²²Ne(p,γ)²³Na · Reaction atlas

The proton capture on ²²Ne that makes sodium. It is the main way stars produce ²³Na, the only stable sodium isotope, during hydrogen burning.

Many old star clusters in the Milky Way contain stars with more sodium and less oxygen than their neighbours. This pattern, called the sodium–oxygen anticorrelation, is thought to come from material that was burned at high temperature in an earlier generation of stars. Which stars did the burning, for example massive stars on the asymptotic giant branch (AGB stars), is still debated, and the answer depends on how fast ²²Ne turns into sodium. The same reaction sets part of the sodium and neon yields of nova explosions. For decades its rate was uncertain by large factors because several possible low-energy resonances had never been seen; most of them have now been measured or excluded.

Facts

How well known: Underground measurements have found or ruled out the low-energy resonances, and the uncertainty of the rate fell about a thousandfold; some details of the analysis are still debated.
Live evaluation: Plot the data · ²³Na →
Reaction rates: Explore the rates →
Q-value · energy released: 8.794 MeV
Gamow window: 105 ± 31 keVAGB hot-bottom burning, 80 MK (NeNa cycle)
190 ± 66 keVclassical nova, 0.2 GK (NeNa cycle)
Kind: Radiative capture

How it was measured

7 measurements, 2014–2024, 4 at LUNAShow the list

2014
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · E^ₚ = 186 keV resonance
Feasibility study for the underground campaign, including the beam-induced background. First direct observation of the 186 keV resonance, with a lower limit ωγ > 0.12 × 10⁻⁶ eV on its strength. [1]
2015
HZDR Tandetron, Dresden-RossendorfHelmholtz-Zentrum Dresden-Rossendorf
Direct measurement at the surface · E^ₚ = 436–1279 keV (five resonances)
Strengths of the 436, 639 and 661 keV resonances relative to those at 479 and 1279 keV, with a ²²Ne-implanted tantalum target. Consistent with but more precise than the literature, except the 661 keV resonance, which is ten times weaker; improved γ-ray branching ratios. [2]
2015
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · E^ₚ = 156.2, 189.5 and 259.7 keV
First direct observation of the three resonances, with strengths known to 2–7%, and much lower upper limits on three tentative resonances; the full account is in Depalo et al. (2016). An erratum raised the strengths by 18–19% after including the beam energy straggling, with unchanged astrophysical conclusions. [3, 4, 5]
2017
LENA, TUNLTriangle Universities Nuclear Laboratory
Direct measurement at the surface · E^ₚ below 200 keV (ECR ion source) and higher energies (1 MV accelerator)
Independent measurement of the low-energy resonances with ²²Ne implanted in tantalum backings. [6]
2018
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · E^ₚ = 71 and 105 keV, and off-resonance
Upper limits of 6 × 10⁻¹¹ and 7 × 10⁻¹¹ eV (90% CL) on the two suggested resonances, and the off-resonance S-factor at very low energy, which constrains direct capture and a subthreshold resonance. The rate uncertainty at 0.1 GK was reduced by three orders of magnitude. [7]
2020
DRAGON, TRIUMFTRIUMF
Inverse kinematics and recoil separators · E_cm = 149–1222 keV (resonances); 282–511 keV (non-resonant)
First measurement in inverse kinematics, a ²²Ne beam on a windowless H₂ target, with different systematic uncertainties from all earlier work. The 458 keV reference resonance has ωγ = 0.439(22) eV, below the two most recent forward-kinematics values and in agreement with older ones; the rate is a factor of 4 above STARLIB-2013, with little effect on ²³Na in AGB stars but an effect on Ne–Al nuclei in novae. [8, 9]
2024
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · direct capture down to E^ₚ = 188 keV
Full account of the high-statistics LUNA data: new γ-decay branchings for the resonances at E^ₚ = 156.2 and 259.7 keV, and partial cross sections for direct capture to several states of ²³Na down to E^ₚ = 188 keV, the lowest energy so far. A new R-matrix fit gives a revised rate; tensions remain on some branching ratios and on the capture to excited states. [10]

Measurements (EXFOR)

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

32 datasets in 16 EXFOR entries, 1975–2022 · 2 without an energy range, not drawn

Temperature

AGB hot-bottom burning, T₉ = 0.08 (80 MK)classical nova, T₉ = 0.2 (200 MK)

Lowest energy in EXFOR: 149 keV; Cavanna et al., 2015; Depalo et al., 2016; Ferraro et al., 2018; Lennarz et al., 2020; Williams et al., 2020 · ωγ · D4330.002
Distance from the Gamow peak: 0.73 Gamow widths above; E₀ = 104 keV, window 73–135 keV
Rate from energies not in EXFOR: 95%; at T₉ = 0.08, smooth estimate · 95% of it lies below the lowest energy in EXFOR

2 resonance-strength datasets reach into this window: the smooth estimate does not count resonances.

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	1	282 keV – 511 keV
SS-factor	3	183 keV – 1.62 MeV
σ→Eₓpartial	2	406 keV – 1.9 MeV
dσ/dΩangular distribution	2	814 keV – 1.82 MeV
ωγresonance strength	16	67.9 keV – 2.11 MeV
…other	6	149 keV – 611 keV

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 (32)Compound nucleus ²³Na

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.

Open the ²³Na evaluation →doi:10.1103/PhysRevC.109.064627

Details

How well known, in detail: The low-energy resonances are now measured or excluded and the rate uncertainty at 0.1 GK fell by about three orders of magnitude; the normalization to the higher-energy reference resonances and the non-resonant component remain under discussion.

At the temperatures of hot-bottom burning and of novae the rate is a sum of narrow resonances and of a non-resonant component, made of direct capture and of the tails of subthreshold states. Before 2014 several resonances below E^ₚ = 300 keV were known only as upper limits or from indirect data, and the tentative resonances at E^ₚ = 71 and 105 keV, together with the non-resonant component, left the rate at 0.1 GK uncertain by orders of magnitude. LUNA observed the E^ₚ = 186 keV resonance in a feasibility study (Cavanna et al. 2014) and then measured the resonances at E^ₚ = 156.2, 189.5 and 259.7 keV directly for the first time with a windowless ²²Ne gas target and two HPGe detectors (Cavanna et al. 2015; Depalo et al. 2016).

The original strengths were later raised by 18–19% because the energy straggling of the beam had been neglected (erratum, 2018). A second LUNA campaign set upper limits of 6 × 10⁻¹¹ eV and 7 × 10⁻¹¹ eV on the 71 and 105 keV resonances and measured the off-resonance S-factor (Ferraro et al. 2018); a further analysis of direct capture and resonances at low energy followed (Takács et al. 2024). At TUNL, Kelly et al. (2017) measured the low-energy resonances with implanted targets.

At higher energies, the resonances used to normalize the low-energy data were remeasured at HZDR (Depalo et al. 2015) and, in inverse kinematics, at DRAGON (Lennarz et al. 2020; Williams et al. 2020), where the strength of the E_cm = 458 keV reference resonance came out 0.439(22) eV, measured for the first time independently of other resonance strengths: lower than the two most recent forward-kinematics values, in agreement with three older ones.

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) [11]

Open questions

The strength of the E_cm = 458 keV reference resonance, where the DRAGON value, 0.439(22) eV, is lower than the two most recent forward-kinematics results; strengths normalized to it inherit the discrepancy.
The size of the non-resonant component (direct capture and subthreshold states) between the resonances.
Whether the updated rate is enough for AGB models to reproduce the sodium–oxygen anticorrelation in globular clusters.

Related reactions

References

1.
F. Cavanna et al. (LUNA Collaboration)
A new study of the ²²Ne(p,γ)²³Na reaction deep underground: feasibility, setup, and first observation of the 186 keV resonance
Eur. Phys. J. A 50, 179 (2014) · 10.1140/epja/i2014-14179-5 · arXiv:1411.2888LUNA
2.
R. Depalo et al.
Strengths of the resonances at 436, 479, 639, 661, and 1279 keV in the ²²Ne(p,γ)²³Na reaction
Phys. Rev. C 92, 045807 (2015) · 10.1103/PhysRevC.92.045807 · arXiv:1507.03893
3.
F. Cavanna et al. (LUNA Collaboration)
Three new low-energy resonances in the ²²Ne(p,γ)²³Na reaction
Phys. Rev. Lett. 115, 252501 (2015) · 10.1103/PhysRevLett.115.252501 · arXiv:1511.05329LUNA
4.
R. Depalo et al. (LUNA Collaboration)
Direct measurement of low-energy ²²Ne(p,γ)²³Na resonances
Phys. Rev. C 94, 055804 (2016) · 10.1103/PhysRevC.94.055804 · arXiv:1610.00925LUNA
5.
F. Cavanna et al. (LUNA Collaboration)
Erratum: Three new low-energy resonances in the ²²Ne(p,γ)²³Na reaction
Phys. Rev. Lett. 120, 239901 (2018) · 10.1103/PhysRevLett.120.239901LUNA
6.
K. J. Kelly, A. E. Champagne, L. N. Downen, J. R. Dermigny, S. Hunt, C. Iliadis, A. L. Cooper
New measurements of low-energy resonances in the ²²Ne(p,γ)²³Na reaction
Phys. Rev. C 95, 015806 (2017) · 10.1103/PhysRevC.95.015806
7.
F. Ferraro et al. (LUNA Collaboration)
Direct capture cross section and the E^ₚ = 71 and 105 keV resonances in the ²²Ne(p,γ)²³Na reaction
Phys. Rev. Lett. 121, 172701 (2018) · 10.1103/PhysRevLett.121.172701 · arXiv:1810.01628LUNA
8.
A. Lennarz et al.
First inverse kinematics measurement of key resonances in the ²²Ne(p,γ)²³Na reaction at stellar temperatures
Phys. Lett. B 807, 135539 (2020) · 10.1016/j.physletb.2020.135539 · arXiv:1910.00791
9.
M. Williams et al.
First inverse kinematics study of the ²²Ne(p,γ)²³Na reaction and its role in AGB star and classical nova nucleosynthesis
Phys. Rev. C 102, 035801 (2020) · 10.1103/PhysRevC.102.035801 · arXiv:1910.01698
10.
M. P. Takács et al. (LUNA Collaboration)
Direct capture cross section and resonances in the ²²Ne(p,γ)²³Na reaction at low energy
Phys. Rev. C 109, 064627 (2024) · 10.1103/PhysRevC.109.064627LUNA
11.
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)

How to cite this page

J. Skowronski, ²²Ne(p,γ)²³Na, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/22Ne-pg-23Na.

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