¹²C(α,γ)¹⁶O · Reaction atlas

Carbon-12 captures a helium nucleus and becomes oxygen-16. Together with the triple-alpha process, it decides how much carbon and how much oxygen stars make.

While helium burns in the core of a star, carbon is made by the triple-alpha process and destroyed by this reaction. When the helium runs out, the balance between the two leaves a definite ratio of carbon to oxygen. That ratio shapes the rest of the star's life. It decides which fuels burn next, the structure of white dwarfs, the mass of the black holes left by the heaviest stars, and the amounts of many elements thrown out in supernovae. For this reason the reaction is often called the most important one in nuclear astrophysics. It is also one of the hardest to measure: at the energies inside stars the reaction happens far too rarely for any experiment yet to detect it.

Facts

How well known: No experiment has yet reached the energies at which helium burns in stars: the lowest data lie near 1 MeV, about three times higher. The stellar rate comes from extending the measured trend downwards with a nuclear model, and its uncertainty depends on how the reaction divides between its two main ways of emitting the γ-ray.
Live evaluation: No live evaluation yet · Evaluations
Reaction rates: Explore the rates →
Q-value · energy released: 7.162 MeV
Gamow window: 315 ± 85 keVcore helium burning, 0.2 GK (Helium burning)
Kind: Radiative capture

On the timeline

How it was measured

8 measurements, 2001–2026Show the list

2001
Dynamitron, StuttgartInstitut für Strahlenphysik, Universität Stuttgart
Direct measurement at the surface · E1 and E2 capture, forward kinematics
γ-ray angular distributions separated E1 and E2 ground-state capture; the derived rate is about 30% below the NACRE rate near 10⁸ K. [1, 2, 3]
2005
ERNA recoil separatorCIRCE laboratory, Caserta (at Ruhr-Universität Bochum until 2009)
Inverse kinematics and recoil separators · E = 1.9–4.9 MeV
First direct measurement of the total cross section: ¹⁶O recoils detected with the ERNA recoil separator behind a windowless helium gas target, with no γ-ray coincidence. [4]
2006
Dynamitron, StuttgartInstitut für Strahlenphysik, Universität Stuttgart
Direct measurement at the surface · E = 1.30–2.78 MeV
An array of nine EUROGAM HPGe detectors with BGO shields recorded the ground-state angular distributions at all angles at once, with α beams up to 340 µA on implanted ¹²C targets; E1 and E2 S-factors were derived with the mixing phase free or fixed from α + ¹²C scattering. [5]
2006
DRAGON, TRIUMFTRIUMF
Inverse kinematics and recoil separators · E = 2.2–5.42 MeV
Cascade through the 6.05 MeV 0⁺ state, measured with a BGO array in coincidence with recoils at the focal plane; S₆.₀(300 keV) = 25 (+16/−15) keV b, the largest cascade contribution. [6]
2011
ERNA recoil separatorCIRCE laboratory, Caserta (at Ruhr-Universität Bochum until 2009)
Inverse kinematics and recoil separators · E = 3.3–4.5 MeV
The 6.05 MeV cascade was found to be pure E2 in this range; the extrapolation gives a negligible contribution at helium-burning energies, in contrast with the earlier DRAGON result. [7]
2012
Karlsruhe Van de GraaffKernforschungszentrum Karlsruhe (now Karlsruhe Institute of Technology)
Direct measurement at the surface · E = 1.00–1.51 MeV
Nearly 4π BaF₂ array with a pulsed beam; the high efficiency allowed low beam currents, avoiding target degradation, and gave E1 and E2 components with accuracy comparable to the best Ge data. [8]
2023
Q3D magnetic spectrograph
Transfer reactions and ANCs · ¹⁶O ground state via ¹²C(¹¹B,⁷Li)¹⁶O
A new ground-state ANC, addressing a spread of more than two orders of magnitude among earlier values; the resulting total rate is up to 21% above deBoer et al. (2017), and in massive helium-core models it lowers the lower and upper edges of the black-hole mass gap by about 12% and 5%. [9]
2026
HIγS, Triangle Universities Nuclear Laboratory
Photonuclear reactions · ¹⁶O(γ,α)¹²C angular distributions
Background-free angular distributions of the time-reversed reaction, measured with a time projection chamber filled with N₂O gas; the measured E1–E2 mixing phase is reported to agree with the unitarity prediction for the first time. [10]

Measurements (EXFOR)

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

64 datasets in 21 EXFOR entries, 1964–2021 · 2 without an energy range, not drawn

core helium burning, T₉ = 0.2 (200 MK)

Lowest energy in EXFOR: 940 keV; Redder et al., 1987 · S · F0580.002
Distance from the Gamow peak: 3.7 Gamow widths above; E₀ = 315 keV, window 230–401 keV
Rate from energies not in EXFOR: > 99.99%; at T₉ = 0.2, smooth estimate · > 99.99% 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	3	1 MeV – 3.07 MeV
SS-factor	10	225 keV – 4.06 MeV
σ→Eₓpartial	23	300 keV – 6.3 MeV
dσ/dΩangular distribution	21	1 MeV – 31.6 MeV
ωγresonance strength	1	2.4 MeV – 5.29 MeV
…other	4	935 keV – 3.39 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 (64)Compound nucleus ¹⁶O

Details

The stellar energy is near E = 300 keV, where the cross section is far below the sensitivity of any experiment so far. The S-factor is therefore extrapolated with multi-channel R-matrix fits from data above about 1 MeV. The ground-state capture is dominated by two components: E1 capture through the high-energy tail of the 1⁻ subthreshold state at 7.12 MeV interfering with the broad 1⁻ resonance at 9.6 MeV, and E2 capture through the 2⁺ subthreshold state at 6.92 MeV plus a direct contribution. Separating the two multipoles requires γ-ray angular distributions; the cascade transitions through the 6.05, 6.13, 6.92 and 7.12 MeV states add a few per cent at 300 keV but dominate at higher energies (deBoer et al. 2017).

Surface experiments in forward kinematics with high-intensity α beams and Ge or BaF₂ arrays (Stuttgart, Karlsruhe) measured the E1 and E2 angular distributions; recoil separators (ERNA, DRAGON) measured the total cross section in inverse kinematics, independent of the γ-ray angular distribution. The review of deBoer et al. (2017) combined capture, scattering and β-delayed α-emission data in a global R-matrix analysis and gave the recommended rate used here. Its extrapolation is still debated: a ground-state ANC measured through ¹²C(¹¹B,⁷Li)¹⁶O gives a total rate up to 21% higher (Shen et al. 2023), and a time projection chamber in the γ beam of HIγS measured background-free angular distributions of the inverse reaction ¹⁶O(γ,α)¹²C, with an E1–E2 phase reported to agree with unitarity for the first time (Haverson et al. 2026).

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.

—R. J. deBoer et al., Rev. Mod. Phys. 89, 035007 (2017) [11]
—C. Angulo, M. Arnould, M. Rayet et al. (NACRE Collaboration), Nucl. Phys. A 656, 3 (1999) [12]
—Y. Xu et al., Nucl. Phys. A 918, 61 (2013) [13]

Open questions

Direct data below 1 MeV, which need an underground accelerator able to deliver intense α beams, or high-intensity γ beams for the inverse reaction ¹⁶O(γ,α)¹²C.
The E2 ground-state S-factor, whose extrapolation depends on the ANC of the 6.92 MeV subthreshold state and on the interference with the direct capture.
The contribution of the 6.05 MeV cascade at low energy, where the DRAGON and ERNA analyses differ.

Discussed on the open-questions page

Related reactions

References

1.
R. Kunz, M. Jaeger, A. Mayer, J. W. Hammer, G. Staudt, S. Harissopulos, T. Paradellis
¹²C(α,γ)¹⁶O: the key reaction in stellar nucleosynthesis
Phys. Rev. Lett. 86, 3244 (2001) · 10.1103/PhysRevLett.86.3244
2.
R. Kunz, M. Jaeger, A. Mayer, J. W. Hammer, G. Staudt, S. Harissopulos, T. Paradellis
Astrophysical reaction rate of ¹²C(α,γ)¹⁶O
Astrophys. J. 567, 643 (2002) · 10.1086/338384
3.
J. W. Hammer, M. Fey, R. Kunz et al.
E1 and E2 capture cross section and astrophysical reaction rate of the key reaction ¹²C(α,γ)¹⁶O
Nucl. Phys. A 758, 363 (2005) · 10.1016/j.nuclphysa.2005.05.066
4.
D. Schürmann et al.
First direct measurement of the total cross-section of ¹²C(α,γ)¹⁶O
Eur. Phys. J. A 26, 301 (2005) · 10.1140/epja/i2005-10175-2 · arXiv:nucl-ex/0511050
5.
M. Assunção et al.
E1 and E2 S factors of ¹²C(α,γ₀)¹⁶O from γ-ray angular distributions with a 4π-detector array
Phys. Rev. C 73, 055801 (2006) · 10.1103/PhysRevC.73.055801
6.
C. Matei, L. Buchmann, W. R. Hannes, D. A. Hutcheon, C. Ruiz, C. R. Brune, J. Caggiano, A. A. Chen, J. D'Auria, A. Laird et al.
Measurement of the cascade transition via the first excited state of ¹⁶O in the ¹²C(α,γ)¹⁶O reaction, and its S factor in stellar helium burning
Phys. Rev. Lett. 97, 242503 (2006) · 10.1103/PhysRevLett.97.242503
7.
D. Schürmann, A. Di Leva, L. Gialanella, R. Kunz, F. Strieder et al.
Study of the 6.05 MeV cascade transition in ¹²C(α,γ)¹⁶O
Phys. Lett. B 703, 557 (2011) · 10.1016/j.physletb.2011.08.061
8.
R. Plag, R. Reifarth, M. Heil, F. Käppeler, G. Rupp, F. Voss, K. Wisshak
¹²C(α,γ)¹⁶O studied with the Karlsruhe 4π BaF₂ detector
Phys. Rev. C 86, 015805 (2012) · 10.1103/PhysRevC.86.015805
9.
Y. P. Shen et al.
New determination of the ¹²C(α,γ)¹⁶O reaction rate and its impact on the black-hole mass gap
Astrophys. J. 945, 41 (2023) · 10.3847/1538-4357/acb7de
10.
K. Haverson, R. Smith, M. Gai et al.
Background-free ¹²C(α,γ) angular distribution measurements with a time projection chamber operating in gamma beams
Commun. Phys. 9, 27 (2026) · 10.1038/s42005-025-02458-7
11.
R. J. deBoer, J. Görres, M. Wiescher, R. E. Azuma, A. Best, C. R. Brune, C. E. Fields, S. Jones, M. Pignatari, D. Sayre, K. Smith, F. X. Timmes, E. Uberseder
The ¹²C(α,γ)¹⁶O reaction and its implications for stellar helium burning
Rev. Mod. Phys. 89, 035007 (2017) · 10.1103/RevModPhys.89.035007 · arXiv:1709.03144
12.
C. Angulo, M. Arnould, M. Rayet et al. (NACRE Collaboration)
A compilation of charged-particle induced thermonuclear reaction rates
Nucl. Phys. A 656, 3 (1999)
13.
Y. Xu, K. Takahashi, S. Goriely, M. Arnould, M. Ohta, H. Utsunomiya
NACRE II: an update of the NACRE compilation of charged-particle-induced thermonuclear reaction rates for nuclei with mass number A < 16
Nucl. Phys. A 918, 61 (2013) · 10.1016/j.nuclphysa.2013.09.007 · arXiv:1310.7099
14.
R. Farmer, M. Renzo, S. E. de Mink, M. Fishbach, S. Justham
Constraints from gravitational-wave detections of binary black hole mergers on the ¹²C(α,γ)¹⁶O rate
Astrophys. J. Lett. 902, L36 (2020) · arXiv:2006.06678

How to cite this page

J. Skowronski, ¹²C(α,γ)¹⁶O, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/12C-ag-16O.

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