Carbon burning is a key step in the evolution of massive stars, Type 1a supernovae and super- bursts in x-ray binary systems. Nevertheless, our understanding of this critical fusion reaction is not as complete as might be desirable to fully constrain astrophysical models. This limitation cen- tres of the difficulty in determining the 12C+12C fusion cross section at energies corresponding to the Gamow window for these different scenarios as it relies on extrapolation of direct measurements made at higher energies. Such direct fusion measurements are complicated by the presence of res- onances at and below the Coulomb barrier. These resonances have traditionally been associated with the formation of short-lived molecular states based on 12C+12C or similar alpha-conjugate systems. Despite study of these resonances over many years, a comprehensive theoretical model accounting for their existence and structure is presently lacking.
Given the difficulties associated with direct fusion studies of the 12C+12C reaction, indirect studies which can identify potential resonances within the respective Gamow windows are of high value. In this respect, a study of the 24Mg(α,α’)24Mg reaction has identified several 0+ states in 24Mg, close to the 12C+12C threshold, which predominantly decay to 20Ne(ground state) + α . Not only were these states newly identified but surprisingly they were not observed in previously well-studied 20Ne(α,α0)20Ne resonance scattering, potentially suggesting that they have a dominant 12C+12C cluster structure. Given the very low angular momentum associated with sub-barrier fusion, these states, which sit in the Gamow window for massive stars, may play a decisive role in 12C+12C fusion. We present estimates of updated 12C+12C fusion reaction rates based on likely parameters for such resonances .
A fascinating aspect of the identification of these potential 0+ cluster states in 24Mg close to the break-up threshold for 12C+12C and similar channels such as 16O+8Be is the circumstantial similarity to the situation in 12C with the Hoyle state at the break-up threshold and the critical role that it plays in in helium burning.
 P. Adsley, M. Heine, D.G. Jenkins et al. Phys. Rev. Lett. 129, 102701 (2022).