¹²C(¹²C,α)²⁰Ne · Reaction atlas

Two carbon nuclei fuse, and the compound nucleus breaks up into neon-20 and a helium nucleus. This is the main way carbon burns in stars.

When a star of more than about eight solar masses has used up its helium, its core is mostly carbon and oxygen. The core contracts and heats until carbon nuclei collide hard enough to fuse. Each fusion makes a highly excited magnesium-24, which at once falls apart, most often into neon-20 and an alpha particle or into sodium-23 and a proton. The neon left by this branch is the fuel of the next stage, neon burning. How fast carbon fuses decides how long carbon burning lasts, how hot it must be, and so the inner structure of the star before it explodes. The same reaction starts the explosion of a white dwarf in a type Ia supernova and the rare, long X-ray flashes called superbursts on neutron stars. Its rate at stellar energies is still uncertain: experiments disagree by large factors.

Facts

How well known: Direct measurements reach only the upper part of the energies at which carbon burns in massive stars, and the measured cross section is full of resonances. The ways of extending it downwards, and an indirect measurement that reaches those energies, disagree by orders of magnitude.
Live evaluation: No live evaluation yet · Evaluations
Q-value · energy released: 4.617 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

10 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 (High and Čujec recorded the γ-rays at 90° and 270°; Becker et al. detected the particles); 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 with thick carbon targets whose hydrogen contamination was made very low. A strong resonance at 2.14 MeV, at the Gamow peak of core carbon burning (0.83 GK) and above the window of superburst ignition (0.5 GK), raises the α-channel rate by about a factor of five near 0.8 GK. [6]
2018
INFN LNS, CataniaLaboratori Nazionali del Sud (INFN)
Trojan Horse method · E = 0.8–2.7 MeV, from ¹²C(¹⁴N,α²⁰Ne)²H
Several resonances across the Gamow window; the combined α and p rate is more than 25 times the reference rate near 0.5 GK. The analysis was disputed by Mukhamedzhanov et al. (2019), who found that the rise disappears once Coulomb–nuclear distortions are included. [7, 8]
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 between the silicon array and LaBr₃ detectors, with a rotating target, remove the ambiguities of γ-only or particle-only measurements. The data span more than eight orders of magnitude and support the fusion-hindrance model. [9, 10]
2020
Nuclear Science Laboratory, Notre DameUniversity of Notre Dame
Direct measurement at the surface · thick-target yield in 50 keV steps
Particle–γ coincidences with the SAND silicon array at the 5U Pelletron on highly ordered pyrolytic graphite targets. The results disagree strongly with the Trojan Horse measurement. [11]
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. [12]
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. [13, 14, 15]
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 near its lowest coincidence points: a lower average S-factor than standard extrapolations between 2.2 and 2.6 MeV, and no confirmation of an overall rise of the S-factor at deep sub-barrier energies. [16]
2026
HI-13 tandem accelerator, China Institute of Atomic Energy, Beijing
Trojan Horse method · Gamow window, resonances near 1.5 MeV
An independent Trojan Horse measurement with ¹⁶O, not ¹⁴N, as the Trojan horse nucleus and the spectator α detected near 0°, which the authors describe as a first for the method; their analysis, DWBA-based as they describe it, gives resonances near 1.5 MeV in both the α₀ and α₁ channels. A preprint argues that the plane-wave approximation behind the analysis breaks down once Coulomb distortions are included (Mukhamedzhanov 2026); no reply has appeared yet. [17, 18]

Measurements (EXFOR)

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

15 datasets in 12 EXFOR entries, 1973–2024

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: 2.13 MeV; Spillane et al., 2007 · S · O1712.002
Distance from the Gamow peak: Inside the window; E₀ = 2130 keV, window 1680–2590 keV
Rate from energies not in EXFOR: 45%; at T₉ = 0.83, smooth estimate · 45% 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	2.11 MeV – 5.34 MeV
σ→Eₓpartial	7	2.2 MeV – 6.01 MeV
dσ/dΩangular distribution	4	2.9 MeV – 35.8 MeV
…other	1	4.88 MeV – 7.5 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 (15)Compound nucleus ²⁴Mg

Details

¹²C + ¹²C forms ²⁴Mg at an excitation energy of about 13.9 MeV plus the centre-of-mass energy, which decays mainly by α emission to ²⁰Ne and by proton emission to ²³Na; the neutron channel to ²³Mg is closed below 2.6 MeV. The Gamow window for core carbon burning in a 15 M☉ star (0.83 GK) spans about 1.7–2.6 MeV, with its peak at 2.1 MeV; at the ignition of a superburst on an accreting neutron star, near 0.5 GK (Cooper et al. 2009), it moves down to about 1.2–1.8 MeV. Unlike most heavy-ion systems, the excitation function shows pronounced resonant structure down to the lowest measured energies, which makes any extrapolation from the data uncertain (Spillane et al. 2007; Zickefoose et al. 2018; Morales-Gallegos et al. 2024). The cross section of the neighbouring system ¹²C + ¹³C, which has no such resonances, has been used to set an upper limit on the non-resonant part (Zhang et al. 2020).

The excitation function is conventionally shown as the modified S-factor S*(E) = σ(E) E exp(87.21/√E + 0.46 E), with E in MeV, which removes most of the strong energy dependence that remains in the ordinary S-factor of this heavy system; the standard rate of Caughlan and Fowler (1988) assumes a constant S* below the data.

Below the data, two descriptions of the non-resonant trend compete. The fusion-hindrance model (Jiang et al. 2007) predicts that the S-factor passes through a maximum and falls at deep sub-barrier energies; the rates of Jiang et al. (2018) and Monpribat et al. (2022) are built on it, as alternatives to the standard rate of Caughlan and Fowler (1988). The particle–γ coincidence measurements at Orsay (STELLA, Fruet et al. 2020; Nippert et al. 2025) and at Notre Dame (Tan et al. 2020) remove most of the background from hydrogen and deuterium in the target that limited earlier singles measurements; the STELLA data support the hindrance trend. A refit of the same data sets with a free exponent in the logarithmic-slope parametrization finds no hindrance (Uzawa and Hagino 2025), so the question remains open.

The Trojan Horse measurement of Tumino et al. (2018), through ¹²C(¹⁴N,α²⁰Ne)²H and ¹²C(¹⁴N,p²³Na)²H in quasi-free kinematics, reported resonances between 0.8 and 2.7 MeV that raise the rate by more than a factor of 25 near 0.5 GK. Mukhamedzhanov et al. (2019) argued that the rise is an artefact of the plane-wave approximation used in the analysis and disappears when Coulomb–nuclear distortions are included; the direct coincidence data of Tan et al. (2020) disagree strongly with the Trojan Horse result. A possible physical origin for low-energy resonances is a set of 0⁺ states of ²⁴Mg near the ¹²C + ¹²C threshold, found in ²⁴Mg(α,α′) and decaying mostly to ²⁰Ne + α, which may be ¹²C + ¹²C cluster states playing a role like the Hoyle state's in helium burning (Adsley et al. 2022). LUNA is preparing a direct measurement of the γ-rays from the α and p channels 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

Whether the S-factor falls at deep sub-barrier energies (fusion hindrance) or keeps rising; the answer depends on fitting choices and on which of the many data sets are used.
Whether resonances below 2 MeV exist and how strong they are, as the Trojan Horse analysis suggests and its critics dispute.
Direct data below 2.1 MeV, the aim of the underground LUNA campaign.

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.
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
8.
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
9.
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
10.
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
11.
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
12.
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
13.
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
14.
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
15.
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
16.
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
17.
C. Li, H. Jia, Q. Wen, C. Lin et al.
S*(E) measurement of the ¹²C(¹²C,α)²⁰Ne reaction at astrophysical energies via the Trojan horse method with ¹⁶O quasi-free breakup
Phys. Lett. B 879, 140675 (2026) · arXiv:2609.08819
18.
A. M. Mukhamedzhanov
Breakdown of the plane-wave Trojan horse analysis of the ¹²C+¹²C fusion reaction: critical role of Coulomb distortions
arXiv preprint (2026) · arXiv:2609.04498
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
J. Phys. G 52, 105103 (2025) · 10.1088/1361-6471/ade0dc · arXiv:2601.05285
25.
R. L. Cooper, A. W. Steiner, E. F. Brown
Possible resonances in the ¹²C + ¹²C fusion rate and superburst ignition
Astrophys. J. 702, 660 (2009) · 10.1088/0004-637X/702/1/660 · arXiv:0903.3994
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,α)²⁰Ne, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/12C-12Ca-20Ne.

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