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An increase in the 12C + 12C fusion rate from resonances at astrophysical energies

A Publisher Correction to this article was published on 28 June 2018

This article has been updated


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 × 109 kelvin, corresponding to astrophysical energies exceeding a megaelectronvolt, at which such nuclear reactions are more likely to occur in stars. The cross-sections4 for those carbon fusion reactions (probabilities that are required to calculate the rate of the reactions) have hitherto not been measured at the Gamow peaks4 below 2 megaelectronvolts because of exponential suppression arising from the Coulomb barrier. The reference rate5 at temperatures below 1.2 × 109 kelvin 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 method6,7 and 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 × 108 kelvin, 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 densities8 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 models3.

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Fig. 1: Excitation functions from THM experimental yields.
Fig. 2: 12C + 12C astrophysical S(E)* factors.
Fig. 3: 12C + 12C reaction rate ratio.

Change history

  • 28 June 2018

    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 J assignments are uncertain by ±1.” has been added. These errors have all been corrected online.


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We thank V. Z. Goldberg for having inspired the idea of the experiment and for discussions and assistance. We thank A. M. Mukhamedzhanov for having developed the theoretical framework of the THM. The aid of the technical staff of INFN-LNS during the preparation of the experiment is gratefully acknowledged. We thank M. Wiescher and F. X. Timmes for comments.

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Authors and Affiliations



A.T. and C.S. proposed the experiment. A.T., C.S., M.L.C., G.L.G., I.I., L.L., R.G.P., S.M.R.P., R.S. and G.G.R. set up and ran the experiment, which lasted about one month. S.C., M.G., S.H., H.P., M.L.S., S.R. and L.T. participated in the data collection. A.T. performed the data reduction and analysis. M.L.C. developed the modified R-matrix code for the one-level many-channel case. A.T. and M.L.C. performed the statistical analysis. A.T. performed R-matrix calculations, interpreted the results, prepared the figures and wrote the manuscript. C.S. and M.L.C. contributed on the interpretation of the results. M.L.C. assisted with the figure preparation. L.L., R.G.P. and R.S. assisted with the astrophysical interpretation. A.T., C.S., M.L.C., S.C., G.L.G., I.I., L.L., R.G.P., G.G.R., R.S., S.R. and L.T. revised the manuscript.

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Correspondence to A. Tumino.

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Extended data figures and tables

Extended Data Fig. 1 Deuteron momentum distribution.

The experimental distribution Φ2(pd) is shown as filled black circles. Error bars represent standard 1σ uncertainties. The black line represents the theoretical shape (see text for details).

Extended Data Fig. 2 Pole diagram describing the quasi-free mechanism in the A(a,bB)s reaction.

The upper vertex refers to the break-up of a and the lower vertex shows the A(x,b)B process. Colours help to highlight the role of individual particles in the mechanism.

Extended Data Fig. 3 Typical ∆E–E spectrum.

The strongest loci from the bottom to the top correspond to p, d and α. ADC, analogue-to-digital converter.

Extended Data Fig. 4 Q-value as a function of the α detection angle Θα for the 12C(14N,α20Ne)2H reaction.

Blue and red solid lines cross the Q-value axis at −5.65 MeV and −7.28 MeV, highlighting the contributions of the ground and first excited states, respectively.

Extended Data Table 1 Resonance parameters of 24Mg levels entering the R-matrix fit and total plus partial widths resulting from the fit
Extended Data Table 2 Reaction rate of the 12C + 12C fusion reaction

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Tumino, A., Spitaleri, C., La Cognata, M. et al. An increase in the 12C + 12C fusion rate from resonances at astrophysical energies. Nature 557, 687–690 (2018).

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