¹²C(¹²C,p)²³Na · Reaction atlas

Two carbon nuclei fuse, and the compound nucleus breaks up into sodium-23 and a proton. Together with the branch to neon-20, it is how carbon burns in stars.

Carbon fusion has two main outcomes: neon-20 with an alpha particle, and sodium-23 with a proton. This branch makes sodium. The protons it frees do not survive long in the hot core: they are captured by the nuclei around them, and on sodium-23 they make neon-20 or magnesium-24. The balance between the two branches, and how fast carbon fuses at all, sets how much sodium and neon a massive star leaves behind. Measuring the reaction at the energies of a stellar core is very hard, and the results of different methods still disagree by large factors.

Facts

How well known: The measured cross section is full of resonances, direct data reach only the upper part of the energies that matter in stars, and the ways of extending them downwards disagree by orders of magnitude.
Live evaluation: No live evaluation yet · Evaluations
Q-value · energy released: 2.241 MeV
Gamow window: 2135 ± 450 keVcore carbon burning, 15 M☉ star, 0.83 GK (Carbon burning)
1525 ± 295 keVsuperburst ignition, accreting neutron star, 0.5 GK (Carbon burning)
Kind: Fusion

On the timeline

How it was measured

11 measurements, 1969–2026Show the list

1969
Direct measurement at the surface · down to E ≈ 2.5 MeV
Early measurements of the α and p channels by charged-particle or γ-ray spectroscopy; together they covered the cross section down to about 2.5 MeV. [1, 2, 3, 4]
2006
Direct measurement at the surface
γ-ray measurement of the α and p channels, aimed at bringing the earlier, mutually inconsistent data sets into agreement. [5]
2007
Dynamitron Tandem Laboratory, BochumRuhr-Universität Bochum
Direct measurement at the surface · E = 2.10–4.75 MeV
γ-ray spectroscopy of both channels on targets with very low hydrogen contamination; new resonances at and below 3 MeV, the strongest at 2.14 MeV. [6]
2018
Direct measurement at the surface · E = 2.00–4.00 MeV
Proton spectroscopy: broad resonances above 3.00 MeV, and data compatible with the resonance structure near 2.1 MeV. The low-energy points are limited by count rate and possible background from hydrogen in the target; the authors judge any extrapolation highly uncertain. [7]
2018
INFN LNS, CataniaLaboratori Nazionali del Sud (INFN)
Trojan Horse method · E = 0.8–2.7 MeV, from ¹²C(¹⁴N,p²³Na)²H
Several resonances across the Gamow window and a combined rate more than 25 times the reference rate near 0.5 GK; disputed by Mukhamedzhanov et al. (2019). [8, 9]
2020
Andromède, OrsayInstitut de Physique Nucléaire d'Orsay (IPN Orsay)
Direct measurement at the surface · into the Gamow window of massive stars
STELLA particle–γ coincidences; the data support the fusion-hindrance model. [10, 11]
2020
Nuclear Science Laboratory, Notre DameUniversity of Notre Dame
Direct measurement at the surface · thick-target yield in 50 keV steps
SAND particle–γ coincidences; strong disagreement with the Trojan Horse result. [12]
2020
Activation · ¹²C + ¹³C down to E = 2.32 MeV
Not ¹²C + ¹²C itself: ¹²C(¹³C,p)²⁴Na measured by counting the ²⁴Na activity in an underground counting laboratory. Models normalized to these data give an upper limit on the non-resonant ¹²C + ¹²C cross section at stellar energies and argue against the S-factor maximum of the hindrance model. [13]
2022
CIRCE, CasertaCenter for Isotopic Research on Cultural and Environmental heritage (Università della Campania and INNOVA)
Direct measurement at the surface · E = 2.51–4.36 MeV
Protons and α particles identified with ΔE–E telescopes, in steps of 10–25 keV. The branching ratios of the individual proton and α groups change strongly with energy, and the angular distributions (three angles) are not isotropic, a possible cause of the disagreement between data sets. A first journal article (Eur. Phys. J. A 58, 65, 2022) was retracted (Eur. Phys. J. A 59, 120, 2023) because of an error in the script that computed the beam energy loss; the corrected article (Eur. Phys. J. A 60, 2024) keeps the general conclusions. [14, 15, 16]
2025
Andromède, OrsayInstitut de Physique Nucléaire d'Orsay (IPN Orsay)
Direct measurement at the surface · E ≈ 2.2–2.6 MeV; 3.23 MeV
Refined STELLA excitation function: a lower average S-factor than standard extrapolations between 2.2 and 2.6 MeV, and at 3.23 MeV a ratio of only about 2% between the proton and α branches to the first excited states. [17]
2026
HI-13 tandem accelerator, China Institute of Atomic Energy, Beijing
Trojan Horse method · Gamow window, resonances near 1.5 MeV
Preprint. The same ¹⁶O-breakup technique as for the α channel shows resonant structure near 1.5 MeV in the p₀ and p₁ channels and no hindrance in the measured range; the trend is qualitatively like that of Tumino et al. (2018) and unlike the modified analysis of Mukhamedzhanov et al. (2019). [18]

Measurements (EXFOR)

Every dataset EXFOR holds for this reaction, drawn by the energies it covers, against the energies a star uses.

25 datasets in 10 EXFOR entries, 1977–2024

Temperature

core carbon burning, 15 M☉ star, T₉ = 0.83 (830 MK)superburst ignition, accreting neutron star, T₉ = 0.5 (500 MK)

Lowest energy in EXFOR: 2.16 MeV; Spillane et al., 2007 · S · O1712.003
Distance from the Gamow peak: Inside the window; E₀ = 2130 keV, window 1680–2590 keV
Rate from energies not in EXFOR: 48%; at T₉ = 0.83, smooth estimate · 48% of it lies below the lowest energy in EXFOR

Gamow window, hatched where no measurement reaches
Outlined bars are shown but not counted (the rule is under “How these numbers are made”).
A diamond is a dataset at a single energy. Bars running off the right edge continue to higher energies.

The datasets of the gap map, by quantity

The datasets of the gap map, by quantity
Quantity	Datasets	E_cm range (keV)
σcross section	1	4.42 MeV – 6.48 MeV
SS-factor	2	2.13 MeV – 5.35 MeV
σ→Eₓpartial	20	2.2 MeV – 6.01 MeV
dσ/dΩangular distribution	1	2.52 MeV – 4.35 MeV
Yyield	1	2 MeV – 4 MeV

How these numbers are made

Lowest measured energy, everywhere in the data explorer: the lowest centre-of-mass energy at which a dataset in EXFOR measures the reaction itself (cross section, S-factor, angular distribution, yield or resonance strength), judged point by point. A point counts when it is a value, not an upper or lower limit, when it lies at least one standard deviation above zero, and when its energy is physical: at least 1 keV for charged particles, and not below the threshold of an endothermic reaction. Not counted: extrapolated, calculated, evaluated or derived values; superseded, deleted or preliminary data; ratios; a single S-factor value, which in EXFOR is a fit result; and indirect methods (Trojan horse, Coulomb dissociation, ANC, surrogate reactions), recognized from EXFOR's method and analysis codes, their text and the title. Frame and unit errors of EXFOR are corrected first, and values the literature shows to be upper limits are read as limits, from a list that gives the evidence for each. Datasets that reach the same energy within 0.5% are all credited, earliest first. Rate from energies not in EXFOR: the share of the rate integrand at that temperature outside the energy ranges the counted datasets cover (from their lowest measured point to their highest), with a constant S-factor (σ ∝ S(E₀)/E · e^−2πη, so the integrand is e^(−E/kT − 2πη)); for a neutron capture, σ ∝ 1/v. Resonances make the real integrand lumpy, so read it as a smooth baseline.

All measurements (25)Compound nucleus ²⁴Mg

Details

The proton channel (Q = 2.24 MeV) is measured either by detecting the protons, whose spectrum resolves the ²³Na final states, or through the γ rays of ²³Na, mainly the 440 keV line from its first excited state, which cannot see the decays that feed the ground state directly. Hydrogen and deuterium in the carbon target produce a beam-induced background that dominates singles measurements at the lowest energies (Zickefoose et al. 2018). Particle–γ coincidences (Fruet et al. 2020; Tan et al. 2020; Nippert et al. 2025) select the protons in coincidence with the de-excitation γ-rays and suppress this background, at the cost of the ground-state branch, which must be inferred.

The excitation function shows resonances down to about 2.1 MeV (Spillane et al. 2007; Zickefoose et al. 2018), with branching ratios of the individual proton groups that change strongly from one energy to the next (Morales-Gallegos et al. 2024). The Gamow window spans about 1.7–2.6 MeV for core carbon burning at 0.83 GK and about 1.2–1.8 MeV for superburst ignition near 0.5 GK (Cooper et al. 2009), so direct data cover only the upper half of the first and none of the second. Below the data the same questions apply as for the α channel: fusion hindrance or a rising S-factor, and the disputed Trojan Horse resonances (Tumino et al. 2018; Mukhamedzhanov et al. 2019). The p channel also serves as the mirror reference for extrapolating the n channel, ¹²C(¹²C,n)²³Mg (Bucher et al. 2015). LUNA is preparing a direct measurement of the γ-rays of the p and α channels below 2.1 MeV at the underground Bellotti Ion Beam Facility, with an HPGe detector inside an active NaI(Tl) veto (Gesuè et al. 2025).

Peak energy E₀ ± half the 1/e width, centre of mass, from the AME2020 masses.

Evaluations

Compilations that combine the data into a recommended rate.

—G. R. Caughlan, W. A. Fowler, At. Data Nucl. Data Tables 40, 283 (1988) [19]
—C. L. Jiang, D. Santiago-Gonzalez, S. Almaraz-Calderon, K. E. Rehm et al., Phys. Rev. C 97, 012801 (2018) [20]
—E. Monpribat, S. Martinet, S. Courtin, M. Heine, S. Ekström, D. G. Jenkins, A. Choplin et al., Astron. Astrophys. 660, A47 (2022) [21]

Open questions

The ground-state proton branch, which γ-ray and coincidence measurements do not see directly.
The p/α branching at the energies of carbon burning, which decides the sodium yield.
Whether the S-factor falls (fusion hindrance) or keeps rising below the data.

Discussed on the open-questions page

Carbon fusion at stellar energies

Related reactions

References

1.
J. R. Patterson, H. Winkler, C. S. Zaidins
Experimental investigation of the stellar nuclear reaction ¹²C + ¹²C at low energies
Astrophys. J. 157, 367 (1969)
2.
M. G. Mazarakis, W. E. Stephens
Experimental measurements of the ¹²C + ¹²C nuclear reactions at low energies
Phys. Rev. C 7, 1280 (1973) · 10.1103/PhysRevC.7.1280
3.
M. D. High, B. Čujec
The ¹²C + ¹²C sub-Coulomb fusion cross section
Nucl. Phys. A 282, 181 (1977) · 10.1016/0375-9474(77)90179-8
4.
H. W. Becker, K. U. Kettner, C. Rolfs, H. P. Trautvetter
The ¹²C + ¹²C reaction at subcoulomb energies (II)
Z. Phys. A 303, 305 (1981) · 10.1007/BF01421528
5.
E. F. Aguilera, P. Rosales, E. Martinez-Quiroz, G. Murillo, M. Fernández et al.
New γ-ray measurements for ¹²C + ¹²C sub-Coulomb fusion: toward data unification
Phys. Rev. C 73, 064601 (2006) · 10.1103/PhysRevC.73.064601
6.
T. Spillane, F. Raiola, C. Rolfs, F. Strieder, S. Zeng, H.-W. Becker et al.
Study of the ¹²C + ¹²C fusion reactions near the Gamow energy
Phys. Rev. Lett. 98, 122501 (2007) · 10.1103/PhysRevLett.98.122501 · arXiv:nucl-ex/0702023
7.
J. Zickefoose, A. Di Leva, F. Strieder, L. Gialanella, G. Imbriani, N. De Cesare, C. Rolfs, J. Schweitzer, T. Spillane, O. Straniero, F. Terrasi
Measurement of the ¹²C(¹²C,p)²³Na cross section near the Gamow energy
Phys. Rev. C 97, 065806 (2018) · 10.1103/PhysRevC.97.065806
8.
A. Tumino, C. Spitaleri, M. La Cognata, S. Cherubini, G. L. Guardo, M. Gulino, S. Hayakawa, I. Indelicato et al.
An increase in the ¹²C + ¹²C fusion rate from resonances at astrophysical energies
Nature 557, 687 (2018) · 10.1038/s41586-018-0149-4
9.
A. M. Mukhamedzhanov, D. Y. Pang, A. S. Kadyrov
Astrophysical factors of ¹²C + ¹²C fusion extracted using the Trojan horse method
Phys. Rev. C 99, 064618 (2019) · 10.1103/PhysRevC.99.064618 · arXiv:1806.08828
10.
G. Fruet, S. Courtin, M. Heine et al. (STELLA collaboration)
Advances in the direct study of carbon burning in massive stars
Phys. Rev. Lett. 124, 192701 (2020) · 10.1103/PhysRevLett.124.192701
11.
M. Heine et al.
The STELLA apparatus for particle-gamma coincidence fusion measurements with nanosecond timing
Nucl. Instrum. Methods A 903, 1 (2018) · 10.1016/j.nima.2018.06.058 · arXiv:1802.07679
12.
W. P. Tan et al.
New measurement of ¹²C + ¹²C fusion reaction at astrophysical energies
Phys. Rev. Lett. 124, 192702 (2020) · 10.1103/PhysRevLett.124.192702 · arXiv:2005.03196
13.
N. T. Zhang et al.
Constraining the ¹²C + ¹²C astrophysical S-factors with the ¹²C + ¹³C measurements at very low energies
Phys. Lett. B 801, 135170 (2020) · arXiv:1909.07012
14.
L. Morales-Gallegos, M. Aliotta, L. Gialanella et al.
Direct measurements of the ¹²C(¹²C,p)²³Na and ¹²C(¹²C,α)²⁰Ne reactions at low energies for nuclear astrophysics
EPJ Web Conf. 260, 01006 (2022) · 10.1051/epjconf/202226001006
15.
L. Morales-Gallegos, M. Aliotta, L. Gialanella et al.
Retraction Note: Direct measurements of the ¹²C + ¹²C reactions cross-sections towards astrophysical energies
Eur. Phys. J. A 59, 120 (2023) · 10.1140/epja/s10050-023-01022-7
16.
L. Morales-Gallegos et al.
Direct measurements of the ¹²C+¹²C reactions cross-sections towards astrophysical energies
Eur. Phys. J. A 60, 11 (2024) · 10.1140/epja/s10050-024-01233-6
17.
J. Nippert, S. Courtin, M. Heine, D. G. Jenkins, P. Adsley et al. (STELLA collaboration)
Refining the deep sub-barrier ¹²C + ¹²C fusion excitation function with the STELLA apparatus
Phys. Rev. C 111, 065804 (2025) · 10.1103/PhysRevC.111.065804 · arXiv:2509.14717
18.
C. Li, H. Jia et al.
Indirect measurement of the S*(E) factor for ¹²C(¹²C,p)²³Na at Gamow energies via the Trojan horse method with near-0 degree spectator detection
arXiv preprint (2026) · arXiv:2609.08837
19.
G. R. Caughlan, W. A. Fowler
Thermonuclear reaction rates V
At. Data Nucl. Data Tables 40, 283 (1988)
20.
C. L. Jiang, D. Santiago-Gonzalez, S. Almaraz-Calderon, K. E. Rehm et al.
Reaction rate for carbon burning in massive stars
Phys. Rev. C 97, 012801 (2018) · 10.1103/PhysRevC.97.012801
21.
E. Monpribat, S. Martinet, S. Courtin, M. Heine, S. Ekström, D. G. Jenkins, A. Choplin et al.
A new ¹²C + ¹²C nuclear reaction rate: impact on stellar evolution
Astron. Astrophys. 660, A47 (2022) · 10.1051/0004-6361/202141858 · arXiv:2111.15224
22.
C. L. Jiang et al.
Expectations for ¹²C and ¹⁶O induced fusion cross sections at energies of astrophysical interest
Phys. Rev. C 75, 015803 (2007) · 10.1103/PhysRevC.75.015803
23.
K. Uzawa, K. Hagino
Re-examination of fusion hindrance in astrophysical ¹²C + ¹²C and ¹²C + ¹³C reactions
Phys. Rev. C 112, L061601 (2025) · arXiv:2507.18065
24.
R. M. Gesuè, S. Turkat, J. Skowronski, M. Aliotta et al. (LUNA Collaboration)
Detector characterization for a new ¹²C + ¹²C reaction study at LUNA
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25.
R. L. Cooper, A. W. Steiner, E. F. Brown
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26.
P. Adsley et al.
Extending the Hoyle-state paradigm to ¹²C + ¹²C fusion
Phys. Rev. Lett. 129, 102701 (2022) · 10.1103/PhysRevLett.129.102701

How to cite this page

J. Skowronski, ¹²C(¹²C,p)²³Na, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/12C-12Cp-23Na.

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