{I}\pm$ rate at $T_9\gtrsim 2$ and ultimately, the predicted nucleosynthesis in explosive stars.

8 pages, 5 figures