Consistent analysis of the 2+excitation of the12C Hoyle state populated in proton and α-particle inelastic scattering

The ${}^{12}$C excitation energy spectra populated in both proton and $\ensuremath{\alpha}$-particle inelastic scattering measurements are examined. The data indicate the existence of a 2${}^{+}$ state at ${E}_{x}=9.75$(0.15) MeV with a width of 750(150) keV. It is believed that this state corresponds to the 2${}^{+}$ excitation of the 7.65 MeV, 0${}^{+}$, Hoyle state, which acts as the main path by which carbon is synthesized in stars. A simultaneous $R$-matrix analysis of the two sets of data indicates that the 2${}^{+}$ state possesses a very large $\ensuremath{\alpha}$-reduced width, approaching the Wigner limit. This would indicate that the state is associated with a highly clustered structure. The potential geometric arrangements of the clusters is discussed.