Investigating the predicted breathing-mode excitation of the Hoyle state

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