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 .

In this review, we discuss the present status of three indirect techniques that are used to determine reaction rates for stellar burning processes, asymptotic normalization coefficients, the Trojan Horse method and Coulomb dissociation. A comprehensive review of the theory behind each of these techniques is presented. This is followed by an overview of the experiments that have been carried out using these indirect approaches.

We present computations of nucleosynthesis in low-mass (LM) red giant branch (RGB) and asymptotic giant branch (AGB) stars of Population I experiencing extended mixing. We adopt the updated version of the FRANEC evolutionary model, a new post-process code for non-convective mixing and the most recent revisions for solar abundances. In this framework, we discuss the effects of recent improvements in relevant reaction rates for proton captures on intermediate-mass (IM) nuclei (from carbon to aluminum). For each nucleus, we briefly discuss the new choices and their motivations. The calculations are then performed on the basis of a parameterized circulation, where the effects of the new nuclear inputs are best compared to previous works. We find that the new rates (and notably the one for the 14 N(p, γ ) 15 O reaction) imply considerable modifications in the composition of post-mainsequence stars. In particular, the slight temperature changes due to the reduced efficiency of proton captures on 14 N induce abundance variations at the first dredge-up (especially for 17 O, whose equilibrium ratio to 16 O is very sensitive to the temperature). In this new scenario, presolar oxide grains of AGB origin turn out to be produced almost exclusively by very low mass stars (M 1.5-1.7 M ), never becoming C-rich. The whole population of grains with 18 O/ 16 O below 0.0015 (the limit permitted by first dredge-up) is now explained. Also, there is now no forbidden area for very low values of 17 O/ 16 O (below 0.0005), contrary to previous findings. A rather shallow type of transport seems to be sufficient for the CNO changes in RGB stages. Both thermohaline diffusion and magnetic-buoyancy-induced mixing might provide a suitable physical mechanism for this. Thermohaline mixing is in any case certainly inadequate to account for the production of 26 Al on the AGB. Other transport mechanisms must therefore be at play. In general, observational constraints from RGB and AGB stars, as well as from presolar grains, are well reproduced by our approach. The nitrogen isotopic ratio in mainstream SiC grains remains an exception. For the low values measured in them (i.e., for 14 N/ 15 N 2000), we have no explanation. Actually, for the several grains with subsolar nitrogen isotopic ratios, no known stellar process acting in LM stars can provide a clue. This might be an evidence that some form of contamination from cosmic ray spallation occurs in the interstellar medium, adding fresh 15 N to the grains.