Extending the Hoyle-State Paradigm to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:mmultiscripts><mml:mo>+</mml:mo><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> Fusion
P. Adsley, M. Heine, D. G. Jenkins, S. Courtin, R. Neveling, J. W. Brümmer, L. M. Donaldson, N. Y. Kheswa, K. C. W. Li, D. J. Marı́n-Lámbarri, P.Z. Mabika, P. Papka, L. Pellegri, V. Pesudo, B. Rebeiro, F. D. Smit, W. Yahia-Chérif
Abstract
Carbon burning is a key step in the evolution of massive stars, Type 1a supernovae and superbursts in x-ray binary systems. Determining the $^{12}\mathrm{C}+^{12}\mathrm{C}$ 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 $^{24}\mathrm{Mg}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})^{24}\mathrm{Mg}$ reaction has identified several ${0}^{+}$ states in $^{24}\mathrm{Mg}$, close to the $^{12}\mathrm{C}+^{12}\mathrm{C}$ threshold, which predominantly decay to $^{20}\mathrm{Ne}(\text{ground state})+\ensuremath{\alpha}$. These states were not observed in $^{20}\mathrm{Ne}(\ensuremath{\alpha},{\ensuremath{\alpha}}_{0})^{20}\mathrm{Ne}$ resonance scattering suggesting that they may have a dominant $^{12}\mathrm{C}+^{12}\mathrm{C}$ cluster structure. Given the very low angular momentum associated with sub-barrier fusion, these states may play a decisive role in $^{12}\mathrm{C}+^{12}\mathrm{C}$ fusion in analogy to the Hoyle state in helium burning. We present estimates of updated $^{12}\mathrm{C}+^{12}\mathrm{C}$ fusion reaction rates.