A proton capture that destroys sodium and makes magnesium. It competes with 23Na(p,α)20Ne, which also destroys sodium but returns the material to neon.
When 23Na captures a proton, the new nucleus either emits an alpha particle and goes back to 20Ne, closing the NeNa cycle, or emits a γ-ray and becomes 24Mg, leaking material into the MgAl cycle. This reaction is the leak. Together with its competitor it decides how much sodium survives hydrogen burning, which matters for the sodium-rich and oxygen-poor stars observed in old star clusters, and how much material flows on from neon to magnesium and aluminium.
Facts
- How well known
- Its two key resonances were measured at LUNA, which narrows the rate to between about a third lower and a half higher than its best value; direct and indirect data still disagree on the lowest resonance.
- Live evaluation
- 23Na(p,p)23Na (24Mg) evaluation →
- Reaction rates
- Explore the rates →
- Q-value · energy released
- 11.693 MeV
- Gamow window
- 110 ± 32 keVAGB hot-bottom burning, 80 MK (NeNa cycle)
- 205 ± 68 keVclassical nova, 0.2 GK (NeNa cycle)
- 525 ± 225 keVcore carbon burning, 15 M☉ star, 0.83 GK (Carbon burning)
- 375 ± 145 keVsuperburst ignition, accreting neutron star, 0.5 GK (Carbon burning)
- Kind
- Radiative capture
How it was measured
4 measurements, 2013–2023, 1 at LUNAShow the listHide the list
2013
LENA, TUNLTriangle Universities Nuclear Laboratory
Direct measurement at the surface · E_cm = 138 keV resonance
Search for the 138 keV resonance with the 200 kV accelerator and its ECR ion source; only an upper limit on the strength could be set, 5.17 neV at 95% confidence. [1]
2019
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · Eₚ = 140 and 251 keV resonances
First direct observation of the 140 keV resonance (4π BGO), ωγ = 1.46 (+0.58/−0.53) neV, and the 251 keV resonance (HPGe), ωγ = 482(82) μeV. The rate uncertainty at 0.07 GK is reduced to at most −35%/+50%. [2]
2022
Nuclear Science Laboratory, Notre DameUniversity of Notre Dame
Direct measurement at the surface · Eₚ = 0.5–1.05 MeV
Off-resonance cross section, to determine the direct capture component that extrapolates to low energies. [3]
2023
TUNL, Durham
Transfer reactions and ANCs · states of 24Mg near the proton threshold
23Na(3He,d)24Mg proton transfer to constrain the proton widths of the low-energy resonances; the width of the 133 keV resonance is in strong disagreement with the LUNA strength. [4]
Measurements (EXFOR)
Every dataset EXFOR holds for this reaction, drawn by the energies it covers, against the energies a star uses.
23 datasets in 11 EXFOR entries, 1961–2019 · 8 without an energy range, not drawn
- Lowest energy in EXFOR
- 469 keV
- Bodart et al., 1977 · Y · D0129.002 Not yet in EXFOR: LUNA 400 kV (2019), Eₚ = 140 and 251 keV resonances.
- Distance from the Gamow peak
- 5.6 Gamow widths above
- E₀ = 111 keV, window 78.8–143 keV
- Rate from energies not in EXFOR
- 100%
- at T₉ = 0.08, smooth estimate · 100% 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
| Quantity | Datasets | E_cm range (keV) |
|---|---|---|
| σ→Eₓpartial | 2 | 3.74 MeV – 13.7 MeV |
| dσ/dΩangular distribution | 4 | 3.82 MeV – 12.2 MeV |
| Yyield | 1 | 469 keV – 958 keV |
| ωγresonance strength | 6 | 138 keV – 1.98 MeV |
| …other | 2 | 488 keV – 1.63 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: The two key resonances were measured directly at LUNA, which limits the rate uncertainty at 0.07 GK to −35%/+50%; the strength of the lowest resonance is still in tension between direct and transfer data.
At 50–110 MK the rate is dominated by narrow resonances at Eₚ = 140 and 251 keV and, at the low end of that range, by direct capture. The 140 keV resonance is quoted as E_cm = 138 keV or 133 keV in different works. A direct search at LENA gave only an upper limit on its strength (Cesaratto et al. 2013).
The LUNA measurement of Boeltzig et al. (2019) observed it directly for the first time with a 4π BGO summing detector, ωγ = 1.46 (+0.58/−0.53) neV, and measured the 251 keV resonance with an HPGe detector, ωγ = 482(82) μeV. Direct capture, which had received little attention, was studied off resonance at Eₚ = 0.5–1.05 MeV by Boeltzig et al. (2022). A new 23Na(3He,d) measurement at TUNL (Marshall et al. 2023) gives a proton width for the 133 keV resonance in clear tension with the LUNA strength.
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.
Open questions
- The strength of the lowest resonance (E_cm ≈ 133 keV), where the direct LUNA value and the transfer data of Marshall et al. (2023) disagree.
- The direct capture S-factor at the energies of the Gamow window, which so far comes from extrapolation.
Related reactions
References
- 1.
J. M. Cesaratto et al.
Phys. Rev. C 88, 065806 (2013) · 10.1103/PhysRevC.88.065806
- 2.
A. Boeltzig et al. (LUNA Collaboration)
Direct measurements of low-energy resonance strengths of the 23Na(p,γ)24Mg reaction for astrophysics
Phys. Lett. B 795, 122 (2019) · 10.1016/j.physletb.2019.05.044LUNA
- 3.
A. Boeltzig, R. J. deBoer et al.
Investigation of direct capture in the 23Na(p,γ)24Mg reaction
Phys. Rev. C 106, 045801 (2022) · 10.1103/PhysRevC.106.045801
- 4.
C. Marshall, K. Setoodehnia, G. C. Cinquegrana, J. H. Kelly, F. Portillo Chaves, A. Karakas, R. Longland
New constraints on sodium production in globular clusters from the 23Na(3He,d)24Mg reaction
Phys. Rev. C 107, 035806 (2023) · 10.1103/PhysRevC.107.035806 · arXiv:2303.06128
- 5.
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)
- 6.
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
How to cite this page
J. Skowronski, 23Na(p,γ)24Mg, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/23Na-pg-24Mg.
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)