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Reaction atlas · CNO cycles

Particle-exchange reaction · CN cycle (CNO-I)

15N(p,α)12C

: nitrogen‑15 + proton → carbon‑12 + helium‑4How to read the notation

On this page

The last step of the CN cycle. Nitrogen-15 captures a proton and splits into carbon-12 and a helium nucleus, so the carbon that started the cycle comes back.

A proton that hits nitrogen-15 can either knock out a helium nucleus, which closes the CN cycle, or stay and make oxygen-16, which opens the second CNO cycle. The first outcome is by far the more frequent. The ratio between the two decides how much material leaks from the CN cycle into the cycles that run through oxygen and fluorine, and so how much oxygen-16 hydrogen burning makes.

Facts

How well known
Direct measurements and the indirect Trojan Horse method agree, with uncertainties of 7% and 19%. The reaction is fast, and its remaining uncertainty does not limit models of the CN cycle.
Live evaluation
No live evaluation yet · Evaluations
Reaction rates
Explore the rates →
Q-value · energy released
4.965 MeV
Gamow window
  • 27 ± 7 keVcentre of the Sun, 15.7 MK (CN cycle (CNO-I))
  • 47 ± 14 keVcore of a 15 M☉ star, 35 MK (CN cycle (CNO-I))
Kind
Particle-exchange reaction

On the timeline

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

How it was measured

3 measurements, 1982–2009Show the list
  1. 1982

    Direct measurement at the surface · 80–810 keV (proton energy)

    Cross section of the α0 channel measured with a 350 kV implanter and a 1 MV accelerator, normalized at Ep = 353.4 keV. For decades this was the main direct data set at low energy and the basis of the recommended S(0). [1]

  2. 2007

    Trojan Horse method · about 20–312 keV

    Bare-nucleus cross section from the quasi-free 2H(15N,α12C)n reaction at 60 MeV beam energy; agrees with the direct data between 70 and 312 keV and extends the S-factor to about 20 keV. [2]

  3. 2009

    Trojan Horse method · R-matrix reanalysis

    R-matrix fits of the direct and Trojan-Horse data, including the finite energy resolution of the latter: S(0) = 73.0 ± 5.0 MeV b from the direct data, adopted by Solar Fusion II, and 70.0 ± 13.5 MeV b from the Trojan-Horse data. [3]

Measurements (EXFOR)

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

138 datasets in 24 EXFOR entries, 1952–2021 · 3 without an energy range, not drawn

Temperature
Lowest energy in EXFOR
69.6 keV
Redder et al., 1982 · dσ/dΩ · A0142.004
Distance from the Gamow peak
3 Gamow widths above
E₀ = 27.5 keV, window 20.4–34.5 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 = 27.5 keVσSσ→Eₓdσ/dΩωγotherlowest in EXFOR 69.6 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 section320 keV – 1.5 MeV
SS-factor119.2 MeV – 576 MeV
σ→Eₓpartial1472.7 keV – 14.2 MeV
dσ/dΩangular distribution11150 keV – 40.6 MeV
ωγresonance strength3314 keV – 1.54 MeV
…other3836 keV – 2.25 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.

Details

The (p,α) channel competes with 15N(p,γ)16O through the same 16O compound states; at low energy both are dominated by the tails of two broad 1− resonances, whose interference fixes the energy dependence of the S-factor. The cross section is large compared with the other CN-cycle reactions, so it never limits the cycle speed; what matters for nucleosynthesis is the ratio to the (p,γ) channel. The direct data of 1982 reach a proton energy of 80 keV.

Trojan-Horse data extend the S-factor down to about 20 keV without Coulomb suppression or electron screening, and agree with the direct data where they overlap. R-matrix fits give S(0) = 73 ± 5 MeV b from the direct data and 70 ± 13.5 MeV b from the Trojan-Horse data.

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.

  • —E. G. Adelberger et al., Rev. Mod. Phys. 83, 195 (2011) [4]
  • —Y. Xu et al., Nucl. Phys. A 918, 61 (2013) [5]
  • —B. Acharya et al., Rev. Mod. Phys. 97, 035002 (2025) [6]

Open questions

  • The electron-screening correction needed to compare direct data at the lowest energies with Trojan-Horse results.

Related reactions

References

  1. 1.

    A. Redder, H. W. Becker, H. Lorenz-Wirzba, C. Rolfs, P. Schmalbrock and H. P. Trautvetter

    The 15N(p,α0)12C reaction at stellar energies

    Z. Phys. A 305, 325 (1982)

  2. 2.
  3. 3.

    M. La Cognata, V. Z. Goldberg, A. M. Mukhamedzhanov, C. Spitaleri and R. E. Tribble

    Improved determination of the astrophysical S(0) factor of the 15N(p,α)12C reaction

    Phys. Rev. C 80, 012801(R) (2009) · 10.1103/PhysRevC.80.012801

  4. 4.

    E. G. Adelberger et al.

    Solar fusion cross sections II: the pp chain and CNO cycles

    Rev. Mod. Phys. 83, 195 (2011) · 10.1103/RevModPhys.83.195

  5. 5.
  6. 6.

How to cite this page

J. Skowronski, 15N(p,α)12C, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/15N-pa-12C.

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

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