¹⁴N(p,γ)¹⁵O · Reaction atlas

The slowest step of the CNO cycle. Its rate decides how fast the cycle runs, how much energy it gives, and how many CNO neutrinos leave the Sun.

In a star burning hydrogen through the CNO cycle, nuclei wait longest as ¹⁴N before they capture the next proton. This one reaction therefore sets the pace of the whole cycle. It controls the energy production of stars more massive than the Sun, the flux of CNO neutrinos from the Sun's core, and, through the lifetime of stars leaving the main sequence, the ages estimated for the oldest star clusters.

Facts

How well known: Measured underground close to the energies of the Sun. What remains uncertain is how the reaction divides among its several ways of giving off γ-rays, and the last step down to solar energies; a 2025 measurement finds a rate about 14% above the recommended one.
Live evaluation: No live evaluation yet · Evaluations
Reaction rates: Explore the rates →
Q-value · energy released: 7.297 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))
Product ¹⁵O: radioactive, t_½ = 2.04 min
Kind: Radiative capture

On the timeline

How it was measured

14 measurements, 2001–2025, 5 at LUNAShow the list

2001
Triangle Universities Nuclear Laboratory, Durham NC
Lifetimes of excited states · 259 keV resonance (Doppler-shift attenuation)
Mean lifetime of the 6793 keV state of ¹⁵O, τ ≈ 1.6 fs (90% C.L.), from the Doppler-shift attenuation method. The value implies a much smaller contribution of the subthreshold state to the ground-state transition than inferred from the (p,γ) data. [1]
2003
Cyclotron Institute, Texas A&MTexas A&M University
Transfer reactions and ANCs · proton-transfer reactions
Asymptotic normalization coefficients for ¹⁴N + p → ¹⁵O from proton-transfer reactions, which fix the normalization of the direct capture to the ¹⁵O states and constrain the S-factor at zero energy. [2]
2004
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · 140–400 keV (proton energy)
First underground measurement with a solid TiN target and a HPGe detector, separating the γ-ray transitions; total S(0) = 1.7 ± 0.2 keV b from an R-matrix analysis. [3]
2005
Triangle Universities Nuclear Laboratory, Durham NC
Direct measurement at the surface · 155–524 keV (proton energy)
Direct measurement of the individual transitions at the surface; the extrapolated total S(0) is close to 1.7 keV b, in agreement with the LUNA result. [4]
2005
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · 119–367 keV (effective)
Full account of the LUNA solid-target campaign with TiN targets and HPGe detectors. Because of the level structure of ¹⁵O, the extrapolated S(0) depends on the R-matrix model. [5]
2006
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · down to 70 keV
Windowless nitrogen gas target and 4π BGO summing detector; the cross section was measured down to 70 keV, where it is 0.24 pb. [6]
2008
Lifetimes of excited states · 278 keV resonance (proton energy; Doppler-shift attenuation)
New Doppler-shift attenuation measurement of the 6792 keV state at the same resonance: the finite lifetime reported in 2001 is not confirmed, and τ < 0.77 fs. [7]
2011
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · proton energies 359, 380 and 399 keV
A composite germanium detector reduced the summing corrections; new cross sections for capture to the ground state and to the 5181, 6172 and 6792 keV states. [8]
2018
HZDR Tandetron, Dresden-RossendorfHelmholtz-Zentrum Dresden-Rossendorf
Direct measurement at the surface · 0.357–1.292 MeV
S-factors at twelve energies for capture to the 6.79 MeV state, the strongest transition, and at ten energies between 0.479 and 1.202 MeV for the second strongest; the total rate uncertainty remained about 8%. [9]
2021
Nuclear Science Laboratory, Notre DameUniversity of Notre Dame
Lifetimes of excited states · Doppler-shift attenuation
Lifetimes of several excited states of ¹⁵O; τ = 0.6 ± 0.4 fs for the 6792 keV state, below the 2001 value and consistent with the 2008 limit. [10]
2022
Atomki, DebrecenInstitute for Nuclear Research (Atomki)
Activation · 550–1400 keV
Total cross section from the ¹⁵O activity, counted through the annihilation radiation of its β⁺ decay, with about 10% uncertainty and no dependence on γ-ray angular distributions or summing. [11]
2022
Nuclear Science Laboratory, Notre DameUniversity of Notre Dame
Direct measurement at the surface · 0.27–1.07 MeV (proton energy)
New data in an energy range where few measurements existed, analysed with a multichannel R-matrix fit of the ground-state and 6.79 MeV transitions; differences between the data and the R-matrix fits remain. [12]
2025
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · about 100–370 keV (campaign under way)
Description of a new LUNA campaign with solid nitrogen targets and a 4π BGO detector, which aims at total and partial cross sections for a rate with 5% precision; no cross sections published yet. [13, 14]
2025
350 kV accelerator, Hefei
Direct measurement at the surface · E^ₚ = 110–260 keV
All transitions measured at once and their S-factors determined together in a multichannel Bayesian analysis of the γ spectra; S(0) = 1.92 ± 0.08 keV b, about 14% above the Solar Fusion III recommendation. The authors discuss what the higher value means for the tension between Borexino's CNO neutrinos and the low-metallicity solar composition. [15]

Measurements (EXFOR)

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

126 datasets in 31 EXFOR entries, 1951–2023 · 15 without an energy range, not drawn

Temperature

centre of the Sun, T₉ = 0.0157 (15.7 MK)core of a 15 M☉ star, T₉ = 0.035 (35 MK)

Lowest energy in EXFOR: 70.1 keV; Bemmerer et al., 2006 · S · O1458.002.A
Distance from the Gamow peak: 3 Gamow widths above; E₀ = 27.4 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

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
Quantity	Datasets	E_cm range (keV)
σcross section	7	70.1 keV – 175 MeV
SS-factor	3	933 eV – 228 keV
σ→Eₓpartial	24	119 keV – 4.88 MeV
dσ/dΩangular distribution	51	126 keV – 17.7 MeV
Aypolarization	1	126 keV – 126 keV
Yyield	2	254 keV – 2.6 MeV
ωγresonance strength	14	118 keV – 6.34 MeV
…other	9	242 keV – 2.24 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.

All measurements (126)Compound nucleus ¹⁵O

Details

How well known, in detail: Direct data reach 70 keV; the remaining uncertainty comes from the split into the individual γ-ray transitions and from the extrapolation to solar energies. Solar Fusion III recommends S(0) = 1.68 ± 0.14 keV b; a 2025 measurement finds 1.92 ± 0.08 keV b.

At solar temperatures the Gamow window lies near 27 keV, where the cross section is far too small to measure, so the S-factor is extrapolated from higher energies with R-matrix fits. The capture proceeds mainly to the 6.79 MeV excited state of ¹⁵O and to its ground state, which makes the extrapolation sensitive to the γ-ray summing. Capture into the 6.79 MeV state carries most of the low-energy S-factor.

As a subthreshold resonance, the state also shapes the ground-state transition, and that contribution scales with its radiative width, i.e. with the inverse of its lifetime; it has been probed through the lifetime and through asymptotic normalization coefficients from transfer reactions. The LUNA measurements at the 400 kV accelerator under Gran Sasso extended the data down to 70 keV, much closer to the solar energies than any surface experiment, and gave a total S(0) near 1.7 keV b; Solar Fusion III recommends S(0) = 1.68 ± 0.14 keV b, an uncertainty of 8.4%. A 2025 measurement at Ep = 110–260 keV with the 350 kV accelerator in Hefei determined all transitions together in a multichannel Bayesian analysis and reports S(0) = 1.92 ± 0.08 keV b, about 14% above the Solar Fusion III value (Chen et al. 2025); the two have not yet been reconciled.

The rate matters for the Sun because Borexino's measurement of the CNO neutrino flux can be turned into the carbon and nitrogen content of the solar core only through it (Borexino 2023). Surface measurements at HZDR and Notre Dame since 2018 cover 0.3–1.3 MeV with high precision and anchor the R-matrix fit above the underground data, and an activation measurement at Atomki gives the total cross section at 0.55–1.4 MeV independently of γ-ray spectroscopy. A new LUNA campaign with solid nitrogen targets and a 4π BGO detector aims at the total and partial cross sections at about 100–370 keV, for a rate with 5% precision (Gosta et al. 2025; Compagnucci et al. 2025).

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) [16]
—Y. Xu et al., Nucl. Phys. A 918, 61 (2013) [17]
—B. Acharya et al., Rev. Mod. Phys. 97, 035002 (2025) [18]

Open questions

The ground-state transition, whose contribution at low energy depends on interference in the R-matrix fit.
The lifetime of the 6.79 MeV state of ¹⁵O, for which the published values disagree.
The total S(0), where the 2025 value of 1.92 ± 0.08 keV b and the Solar Fusion III recommendation of 1.68 ± 0.14 keV b differ by about 14%.

Discussed on the open-questions page

Related reactions

References

1.
P. F. Bertone, A. E. Champagne, D. C. Powell, C. Iliadis, S. E. Hale and V. Y. Hansper
Lifetime of the 6793-keV state in ¹⁵O
Phys. Rev. Lett. 87, 152501 (2001) · 10.1103/PhysRevLett.87.152501
2.
A. M. Mukhamedzhanov, P. Bém, B. A. Brown, V. Burjan, C. A. Gagliardi, V. Kroha, J. Novák, F. M. Nunes, Š. Piskoř, F. Pirlepesov, E. Šimečková, R. E. Tribble and J. Vincour
Asymptotic normalization coefficients for ¹⁴N + p → ¹⁵O and the astrophysical S factor for ¹⁴N(p,γ)¹⁵O
Phys. Rev. C 67, 065804 (2003); erratum Phys. Rev. C 68, 019901 (2003) · 10.1103/PhysRevC.67.065804
3.
A. Formicola et al. (LUNA Collaboration)
Astrophysical S-factor of ¹⁴N(p,γ)¹⁵O
Phys. Lett. B 591, 61 (2004) · 10.1016/j.physletb.2004.03.092 · arXiv:nucl-ex/0312015LUNA
4.
R. C. Runkle, A. E. Champagne et al.
Direct measurement of the ¹⁴N(p,γ)¹⁵O S factor
Phys. Rev. Lett. 94, 082503 (2005) · 10.1103/PhysRevLett.94.082503 · arXiv:nucl-ex/0408018
5.
G. Imbriani et al. (LUNA Collaboration)
S-factor of ¹⁴N(p,γ)¹⁵O at astrophysical energies
Eur. Phys. J. A 25, 455 (2005) · 10.1140/epja/i2005-10138-7 · arXiv:nucl-ex/0509005LUNA
6.
A. Lemut et al. (LUNA Collaboration)
First measurement of the ¹⁴N(p,γ)¹⁵O cross section down to 70 keV
Phys. Lett. B 634, 483 (2006) · 10.1016/j.physletb.2006.02.021 · arXiv:nucl-ex/0602012LUNA
7.
D. Schürmann et al.
Lifetime measurement of the 6792 keV state in ¹⁵O, important for the astrophysical S factor extrapolation in ¹⁴N(p,γ)¹⁵O
Phys. Rev. C 77, 055803 (2008) · 10.1103/PhysRevC.77.055803 · arXiv:0804.1934
8.
M. Marta et al. (LUNA Collaboration)
The ¹⁴N(p,γ)¹⁵O reaction studied with a composite germanium detector
Phys. Rev. C 83, 045804 (2011) · 10.1103/PhysRevC.83.045804 · arXiv:1103.5393LUNA
9.
L. Wagner et al.
Astrophysical S factor of the ¹⁴N(p,γ)¹⁵O reaction at 0.4–1.3 MeV
Phys. Rev. C 97, 015801 (2018) · 10.1103/PhysRevC.97.015801 · arXiv:1711.10847
10.
B. Frentz et al.
Lifetime measurements of excited states in ¹⁵O
Phys. Rev. C 103, 045802 (2021) · 10.1103/PhysRevC.103.045802
11.
Gy. Gyürky, Z. Halász, G. G. Kiss, T. Szücs, Zs. Fülöp
Activation cross section measurement of the ¹⁴N(p,γ)¹⁵O astrophysical key reaction
Phys. Rev. C 105, L022801 (2022) · 10.1103/PhysRevC.105.L022801 · arXiv:2201.10176
12.
B. Frentz et al.
Investigation of the ¹⁴N(p,γ)¹⁵O reaction and its impact on the CNO cycle
Phys. Rev. C 106, 065803 (2022) · 10.1103/PhysRevC.106.065803
13.
G. Gosta et al. (LUNA Collaboration)
The SOCIAL project: measurement of the ¹⁴N(p,γ)¹⁵O cross section
Eur. Phys. J. A 61, 110 (2025) · 10.1140/epja/s10050-025-01561-1LUNA
14.
A. Compagnucci et al. (LUNA Collaboration)
Towards a comprehensive study of the ¹⁴N(p,γ)¹⁵O astrophysical key reaction: description of the experimental technique including novel target preparation
Eur. Phys. J. A 61, 191 (2025) · 10.1140/epja/s10050-025-01658-7LUNA
15.
X. Chen, J. Su, Y. P. Shen et al.
Enhanced S-factor for the ¹⁴N(p,γ)¹⁵O reaction and its impact on the solar composition problem
Phys. Rev. Lett. 135, 232701 (2025) · 10.1103/q756-hzmt · arXiv:2410.16086
16.
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
17.
Y. Xu, K. Takahashi, S. Goriely, M. Arnould, M. Ohta, H. Utsunomiya
NACRE II: an update of the NACRE compilation of charged-particle-induced thermonuclear reaction rates for nuclei with mass number A < 16
Nucl. Phys. A 918, 61 (2013) · 10.1016/j.nuclphysa.2013.09.007 · arXiv:1310.7099
18.
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
19.
Borexino Collaboration
Experimental evidence of neutrinos produced in the CNO fusion cycle in the Sun
Nature 587, 577 (2020) · 10.1038/s41586-020-2934-0
20.
D. Basilico et al. (Borexino Collaboration)
Final results of Borexino on CNO solar neutrinos
Phys. Rev. D 108, 102005 (2023) · arXiv:2307.14636

How to cite this page

J. Skowronski, ¹⁴N(p,γ)¹⁵O, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/14N-pg-15O.

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