Carbon burning powers scenarios that influence the fate of stars, such as the late evolutionary stages of massive stars (exceeding eight solar masses) and superbursts from accreting neutron stars. It proceeds through the C +C fusion reactions that produce an alpha particle and neon-20 or a proton and sodium-23-that is, C(C, α)Ne and C(C, p)Na-at temperatures greater than 0.4 × 10 kelvin, corresponding to astrophysical energies exceeding a megaelectronvolt, at which such nuclear reactions are more likely to occur in stars. The cross-sections for those carbon fusion reactions (probabilities that are required to calculate the rate of the reactions) have hitherto not been measured at the Gamow peaks below 2 megaelectronvolts because of exponential suppression arising from the Coulomb barrier. The reference rate at temperatures below 1.2 × 10 kelvin relies on extrapolations that ignore the effects of possible low-lying resonances. Here we report the measurement of the C(C, α)Ne and C(C, p)Na reaction rates (where the subscripts 0 and 1 stand for the ground and first excited states of Ne andNa, respectively) at centre-of-mass energies from 2.7 to 0.8 megaelectronvolts using the Trojan Horse method and the deuteron in N. The cross-sections deduced exhibit several resonances that are responsible for very large increases of the reaction rate at relevant temperatures. In particular, around 5 × 10 kelvin, the reaction rate is boosted to more than 25 times larger than the reference value . This finding may have implications such as lowering the temperatures and densities required for the ignition of carbon burning in massive stars and decreasing the superburst ignition depth in accreting neutron stars to reconcile observations with theoretical models .

The 13 C(α, n) 16 O reaction is the neutron source for the main component of the s-process, responsible for the production of most of the nuclei in the mass range 90 A 208. This reaction takes place inside the heliumburning shell of asymptotic giant branch stars, at temperatures 10 8 K, corresponding to an energy interval where the 13 C(α, n) 16 O reaction is effective in the range of 140-230 keV. In this regime, the astrophysical S(E)-factor is dominated by the −3 keV sub-threshold resonance due to the 6.356 MeV level in 17 O, giving rise to a steep increase in the S-factor. Its contribution is still controversial as extrapolations, e.g., through the R-matrix and indirect techniques such as the asymptotic normalization coefficient (ANC), yield inconsistent results. The discrepancy amounts to a factor of three or more precisely at astrophysical energies. To provide a more accurate S-factor at these energies, we have applied the Trojan horse method (THM) to the 13 C( 6 Li, n 16 O)d quasi-free reaction. The ANC for the 6.356 MeV level has been deduced through the THM as well as the n-partial width, allowing us to attain unprecedented accuracy for the 13 C(α, n) 16 O astrophysical factor. A larger ANC for the 6.356 MeV level is measured with respect to the ones in the literature, (C 17 O(1/2 + ) α 13 C ) 2 = 7.7 ± 0.3 stat +1.6 −1.5 norm fm −1 , yet in agreement with the preliminary result given in our preceding letter, indicating an increase of the 13 C(α, n) 16 O reaction rate below about 8 × 10 7 K if compared with the recommended values. At ∼10 8 K, our reaction rate agrees with most of the results in the literature and the accuracy is greatly enhanced thanks to this innovative approach.