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Reaction atlas · CNO cycles

Radiative capture · CN cycle (CNO-I)

12C(p,γ)13N

: carbon‑12 + proton → nitrogen‑13 + gamma rayHow to read the notation

ImprovingMeasured at LUNAPlot the data
On this page

The first step of the CN cycle. A carbon-12 nucleus captures a proton, emits a γ-ray and becomes radioactive nitrogen-13, which then decays to carbon-13.

Together with the next proton capture, on carbon-13, this reaction fixes the ratio of the two stable carbon isotopes in gas that has burnt hydrogen. Astronomers measure this ratio in the atmospheres of red giants, where it shows how much material from the burning layers has been mixed to the surface. The same reaction also makes the carbon-13 that, in giant stars, later releases the neutrons needed to build many elements heavier than iron.

Facts

How well known
Measured underground down to low energies with an uncertainty under 10%; the older measurements differ from the new ones by about a quarter overall, and why is still an open question.
Reaction rates
Explore the rates →
Q-value · energy released
1.943 MeV
Gamow window
  • 25 ± 6.7 keVcentre of the Sun, 15.7 MK (CN cycle (CNO-I))
  • 42 ± 13 keVcore of a 15 M☉ star, 35 MK (CN cycle (CNO-I))
Product 13N
radioactive, t½ = 9.96 min
Kind
Radiative capture

On the timeline

  1. 1939Bethe works out the CN cycle in “Energy production in stars”

How it was measured

5 measurements, 1974–2023, 1 at LUNAShow the list
  1. 1974

    Direct measurement at the surface · about 150 keV to 2.5 MeV (proton energy)

    Showed that direct E1 capture to the ground state, interfering with the resonances at proton energies of 457 and 1699 keV, is needed to describe the excitation function; ground-state spectroscopic factor C2S = 0.49 ± 0.15. [1]

  2. 2023

    Atomki, DebrecenInstitute for Nuclear Research (Atomki)

    Activation · 300–1900 keV (proton energy)

    Total cross section from the 13N activity, with uncertainties independent of in-beam γ-ray spectroscopy; covers the region of the 1.7 MeV resonance, where earlier data were scarce. [2]

  3. 2023

    Felsenkeller 5 MVFelsenkeller underground laboratory (HZDR and TU Dresden)

    Direct measurement underground · 320–620 keV

    Shallow-underground measurement across the 422 keV resonance; S-factor about 25% below the literature. The R-matrix fit gives the first excited state of 13N at 2369.6(4) keV with Γγ = 0.49(3) eV and Γp = 34.9(2) keV. [3]

  4. 2023

    Nuclear Science Laboratory, Notre DameUniversity of Notre Dame

    Direct measurement at the surface · 1.0–2.5 MeV (proton energy)

    Absolute cross section over a wide energy range to fix the overall normalization and the interference between overlapping resonances; the extrapolation to low energy uses a Bayesian uncertainty analysis. [4]

  5. 2023

    LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)

    Direct measurement underground · down to 60 keV

    Prompt γ-ray detection and activation, with overall systematic uncertainties of 7–8%; the S-factor is about 25% lower than most earlier data. [5]

Measurements (EXFOR)

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

74 datasets in 34 EXFOR entries, 1950–2023 · 12 without an energy range, not drawn

Temperature
Lowest energy in EXFOR
67.9 keV
Skowronski et al., 2023 · S · O2599.003
Distance from the Gamow peak
3.2 Gamow widths above
E₀ = 24.7 keV, window 18–31.3 keV
Rate from energies not in EXFOR
> 99.99%
at T₉ = 0.0157, smooth estimate · > 99.99% of it lies below the lowest energy in EXFOR
10 keV100 keV1 MeV10 MeV100 MeVCentre-of-mass energy (keV)E₀ = 24.7 keVσSσ→Eₓdσ/dΩAyYωγotherlowest in EXFOR 67.9 keV
  • 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
QuantityDatasetsE_cm range (keV)
σcross section1378.4 keV – 15.1 MeV
SS-factor625 keV – 979 keV
σ→Eₓpartial21.51 MeV – 1.59 MeV
dσ/dΩangular distribution23130 keV – 161 MeV
Aypolarization126.1 MeV – 26.1 MeV
Yyield5175 keV – 2.22 MeV
ωγresonance strength12.37 MeV – 2.37 MeV
…other11148 keV – 2.21 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.

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

How well known, in detail: Direct data now reach 60 keV with systematic uncertainties of 7–8%; the remaining question is the normalization difference of about 25% with respect to the older data sets.

At low energy the capture proceeds by direct E1 capture to the 13N ground state, which interferes with the broad resonance at E = 422 keV formed by the first excited state of 13N. The S-factor at stellar energies is obtained from R-matrix fits, so the result depends on the normalization of the data and on the width of that resonance. Measurements since 2023, prompt-γ and activation, give S-factors about 25% lower than most of the earlier literature. The LUNA data reach E = 60 keV, where the cross section enters the energy range of hydrogen burning in the shells of giant stars.

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.

  • —Y. Xu et al., Nucl. Phys. A 918, 61 (2013) [6]
  • —B. Acharya et al., Rev. Mod. Phys. 97, 035002 (2025) [7]

Open questions

  • The 25% normalization difference between the measurements since 2023 and the older data sets.
  • The radiative width of the 422 keV resonance, which dominates the rate at higher temperatures.

Related reactions

References

  1. 1.
  2. 2.

    Gy. Gyürky, L. Csedreki, T. Szücs, G. G. Kiss, Z. Halász and Zs. Fülöp

    Cross section measurement of the 12C(p,γ)13N reaction with activation in a wide energy range

    Eur. Phys. J. A 59, 59 (2023) · 10.1140/epja/s10050-023-00974-0 · arXiv:2303.05999

  3. 3.
  4. 4.

    K.-U. Kettner, R. J. deBoer, J. Görres, M. Wiescher et al.

    Absolute cross section of the 12C(p,γ)13N reaction

    Phys. Rev. C 108, 035805 (2023) · 10.1103/PhysRevC.108.035805

  5. 5.
  6. 6.
  7. 7.
  8. 8.

    J. Skowronski et al. (LUNA Collaboration)

    A comparative analysis of R-matrix fitting: 12C(p,γ)13N as test case

    Phys. Rev. C 111, 035802 (2025) · 10.1103/PhysRevC.111.035802 · arXiv:2502.14040LUNA

How to cite this page

J. Skowronski, 12C(p,γ)13N, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/12C-pg-13N.

Cite the date you used; it is the last change to this page.

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