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Carbon burning powers scenarios that influence the fate of stars, such as the late evolutionary stages of massive stars1(exceeding eight solar masses) and superbursts from accreting neutron stars2,3. It proceeds through the 12C + 12C fusion reactions that produce an alpha particle and neon-20 or a proton and sodium-23—that is, 12C(12C, α)20Ne and 12C(12C, p)23Na—at temperatures greater than 0.4 × 109kelvin, corresponding to astrophysical energies exceeding a megaelectronvolt, at which such nuclear reactions are more likely to occur in stars. The cross-sections4for those carbon fusion reactions (probabilities that are required to calculate the rate of the reactions) have hitherto not been measured at the Gamow peaks4below 2 megaelectronvolts because of exponential suppression arising from the Coulomb barrier. The reference rate5at temperatures below 1.2 × 109kelvin relies on extrapolations that ignore the effects of possible low-lying resonances. Here we report the measurement of the 12C(12C, α0,1)20Ne and 12C(12C, p0,1)23Na reaction rates (where the subscripts 0 and 1 stand for the ground and first excited states of 20Ne and 23Na, respectively) at centre-of-mass energies from 2.7 to 0.8 megaelectronvolts using the Trojan Horse method6,7and the deuteron in 14N. 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 × 108kelvin, the reaction rate is boosted to more than 25 times larger than the reference value5. This finding may have implications such as lowering the temperatures and densities8required for the ignition of carbon burning in massive stars and decreasing the superburst ignition depth in accreting neutron stars to reconcile observations with theoretical models3. The rate of carbon burning—12C + 12C fusion—in stars is boosted by resonant behaviour at astrophysical energies.

The asymptotic normalization coefficient (ANC) for a nuclear system specifies the normalization of the tail of the nuclear overlap function. ANCs may be determined experimentally by measuring peripheral nuclear reactions. They may be used to calculate the astrophysical S-factors for radiative capture reactions at stellar energies and to determine the halo structure of loosely bound nuclei. A brief introduction to ANCs is given and applications to the 7Be(p, γ)8B and 11C(p, γ)12N reactions and the halo structure of 8B are described.

Abstract:: Peripheral transfer reactions can be used to determine asymptotic normalization coefficients (ANCs). These coefficients, which specify the normalization of the tail of the nuclear overlap function, determine S-factors for direct capture reactions at astrophysical energies. A variety of proton transfer reactions involving both stable and radioactive beams have been used to measure ANCs. Tests have demonstrated that ANCs determined from proton transfer reactions can be used to calculate astrophysical direct capture rates to within 9%. The 10B(7Be, 8B)9Be and 14N(7Be, 8B)13C reactions have been used to measure the ANC appropriate for determining the 7Be(p,γ)8B rate, and the 14N(11C, 12N)13C reaction has been used to measure the ANC required to calculate the 11C(p,γ)12N rate.

S-factors for direct capture reactions can be found at astrophysical energies from asymptotic normalization coefficients which provide the normalization of the tail of the overlap function. For example the overlap for 8B → 7Be+pdefines the S-factor for 7Be (p, γ)8B. Peripheral transfer reactions offer a technique to determine these asymptotic normalization coefficients. As a test of the technique, the 16O(3He, d)17F reaction has been used to determine asymptotic normalization coefficients for transitions to the ground and first excited states of 17F. The S-factors for 16O(p, γ)17F calculated from these 17F → 16O+pasymptotic normalization coefficients are found to be in very good agreement with recent measurements. Following the same technique, the 10B(7Be, 8B)9Be and 14N(7Be, 8B)13C reactions have been used to measure the asymptotic normalization coefficient for 7Be(p, γ)8B. This result provides an indirect determination of S17(0).

In equation (1) of this Letter, the closing bracket was missing; in Extended Data Fig. 1 and the accompanying legend, ‘Φ(pd)’ should have been ‘Φ2(pd)’, and in the Methods the text “Odd Jassignments are uncertain by ±1.” has been added. These errors have all been corrected online.

The level scheme of the neutron deficient isotope111Sb up to about 3.7 MeV is established from in-beam gamma-ray spectroscopy experiments. The identification of the reaction channel using cross bombardments:95Mo+19F (56–68 MeV),106Cd+7Li (20–30 MeV),102Pd+11B (45 MeV), charged partice-? and neutron-? coincidences is discussed.