Multi-probe study of excited states in \(\mathrm{^{12}C}\): disentangling the sources of monopole strength between the Hoyle state and \(E_{x} = 13\) MeV

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. 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. A self-consistent, simultaneous analysis of the inclusive spectra with lineshapes was performed, which accounted for distortion due to nuclear dynamics and experimental effects. Clear evidence was found for excess monopole strength at \(E_{x} \sim 9\) MeV, particularly in the \(\mathrm{^{12}C}(\alpha, \alpha^{\prime})\mathrm{^{12}C}\) reaction at \(0^{\circ}\). This additional strength cannot be reproduced by the previously established monopole states between \(E_{x} = 7\) and 13 MeV. An additional \(0^{+}\) state at \(E_{x} \sim 9\) MeV yielded a significantly improved fit of the data and is the leading candidate for the predicted breathing-mode excitation of the Hoyle state. Alternatively, the results may suggest that a more sophisticated, physically motivated parameterization of the astrophysically important monopole strengths in \(\mathrm{^{12}C}\) is required.