Skip to content
Reaction atlas · CNO cycles

Radiative capture · CN cycle (CNO-I)

13C(p,γ)14N

: carbon‑13 + proton → nitrogen‑14 + gamma rayHow to read the notation

ImprovingMeasured at LUNAPlot the data
On this page

Carbon-13 captures a proton, emits a γ-ray and becomes nitrogen-14. It is the step of the CN cycle that destroys carbon-13.

The balance between this reaction, which destroys carbon-13, and the capture on carbon-12, which makes it, sets the ratio of the two carbon isotopes left behind by hydrogen burning. That ratio is measured in red giants, in planetary nebulae and in meteoritic grains, and is used to test how material is mixed inside stars. The rate also controls how much carbon-13 survives to act as a neutron source in giant stars.

Facts

How well known
Measured underground down to low energies with an uncertainty under 10%; the rate came out lower than in the older tables.
Reaction rates
Explore the rates →
Q-value · energy released
7.551 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))
Kind
Radiative capture

How it was measured

3 measurements, 1994–2025, 1 at LUNAShow the list
  1. 1994

    Direct measurement at the surface · 120–950 keV (proton energy)

    Cross sections for capture to the first six states of 14N, most of them for the first time; resonances at Ep = 450.4 and 557.6 ± 0.5 keV; total S-factor extrapolated to 25 keV of 7.7 ± 1.0 keV b. [1]

  2. 2023

    LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)

    Direct measurement underground · down to 60 keV

    Prompt γ-ray detection with overall systematic uncertainties of 7–8%; the S-factor is about 30% lower than most earlier data. [2]

  3. 2025

    Felsenkeller 5 MVFelsenkeller underground laboratory (HZDR and TU Dresden)

    Direct measurement underground · 310–680 keV (Ep = 330–740 keV)

    Shallow-underground measurement in direct kinematics. The S-factor agrees with LUNA at low energy and is about 20% below the earlier literature over the whole range; new parameters for the two resonances and S_tot(0) = 6.4(4) keV b. [3]

Measurements (EXFOR)

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

49 datasets in 20 EXFOR entries, 1952–2023 · 6 without an energy range, not drawn

Temperature
Lowest energy in EXFOR
60.7 keV
Skowronski et al., 2023 · S · O2599.005
Distance from the Gamow peak
2.7 Gamow widths above
E₀ = 24.7 keV, window 18–31.4 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/dΩωγotherlowest in EXFOR 60.7 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 section3120 keV – 1.95 MeV
SS-factor425 keV – 561 keV
σ→Eₓpartial1685.8 keV – 14.4 MeV
dσ/dΩangular distribution10148 keV – 16.8 MeV
ωγresonance strength5475 keV – 3.5 MeV
…other5510 keV – 14.4 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: Underground data now reach 60 keV with 7–8% systematic uncertainty; the rate is lower than in the compilations based on the 1994 data, and the resonance parameters have been revised.

Below 1 MeV the cross section is the sum of direct capture and of two resonances, a 2− state and a 1− state in 14N observed at proton energies of about 448 and 551 keV. Capture populates the ground state and several excited states of 14N, so the total S-factor at low energy rests on R-matrix fits of the individual transitions. For a long time a single data set reported all transitions. The LUNA measurement extended the data down to E = 60 keV and, together with the later Felsenkeller data, gives S-factors 20–30% lower than the earlier literature.

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) [4]
  • —B. Acharya et al., Rev. Mod. Phys. 97, 035002 (2025) [5]

Open questions

  • The branching of the capture to the excited states of 14N below 300 keV, where only the LUNA data exist.
  • The cause of the 20–30% difference between the recent data and the 1994 data set.

Related reactions

References

  1. 1.

    J. D. King, R. E. Azuma, J. B. Vise, J. Görres, C. Rolfs, H. P. Trautvetter and A. E. Vlieks

    Cross section and astrophysical S-factor for the 13C(p,γ)14N reaction

    Nucl. Phys. A 567, 354 (1994) · 10.1016/0375-9474(94)90154-6

  2. 2.
  3. 3.
  4. 4.
  5. 5.

How to cite this page

J. Skowronski, 13C(p,γ)14N, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/13C-pg-14N.

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

Something wrong or missing? Report an error (opens a new issue on GitHub) · Suggest a reaction (opens a new issue on GitHub)