Extending the Hoyle-State Paradigm to ^{12}C+^{12}C Fusion.

Carbon burning is a key step in the evolution of massive stars, Type 1a supernovae and superbursts in x-ray binary systems. Determining the ^{12}C+^{12}C fusion cross section at relevant energies by extrapolation of direct measurements is challenging due to resonances at and below the Coulomb barrier. A study of the ^{24}Mg(α,α^{'})^{24}Mg reaction has identified several 0^{+} states in ^{24}Mg, close to the ^{12}C+^{12}C threshold, which predominantly decay to ^{20}Ne(ground state)+α. These states were not observed in ^{20}Ne(α,α_{0})^{20}Ne resonance scattering suggesting that they may have a dominant ^{12}C+^{12}C cluster structure. Given the very low angular momentum associated with sub-barrier fusion, these states may play a decisive role in ^{12}C+^{12}C fusion in analogy to the Hoyle state in helium burning. We present estimates of updated ^{12}C+^{12}C fusion reaction rates.