¹³C(α,n)¹⁶O · Reaction atlas

Carbon-13 captures a helium nucleus and releases a free neutron. In stars like the Sun near the end of their lives, this reaction supplies the neutrons that build about half the nuclei heavier than iron.

Elements heavier than iron are made mostly by adding neutrons to existing nuclei. In the slow neutron-capture process, or s-process, the neutrons arrive one at a time, slowly enough that unstable nuclei usually decay before the next one comes. In low-mass stars on the asymptotic giant branch (AGB stars, the last bright phase of stars like the Sun), a thin layer rich in carbon-13 forms between helium flashes. There this reaction releases neutrons at a temperature of about 90 million kelvin, and their number decides how much strontium, barium, lead and many other elements the star makes. The same reaction may also drive the faster intermediate process, or i-process, when hydrogen is mixed into hot helium-burning layers.

The s-process, from iron to lead

Facts

How well known: Measurements deep underground now reach the upper part of the energy range that matters in giant stars, from 230 keV up. Below that, the rate still depends on extending the data with a model of a nuclear state that lies just below the reaction threshold.
Live evaluation: No live evaluation yet · Evaluations
Reaction rates: Explore the rates →
Q-value · energy released: 2.216 MeV
Gamow window: 185 ± 44 keVAGB ¹³C pocket, 90 MK (Neutron sources of the s-process)
Kind: Particle-exchange reaction

On the timeline

How it was measured

8 measurements, 1993–2024, 1 at LUNAShow the list

1993
Direct measurement at the surface
Direct measurement of both s-process neutron sources, ¹³C(α,n)¹⁶O and ²²Ne(α,n)²⁵Mg, with new rates for each. [1]
2008
Forschungszentrum Karlsruhe, Karlsruhe
Direct measurement at the surface
Direct measurement and R-matrix analysis of the cross section; the resulting rate became the reference for later comparisons. [2]
2012
Trojan Horse method · quasi-free ¹³C(⁶Li,n¹⁶O)d
First Trojan Horse study of the −3 keV subthreshold resonance from the 6.356 MeV level of ¹⁷O, which dominates the cross section in the 140–230 keV window. [3]
2015
John D. Fox Accelerator Laboratory, Florida State University, Tallahassee
Transfer reactions and ANCs · ⁶Li(¹³C,d)¹⁷O at sub-Coulomb energy, 8 MeV ¹³C beam
Squared Coulomb-modified α ANC of the 1/2⁺ state at 6.356 MeV, 3.6 ± 0.7 fm⁻¹. The result removes the disagreement between earlier α-transfer measurements; some disagreement with the Trojan Horse result remains. [4]
2021
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · E = 230–300 keV
First direct data reaching the upper edge of the s-process Gamow window (230 keV), measured deep underground with much smaller uncertainties than previous data; stellar models with the revised rate change the yields of ⁶⁰Fe, ²⁰⁵Pb and ¹⁵²Gd in stars of near-solar composition. [5]
2022
JUNAChina Jinping Underground Laboratory
Direct measurement underground · E = 0.24–1.9 MeV (with Sichuan University above ground)
One consistent data set across the s- and i-process windows; the uncertainty at the centre of the i-process window fell from about 60% to 15%, with the first direct determination of the α strength of the near-threshold state. [6]
2023
Edwards Accelerator Laboratory, Ohio University
Direct measurement at the surface · E_α = 2.9–8.0 MeV
Total cross section with a ³He–BF₃ neutron barrel: considerably lower than earlier direct data above E_α = 5 MeV, as corrections based on Hauser–Feshbach estimates had suggested; Hauser–Feshbach branchings do not reproduce the earlier partial-channel data. [7]
2024
Nuclear Science Laboratory, Notre DameUniversity of Notre Dame
Direct measurement at the surface · E_α = 0.8–6.5 MeV, 18 angles (α,n₀)
Differential cross section of the (α,n₀) channel at angles from 0 to 160°, over 700 angular distributions, the first accurate ones below 1 MeV; added to the R-matrix fit, they suggest an extrapolation uncertainty of about 5%, against about 15% before. [8]

Measurements (EXFOR)

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

65 datasets in 31 EXFOR entries, 1956–2024 · 3 without an energy range, not drawn

AGB ¹³C pocket, T₉ = 0.09 (90 MK)

Lowest energy in EXFOR: 233 keV; Ciani et al., 2021 · S · O2548.002.1
Distance from the Gamow peak: 0.53 Gamow widths above; E₀ = 186 keV, window 143–230 keV
Rate from energies not in EXFOR: 89%; at T₉ = 0.09, smooth estimate · 89% 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	12	241 keV – 7.99 MeV
SS-factor	6	233 keV – 1.88 MeV
σ→Eₓpartial	2	626 keV – 4.98 MeV
dσ/dΩangular distribution	22	626 keV – 17.2 MeV
Aypolarization	4	1.59 MeV – 3.75 MeV
Yyield	2	460 keV – 879 keV
ωγresonance strength	2	1.6 MeV – 3.86 MeV
…other	12	788 keV – 4.97 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 (65)Compound nucleus ¹⁷O

Details

At T₉ ≈ 0.09 the Gamow window lies roughly between 140 and 230 keV, where the cross section is dominated by the high-energy tail of the 1/2⁺ state at 6.356 MeV in ¹⁷O, about 3 keV below the α threshold. Its contribution depends on the reduced α width, usually expressed through the asymptotic normalization coefficient (ANC), and on the exact position of the state relative to the threshold (deBoer et al. 2020). Indirect methods, the Trojan Horse method (La Cognata et al. 2012) and α-transfer ANC measurements (Avila et al. 2015), constrain this state, but their results have not always agreed. Avila et al. removed the disagreement among the α-transfer measurements, while a difference from the Trojan Horse value remained.

At the surface, the low event rate against the neutron background kept direct measurements above the Gamow window. The LUNA measurement under Gran Sasso reached E = 230–300 keV, reaching the upper edge of the s-process Gamow window (230 keV) for the first time (the authors describe it as inside the Gamow peak), with much smaller uncertainties than earlier data (Ciani et al. 2021). The JUNA measurement in the China Jinping Underground Laboratory, combined with data taken at Sichuan University, covered 0.24–1.9 MeV in one consistent data set and constrained the near-threshold state directly (Gao et al. 2022). At higher energies, the first accurate differential cross sections below 1 MeV, at 18 angles from 0.8 to 6.5 MeV, resolve long-standing differences between the earlier data and, in an R-matrix fit, could bring the uncertainty of the extrapolation to about 5% (deBoer et al. 2024).

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.

—C. Angulo, M. Arnould, M. Rayet et al. (NACRE Collaboration), Nucl. Phys. A 656, 3 (1999) [9]
—Y. Xu et al., Nucl. Phys. A 918, 61 (2013) [10]
—R. J. deBoer et al., Phys. Rev. C 101, 045802 (2020) [11]

Open questions

The ANC and the exact energy of the 1/2⁺ state at 6.356 MeV in ¹⁷O, which control the extrapolation below 230 keV.
Absolute normalization of the direct data, which depends on target stoichiometry under beam and on the neutron-detection efficiency as a function of neutron energy and angle.
Consistent data over a wide energy range, overlapping the underground and surface measurements, to constrain the R-matrix fit.

Discussed on the open-questions page

Related reactions

References

1.
H. W. Drotleff, A. Denker, H. Knee, M. Soiné, G. Wolf, J. W. Hammer, U. Greife, C. Rolfs, H. P. Trautvetter
Reaction rates of the s-process neutron sources ¹³C(α,n)¹⁶O and ²²Ne(α,n)²⁵Mg
Astrophys. J. 414, 735 (1993)
2.
M. Heil et al.
The ¹³C(α,n) reaction and its role as a neutron source for the s process
Phys. Rev. C 78, 025803 (2008) · 10.1103/PhysRevC.78.025803
3.
M. La Cognata et al.
Measurement of the −3 keV resonance in the reaction ¹³C(α,n)¹⁶O of importance in the s-process
Phys. Rev. Lett. 109, 232701 (2012) · 10.1103/PhysRevLett.109.232701
4.
M. L. Avila et al.
New α ANC measurement of the 1/2⁺ state in ¹⁷O at 6.356 MeV, that dominates the ¹³C(α,n)¹⁶O reaction rate at temperatures relevant for the s-process
Phys. Rev. C 91, 048801 (2015) · 10.1103/PhysRevC.91.048801 · arXiv:1503.08743
5.
G. F. Ciani et al. (LUNA Collaboration)
Direct measurement of the ¹³C(α,n)¹⁶O cross section into the s-process Gamow peak
Phys. Rev. Lett. 127, 152701 (2021) · 10.1103/PhysRevLett.127.152701 · arXiv:2110.00303LUNA
6.
B. Gao, T. Y. Jiao, Y. T. Li et al. (JUNA Collaboration)
Deep underground laboratory measurement of ¹³C(α,n)¹⁶O in the Gamow windows of the s and i processes
Phys. Rev. Lett. 129, 132701 (2022) · 10.1103/PhysRevLett.129.132701 · arXiv:2210.03222
7.
K. Brandenburg et al.
Measurements of the ¹³C(α,n)¹⁶O cross section up to E_α = 8 MeV
Phys. Rev. C 108, L061601 (2023) · 10.1103/PhysRevC.108.L061601
8.
R. J. deBoer et al.
Measurement of the ¹³C(α,n₀)¹⁶O differential cross section from 0.8 to 6.5 MeV
Phys. Rev. Lett. 132, 062702 (2024) · 10.1103/PhysRevLett.132.062702
9.
C. Angulo, M. Arnould, M. Rayet et al. (NACRE Collaboration)
A compilation of charged-particle induced thermonuclear reaction rates
Nucl. Phys. A 656, 3 (1999)
10.
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
11.
R. J. deBoer, C. R. Brune, M. Febbraro, J. Görres, I. J. Thompson, M. Wiescher
Sensitivity of the ¹³C(α,n)¹⁶O S factor to the uncertainty in the level parameters of the near-threshold state
Phys. Rev. C 101, 045802 (2020) · 10.1103/PhysRevC.101.045802

How to cite this page

J. Skowronski, ¹³C(α,n)¹⁶O, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/13C-an-16O.

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