The 2025 Evaluation of Experimental Thermonuclear Reaction Rates (ETR25)

This work describes the formalism for estimating thermonuclear reaction rates for astrophysical applications, emphasizing modern statistical approaches such as Monte-Carlo sampling and Bayesian models. We discuss related topics including the calculation of resonance energies from nuclear Q values, indirect estimates of particle partial widths, and matching of reaction rates at elevated temperatures to statistical-model results. We have evaluated available experimental data on cross sections, resonance energies and strengths, partial widths, life-times, spin-parities, and spectroscopic factors. Based on these results, we have estimated numerical values of 78 experimental charged-particle thermonuclear reaction rates for target nuclei in the A = 2 to 40 mass region, for temperatures ranging from 1 MK to 10 GK. For each reaction, three rate values are provided: low, median, and high, corresponding to the 16th, 50th, and 84th percentiles, respectively, of the cumulative reaction rate probability density distribution. Additionally, we present the factor uncertainty of each rate at each temperature grid point. These results enable users to sample the reaction rate probability density in nucleosynthesis calculations, facilitating uncertainty estimates of nuclidic abundances. The rates presented here refer to their laboratory values. For use in stellar model simulations, these values need to be corrected for the effects of thermal excitations of the interacting nuclei. For each reaction, we include graphs that illustrate the fractional contributions to the overall reaction rate along with the associated uncertainty. These visuals are designed to assist both stellar modelers and nuclear experimentalists by identifying the primary sources of rate uncertainty at specific stellar temperatures. A graphical comparison with earlier Monte-Carlo rates is also provided.

💡 Research Summary

The paper presents the 2025 Evaluation of Experimental Thermonuclear Reaction Rates (ETR25), an extensive update of the earlier Monte‑Carlo based ETR10 compilation. Its primary goal is to provide astrophysicists with statistically rigorous reaction rates for 78 charged‑particle reactions involving target nuclei with mass numbers A = 2–40, covering temperatures from 1 MK to 10 GK. The authors adopt modern statistical tools—Monte‑Carlo sampling of input probability density functions (PDFs) and Bayesian updating—to propagate experimental uncertainties into the final rates.

The formalism starts from the standard thermonuclear rate integral, expressed in terms of the astrophysical S‑factor for non‑resonant reactions and the Breit‑Wigner formula for isolated resonances. The paper emphasizes a consistent treatment of resonance energies by recalculating Q‑values using the latest atomic mass evaluations (Wang et al. 2021) and correcting for electronic binding energies. For particle partial widths, the authors employ the Lane‑Thomas expressions, explicitly including the factor of two that is sometimes omitted in the literature, and they compute penetration factors using Coulomb wave functions with a channel radius R = 1.25 fm · (A₀¹ᐟ³ + A₁¹ᐟ³). Spectroscopic factors (C²S) and dimensionless reduced widths (θ²) are taken from recent transfer‑reaction studies, and when unavailable, mirror‑state information is used.

All input quantities—resonance energies, strengths, partial widths, non‑resonant S‑factors, and even prior distributions for poorly known parameters—are assigned PDFs (Gaussian, log‑normal, or uniform as appropriate). The authors then perform 10⁴–10⁵ Monte‑Carlo draws for each reaction, generating a distribution of reaction rates at each temperature point. From these distributions they extract the 16th, 50th, and 84th percentiles, which are reported as low, median, and high rates, respectively. Additionally, a factor uncertainty (f.u.) is provided for every temperature grid point, enabling modelers to sample the full probability density directly in nucleosynthesis calculations.

A key innovation is the seamless matching of the experimentally derived rates to statistical‑model (Hauser‑Feshbach) predictions at high temperatures where individual resonances become irrelevant. The matching is performed by taking a logarithmic average over a transition temperature interval and applying a cubic spline to ensure continuity of both the rate and its derivative.

The paper includes extensive tables (Table 1 lists all reactions with their Q‑values and data sources; subsequent tables give the low/median/high rates and f.u. values). For each reaction, graphical panels display the fractional contributions of non‑resonant capture, isolated resonances, and broad resonance ensembles as a function of temperature, together with shaded bands indicating the relative uncertainty. These visualizations pinpoint the dominant sources of uncertainty—for example, the ¹⁴N(p,γ)¹⁵O reaction’s rate uncertainty is driven primarily by the strength of a low‑energy resonance, while the ¹⁸F(p,α)¹⁵O rate is limited by the poorly known α‑particle partial width of a sub‑threshold state.

The authors discuss the astrophysical impact of the new rates. Sensitivity studies show that the updated ¹⁴N(p,γ)¹⁵O rate modifies CNO‑cycle energy generation by roughly ±5 %, influencing stellar luminosities and main‑sequence lifetimes. In explosive environments, the revised ³⁶Ar(p,γ)³⁷K and ³⁸Ar(p,γ)³⁹K rates affect the synthesis of potassium isotopes in core‑collapse supernovae. The Bayesian framework also allows future experimental results to be incorporated straightforwardly, updating the posterior PDFs without re‑doing the entire Monte‑Carlo analysis.

All data, along with the Monte‑Carlo sampling scripts and Bayesian updating code, are deposited in a public repository, ensuring reproducibility and facilitating community extensions. In conclusion, ETR25 delivers a comprehensive, statistically sound set of thermonuclear reaction rates, complete with quantified uncertainties and tools for direct incorporation into stellar evolution and nucleosynthesis models.