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Jakub Skowronski
Reaction atlas · Helium burning

Fusion · Helium burning

4He(αα,γ)12C

: helium‑4 + helium‑4 + helium‑4 → carbon‑12 + gamma rayHow to read the notation

Improving3 open questions4He(α,α)4He (8Be) evaluation
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The triple-alpha process: three helium nuclei join to make carbon. Almost all the carbon in the Universe, including the carbon in living things, was made this way inside stars.

Two helium nuclei cannot stick together for long. They form beryllium-8, which falls apart again in a tiny fraction of a second. In the hot, dense core of a helium-burning star a third helium nucleus sometimes arrives before that happens. Carbon then forms, but only because carbon-12 has an excited state, the Hoyle state, at just the right energy to catch the three particles. In 1954 Fred Hoyle argued that such a state had to exist for stars to make as much carbon as we see, and experiments soon found it. The rate of this process sets how fast helium burns and, together with the next step, carbon-12 capturing a helium nucleus, decides how much carbon and how much oxygen a star leaves behind.

Facts

How well known
The rate depends on how often the Hoyle state of carbon-12 settles into stable carbon instead of breaking up again into three helium nuclei. That probability is tiny; a 2020 measurement put it about 30% higher, but the measurements of 2024–2025 and a reanalysis of the 2020 data agree on the earlier value, about 4.1 in 10 000.
Q-value · energy released
7.275 MeV
Energies
Three helium nuclei do not meet at once. Two of them form 8Be, which lives about 10−16 s; a third captures on it through the 7.65 MeV Hoyle state of 12C before it falls apart. The rate is set by the energies and widths of these two resonances, not by a Gamow window.
Kind
Fusion

On the timeline

  1. 1952Salpeter shows how helium burns to carbon
  2. 1953The 7.68 MeV state of carbon-12 is found
  3. 1957Cook, Fowler and the Lauritsens confirm the Hoyle state

How it was measured

9 measurements, 1953–2025Show the list

  1. 1953

    Kellogg Radiation Laboratory, CaltechCalifornia Institute of Technology

    Direct measurement at the surface · 12C excitation 4.4–9.2 MeV via 14N(d,α)12C

    Magnetic analysis of the α spectrum from 14N(d,α)12C found a level at 7.68 ± 0.03 MeV, the state Hoyle had predicted; the paper credits Hoyle with its astrophysical significance. [1]

  2. 1957

    Kellogg Radiation Laboratory, CaltechCalifornia Institute of Technology

    Direct measurement at the surface · β decay of 12B

    α particles following the β decay of 12B showed that the 7.65 MeV state breaks up into 8Be + α, so it can be formed from three α particles in a star; this fixed its energy and spin-parity. [2]

  3. 2005

    ISOLDE, CERN, Geneva, and IGISOL, Jyväskylä

    Direct measurement at the surface · 12C continuum populated in the β decay of 12B and 12N

    12B was produced at ISOLDE and 12N at IGISOL. Breakup spectra of the 12C states fed in their β decay showed a dominant resonance near 11 MeV and no evidence for a previously reported state at 9.1 MeV; the revised rate is higher below 5×107 K and much lower above 109 K. [3]

  4. 2020

    Heavy Ion Accelerator Facility, ANUAustralian National University

    Direct measurement at the surface · E0 pair decay of the 7.65 MeV state, 12C(p,p′) at 10.5 MeV

    e+e− pairs detected with the Super-e spectrometer. New pair-decay branching ratio, 14% larger than the adopted Γ_π/Γ = 6.7(6)×10−6, with the uncertainty reduced from 9% to 5%; on its own it lowers Γ_rad and the rate by 11%. [4]

  5. 2020

    Oslo Cyclotron LaboratoryUniversity of Oslo

    Direct measurement at the surface · 12C(p,p′) at 10.7 MeV

    Proton–γ–γ triple coincidences gave Γ_rad/Γ = 6.2(6)×10−4 and Γ_rad = 5.1(6)×10−3 eV, 34% above the adopted value. [5]

  6. 2021

    RCNP, OsakaResearch Center for Nuclear Physics, Osaka University

    Inverse kinematics and recoil separators · 1H(12C,12C p), 3−₁ state at 9.64 MeV

    First experimental radiative-decay probability of the 3−₁ state, 1.3 (+1.2/−1.1)×10−6; the state increases the triple-α rate at high temperature, where it had been assumed to be negligible. [6]

  7. 2024

    Variable Energy Cyclotron Centre, Kolkata

    Direct measurement at the surface · 12C(p,p′γγ) triple coincidences, and a kinematically complete 12C(p,p′) measurement

    Γ_rad/Γ = 4.01(30)×10−4, and 4.04(30)×10−4 from the independent kinematically complete experiment; with the adopted pair-decay values, Γ_rad = 3.75(40)×10−3 eV, consistent with the value adopted before 2020 and not with the 34% increase. [7]

  8. 2024

    Direct measurement at the surface · Hoyle state, charged-particle coincidences

    An almost background-free measurement with charged-particle coincidences and a two-dimensional map of the coincidence efficiency: Γ_rad/Γ = 4.4(6)×10−4. [8]

  9. 2025

    Oslo Cyclotron LaboratoryUniversity of Oslo

    Direct measurement at the surface · 12C(p,p′) at 10.8 MeV

    Remeasurement of the γ-decay branching ratio from triple coincidences, checked with a surrogate γ-ray cascade in 28Si, together with a reanalysis of the 2014 data used by Kibédi et al.: Γ_γ/Γ = 4.0(3)×10−4 and Γ_rad/Γ = 4.1(4)×10−4; the corrected analysis of the 2014 data gives 4.6(6)×10−4, no longer in conflict with the ENSDF average. [9]

Try it: an R-matrix evaluation

This system has a live AZURE2 model on this site: change the energies and widths of its levels and see how the fit to the data and the extrapolation to stellar energies change.

Details

At helium-burning temperatures (T9 ≈ 0.1–0.2) the rate proceeds sequentially: α + α forms the unbound 8Be ground state in equilibrium, and 8Be + α populates the 7.65 MeV 0+ Hoyle state of 12C (Salpeter 1952; Hoyle 1954). The Hoyle state decays almost always back to three α particles; the rate is therefore proportional to its radiative width Γ_rad = Γ_γ + Γ_π, the sum of the γ-decay and E0 pair-decay widths. Γ_rad is not measured directly but obtained as the product of three quantities: the γ-decay branching ratio Γ_rad/Γ, the pair-decay branching ratio Γ_π/Γ and the pair-decay width Γ_π (Freer and Fynbo 2014).

Recent work has questioned the adopted Γ_rad/Γ. Kibédi et al. (2020) found Γ_rad/Γ = 6.2(6)×10−4 from p–γ–γ coincidences and, combined with the new pair-decay branching ratio of Eriksen et al. (2020), Γ_rad = 5.1(6)×10−3 eV, about 34% above the previously adopted value. Eriksen et al. alone had lowered Γ_rad by 11% through a 14% larger Γ_π/Γ. Rana et al. (2024) found Γ_rad/Γ = 4.01(30)×10−4 from p–γ–γ triple coincidences, consistent with the previously adopted value and not with the 34% increase. Dell'Aquila et al. (2024), with charged-particle coincidences, found Γ_rad/Γ = 4.4(6)×10−4. Paulsen et al. (2025) remeasured the γ-decay branching ratio at Oslo, Γ_γ/Γ = 4.0(3)×10−4 and Γ_rad/Γ = 4.1(4)×10−4, and reanalysed the 2014 data used by Kibédi et al.: after correcting several issues in that analysis they obtain 4.6(6)×10−4, no longer discrepant with the ENSDF average of 4.16(11)×10−4. The measurements have therefore converged on the value adopted before 2020, with Kibédi et al. (2020) the outlier, now reanalysed. At high temperatures (T9 ≳ 1) broader states above the Hoyle state and non-resonant contributions matter: Fynbo et al. (2005) mapped the 12C continuum in β decay, and Tsumura et al. (2021) gave the first value for the radiative-decay probability of the 3−₁ state.

Evaluations

Compilations that combine the data into a recommended rate.

  • —C. Angulo, M. Arnould, M. Rayet et al. (NACRE Collaboration), Nucl. Phys. A 656, 3 (1999) [10]
  • —M. Freer, H. O. U. Fynbo, Prog. Part. Nucl. Phys. 78, 1 (2014) [11]

Open questions

  • The γ-decay branching ratio of the Hoyle state has converged (Rana 2024, Dell'Aquila 2024, Paulsen 2025 and the reanalysis of the 2020 data agree at about 4.1×10−4); Γ_rad still depends on the pair-decay quantities Γ_π/Γ and Γ_π that multiply it.
  • The rate at T9 ≳ 1, which depends on broad higher-lying states and on the 3−₁ radiative width, known only to about a factor of two.

Discussed on the open-questions page

Related reactions

References

  1. 1.

    D. N. F. Dunbar, R. E. Pixley, W. A. Wenzel, W. Whaling

    The 7.68-MeV state in C12

    Phys. Rev. 92, 649 (1953) · 10.1103/PhysRev.92.649

  2. 2.

    C. W. Cook, W. A. Fowler, C. C. Lauritsen, T. Lauritsen

    B12, C12, and the red giants

    Phys. Rev. 107, 508 (1957) · 10.1103/PhysRev.107.508

  3. 3.

    H. O. U. Fynbo, C. Aa. Diget, U. C. Bergmann et al.

    Revised rates for the stellar triple-α process from measurement of 12C nuclear resonances

    Nature 433, 136 (2005) · 10.1038/nature03219

  4. 4.

    T. K. Eriksen, T. Kibédi, M. W. Reed et al.

    Improved precision on the experimental E0 decay branching ratio of the Hoyle state

    Phys. Rev. C 102, 024320 (2020) · 10.1103/PhysRevC.102.024320 · arXiv:2007.15374

  5. 5.

    T. Kibédi et al.

    Radiative width of the Hoyle state from γ-ray spectroscopy

    Phys. Rev. Lett. 125, 182701 (2020) · 10.1103/PhysRevLett.125.182701 · arXiv:2009.10915

  6. 6.

    M. Tsumura et al.

    First experimental determination of the radiative-decay probability of the 3−₁ state in 12C for estimating the triple alpha reaction rate in high temperature environments

    Phys. Lett. B 817, 136283 (2021) · 10.1016/j.physletb.2021.136283

  7. 7.

    T. K. Rana et al.

    New measurement of the Hoyle state radiative transition width

    Phys. Lett. B 859, 139083 (2024) · arXiv:2311.08781

  8. 8.

    D. Dell'Aquila et al.

    Clarifying the radiative decay of the Hoyle state with charged-particle spectroscopy

    Sci. Rep. 14 (2024) · 10.1038/s41598-024-68415-6 · arXiv:2401.18026

  9. 9.

    W. Paulsen et al.

    Remeasuring the γ-decay branching ratio of the Hoyle state

    Phys. Rev. C 112, 015803 (2025) · 10.1103/2h2s-sbyx · arXiv:2406.00397

  10. 10.

    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)

  11. 11.

    M. Freer, H. O. U. Fynbo

    The Hoyle state in 12C

    Prog. Part. Nucl. Phys. 78, 1 (2014) · 10.1016/j.ppnp.2014.06.001

How to cite this page

J. Skowronski, 4He(αα,γ)12C, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/4He-aa-12C.

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