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.
- Live evaluation
- Plot the data · 13N →
- Reaction rates
- Explore the rates →
- Q-value · energy released
- 1.943 MeV
- Product 13N
- radioactive, t½ = 9.96 min
- Kind
- Radiative capture
On the timeline
How it was measured
5 measurements, 1974–2023, 1 at LUNAShow the listHide the list
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]
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]
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]
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]
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
- 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
- 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
| Quantity | Datasets | E_cm range (keV) |
|---|---|---|
| σcross section | 13 | 78.4 keV – 15.1 MeV |
| SS-factor | 6 | 25 keV – 979 keV |
| σ→Eₓpartial | 2 | 1.51 MeV – 1.59 MeV |
| dσ/dΩangular distribution | 23 | 130 keV – 161 MeV |
| Aypolarization | 1 | 26.1 MeV – 26.1 MeV |
| Yyield | 5 | 175 keV – 2.22 MeV |
| ωγresonance strength | 1 | 2.37 MeV – 2.37 MeV |
| …other | 11 | 148 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.
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.
C. Rolfs and R. E. Azuma
Interference effects in 12C(p,γ)13N and direct capture to unbound states
Nucl. Phys. A 227, 291 (1974) · 10.1016/0375-9474(74)90798-2
- 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.
J. Skowronski et al.
Improved S factor of the 12C(p,γ)13N reaction at E = 320–620 keV and the 422 keV resonance
Phys. Rev. C 107, L062801 (2023) · 10.1103/PhysRevC.107.L062801 · arXiv:2306.09022
- 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.
J. Skowronski et al. (LUNA Collaboration)
Proton-capture rates on carbon isotopes and their impact on the astrophysical 12C/13C ratio
Phys. Rev. Lett. 131, 162701 (2023) · 10.1103/PhysRevLett.131.162701 · arXiv:2308.16098LUNA
- 6.
Y. Xu, K. Takahashi, S. Goriely, M. Arnould, M. Ohta, H. Utsunomiya
Nucl. Phys. A 918, 61 (2013) · 10.1016/j.nuclphysa.2013.09.007 · arXiv:1310.7099
- 7.
B. Acharya et al.
Solar fusion III: New data and theory for hydrogen-burning stars
Rev. Mod. Phys. 97, 035002 (2025) · 10.1103/8lm7-gs18 · arXiv:2405.06470
- 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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