Open questions

Global R-matrix analysis

deBoer et al. (2017) fitted capture, scattering and β-delayed α data together and gave the recommended rate; the lowest capture data lie near 1 MeV, about three times above the stellar energy of 300 keV. [1]

Larger asymptotic normalization coefficients

A ground-state ANC from ¹²C(¹¹B,⁷Li)¹⁶O gives a total rate up to 21% higher (Shen et al. 2023); with larger subthreshold ANCs, Mukhamedzhanov, deBoer et al. (2024) obtain S(300 keV) = 174 keV b, against 137 keV b in the 2017 fit. [2, 3]

Inverse reaction with γ beams

A time projection chamber in the HIγS γ beam measured background-free angular distributions of ¹⁶O(γ,α)¹²C; the E1–E2 phase is reported to agree with unitarity for the first time, removing one source of disagreement among earlier data (Haverson et al. 2026). [4]

Gravitational waves

From the first ten black-hole mergers, Farmer et al. (2020) infer S(300 keV) > 175 keV b at 68% confidence, and expect about fifty detections to pin it to ±10–30 keV b. [7]

Nuclear physics

The laboratory rates are lower: the 2017 R-matrix fit gives S(300 keV) = 137 keV b, a 2024 refit with larger ANCs 174 keV b, and the rate of Shen et al. (2023) lowers the edges of the gap by about 12% and 5%. [1, 3, 2]

Kibédi et al. (2020)

Proton–γ–γ coincidences gave Γ_rad/Γ = 6.2(6)×10⁻⁴ and, with a new pair-decay branching ratio, Γ_rad 34% above the adopted value. [8, 9]

Measurements of 2024–2025

Rana et al. find 4.01(30)×10⁻⁴, Dell'Aquila et al. 4.4(6)×10⁻⁴ and Paulsen et al. 4.1(4)×10⁻⁴; Paulsen et al. reanalysed the 2014 data behind the 2020 value, found several issues and obtain 4.6(6)×10⁻⁴, no longer discrepant with the ENSDF average of 4.16(11)×10⁻⁴. [10, 11, 12]

Continuum-discretized coupled channels (CDCC)

Ogata, Kan and Kamimura (2009) solved the three-body problem with CDCC and found a rate about 20 orders of magnitude above NACRE near 10⁷ K. [13]

Hyperspherical harmonics with R-matrix

Nguyen et al. (2012) agree with NACRE above 0.07 GK but find an enhancement of about 10¹² at 0.02 GK, much smaller than the CDCC one; with it, red giants still evolve as observed. [14, 15]

Solar Fusion III

Recommends S(0) = 0.561 ± 0.018 (exp) ± 0.022 (theory) keV b; the theoretical uncertainty has grown since Solar Fusion II and is now comparable to the experimental one. [16]

Data above 1 MeV

The recoil-separator data of ERNA differ from the γ-ray data above 1 MeV in both normalization and slope, which pulls fits of the energy dependence apart; activation data now extend above the proton threshold of ⁷Be. [17, 18]

Direct experiments with ⁷Be targets

Extrapolated S(0) values range from 18.5 ± 2.4 eV b (Orsay) to 21.5 ± 0.6 ± 0.6 eV b (Seattle), with target characterization the main systematic uncertainty. [21, 22]

Coulomb dissociation and Solar Fusion III

Solar Fusion III combines the direct and Coulomb-dissociation data in a halo effective field theory and recommends S(0) = 20.5 ± 0.7 eV b, where Solar Fusion II had used the direct data alone. [16, 23, 24]

Low metallicity

Asplund, Amarsi and Grevesse (2021) give Z = 0.0139 and find that the solar modelling problem remains with their abundances. [26]

High metallicity

Magg et al. (2022) find Z/X = 0.0225 and report that the mismatch with helioseismology is resolved. Borexino's final CNO flux, 6.7 (+1.2/−0.8) × 10⁸ cm⁻² s⁻¹, with its ⁷Be and ⁸B data, disfavours the low-metallicity standard solar model at 3.2σ. [27, 28]

The nuclear input

Solar Fusion III recommends S(0) = 1.68 ± 0.14 keV b for ¹⁴N(p,γ)¹⁵O; a 2025 measurement in Hefei finds 1.92 ± 0.08 keV b. The core C + N inferred from the neutrino flux depends directly on this rate. [16, 29]

Doppler-shift lifetimes

Bertone et al. (2001) found τ ≈ 1.6 fs; Schürmann et al. (2008) set τ < 0.77 fs; Frentz et al. (2021) found τ = 0.6 ± 0.4 fs. A lifetime measurement with AGATA is under review. [32, 33, 34]

Transfer reactions and R-matrix fits

ANCs from transfer reactions fix the state's contribution in another way; R-matrix fits of the capture data, including the ground-state transition with which it interferes, still leave differences between data and fits. [35, 36]

Direct underground measurement

JUNA measured ¹⁹F(p,γ)²⁰Ne down to 186 keV and found a resonance at 225 keV that raises the rate near 0.1 GK by up to a factor of 7.4; with it, stellar models give a leak strong enough to be a possible source of the calcium (Zhang et al. 2022). [38]

R-matrix evaluation

Before the JUNA result, a combined fit of the (p,γ), (p,α) and (p,p) data found the (p,γ) rate uncertainty considerably larger than previously reported. It traced this to unresolved interferences, possible threshold and subthreshold states and direct capture, and concluded that more experiments are needed to answer the calcium question (deBoer et al. 2021). [39]

Nuclear theory

A Gamow shell model calculation in the coupled-channel representation gives, near 0.1 GK, a rate close to the JUNA one (Dong et al. 2024, preprint). [40]

Direct measurements

³He(d,p)⁴He gives U_e = 219 ± 7 eV against the adiabatic limit of 120 eV (Aliotta et al. 2001); a hierarchical Bayesian reanalysis keeps it high, 213 ± 13 eV (de Souza et al. 2019). [42, 43]

Trojan Horse method

The bare S-factor measured indirectly, compared with direct data, gives U_e = 330 ± 40 eV for ⁷Li(p,α)α against 175 eV adiabatic (Lattuada et al. 2001); for ³He(d,p) the Trojan Horse bare S-factor was also used to extract the screening. [44, 45]

Agreement

With the LUNA data, deuterium points to a baryon density in excellent agreement with Planck (Mossa et al. 2020; Pisanti et al. 2021). [46, 47]

A small tension

Pitrou et al. (2021) find a tension of about 1.8σ between the baryon density from the light elements and from the CMB and baryon acoustic oscillations. [48]

Strength of the 92 keV resonance

Measured underground, first at LUNA and then at JUNA. [49, 50]

Ground-state fraction

Kankainen et al. (2021) find f₀ = 0.52(2)(6), the most precise value and at the lower end of the range adopted before, which means less ground-state ²⁶Al and less 1809 keV emission. [51]

Fusion hindrance

Jiang et al. (2007) predict an S-factor that peaks and falls at low energy. Uzawa and Hagino (2025), refitting the same data with a free exponent, find no hindrance; the answer depends on the fit and on the data sets chosen. [53, 54]

Low-energy resonances

The Trojan Horse data of Tumino et al. (2018) show resonances that would raise the rate strongly; Mukhamedzhanov et al. (2019) attribute the rise to the plane-wave approximation, and the direct data of Tan et al. (2020) disagree with it. 0⁺ cluster states of ²⁴Mg near threshold are a possible physical origin (Adsley et al. 2022). [55, 56, 57, 58]

A second Trojan Horse experiment

At CIAE, Li et al. (2026) used ¹⁶O instead of ¹⁴N as the Trojan horse nucleus and report resonances near 1.5 MeV in the α₀ and α₁ channels; a companion preprint finds the same in the p₀ and p₁ channels, with no hindrance in the measured range. Mukhamedzhanov (2026, preprint) argues that Coulomb distortions make the plane-wave analysis of these data unreliable. [59, 60, 61]

Recent direct data

STELLA finds a lower average S-factor than standard extrapolations at 2.2–2.6 MeV and cannot confirm an overall rise at deep sub-barrier energies. [62]

Transfer reactions and evaluation

α-transfer at Texas A&M (Ota et al. 2020; Jayatissa et al. 2020) and the evaluation of Adsley et al. (2021), which lowered the (α,n) rate substantially and left the (α,γ) rate almost unchanged. [65, 66, 67]

Direct measurements

The strength of the 830 keV resonance in (α,n), remeasured with a stilbene detector, is about three times that in (α,γ) (Shahina et al. 2024). [68, 69]

Overshoot and rotation

Exponentially decaying overshoot at third dredge-up forms the pocket, and rotation keeps mixing it in the interpulse (Herwig and Langer 2000). [71]

Magnetic buoyancy

Mixing driven by magnetic buoyancy, built into stellar models, fits the Ni, Sr, Zr, Mo and Ba isotope ratios of presolar SiC grains with one field configuration (Vescovi et al. 2020). [72]

Storage-ring measurements

Bound-state β decay of bare ¹⁸⁷Re, 32.9 ± 2.0 yr (Bosch et al. 1996), and of bare ²⁰⁵Tl, 291 (+33/−27) d, longer than the earlier theoretical estimate (Leckenby et al. 2024). [77, 78]

Tabulated stellar rates

Most stellar decay rates in s-process models are calculated, many of them taken from Takahashi and Yokoi (1987), and few can be tested in the laboratory. [79]

Network calculations

Constant neutron densities between those of the s- and r-processes reproduce carbon-enhanced metal-poor stars with both s and r signatures (Hampel et al. 2016). [80]

Candidate sites

Proton ingestion events in low-mass, low-metallicity AGB stars are a promising candidate, but the site of the i-process is still a matter of debate (Choplin et al. 2022). [81]