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 $3α$ reaction and of $α$-particle clustering. The $\mathrm{^{12}C}(α, α^{\prime})\mathrm{^{12}C}$ 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 $\mathrm{^{12}C}(α, α^{\prime})\mathrm{^{12}C}$ 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.

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