The 2025 Evaluation of Experimental Thermonuclear Reaction Rates (ETR25)

TL;DR

ETR25 delivers a statistically rigorous, experiment-driven evaluation of thermonuclear reaction rates for charged-particle processes with $A\le 40$ over a wide stellar temperature range. The work combines Bayesian hierarchical modeling and Monte-Carlo sampling to propagate uncertainties from resonance energies, partial widths, and nonresonant $S$ factors into posterior rate densities, providing low, median, and high rates along with factor uncertainties. It introduces refined input updates (masses, Q-values, excitation data) and a consistent treatment of systematic, extrinsic, and correlated uncertainties, applying Class I–III considerations and rate-extrapolation via the ETER–TALYS framework to high temperatures. The study delivers 78 experimentally constrained rates with uncertainty quantification, accompanied by open-source software (RatesMC) and data in appendices, enabling robust uncertainty propagation in nucleosynthesis simulations and model comparisons. The methodology enhances predictive power for stellar and Big Bang nucleosynthesis, while the transparency and reproducibility of inputs and code facilitate broad adoption and future refinements.

Abstract

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.

Figures (4)

• Figure 1: Idealized picture of various $S$-factor contributions to charged-particle reaction rates. In each panel, the energy range is divided into three regions. Green, Left: Directly measured $S$ factor data are not available because of the small transmission through the Coulomb barrier. Red, Middle: Region where $S$ factor data have been obtained in the laboratory. Blue, right: No data are available because of experimental limitations in the attainable beam energy. Three fundamentally different situations are encountered in practice, depending on the nature of contributions in the middle (red) region. (a) Class I reactions: nonresonant $S$ factor contributions only. (b) Class II reactions: main contributions from non-interfering (i.e., narrow) resonances. (c) Class III reactions: main contribution from interfering (i.e., broad) resonances. See text.
• Figure 2: Ratio of proton partial widths estimated from Equation (\ref{['eq:partpartwidth']}) to those measured in resonance reaction studies versus magnitude of the transfer spectroscopic factor, $C^2S$. The displayed data, courtesy of Art Champagne, form the basis of Figure 7 in PhysRevC.70.045802. The red and blue circles refer to pure and mixed transitions, respectively. The gray-shaded area indicates a factor of $1.6$ uncertainty band. See text.
• Figure 3: Direct capture $S$ factor in $^{17}$O(p,$\gamma$)$^{18}$F, summed over transitions to $21$ levels in $^{18}$F. (Blue line) $S$ factor calculated from Equation (\ref{['eq:dc']}), assuming a zero-depth nuclear potential for the calculation of the radial scattering wave function, $u_s$; (Red line) $S$ factor calculated from Equation (\ref{['eq:dc']}), assuming a hard-sphere scattering potential; (Dashed black line) From buckner2015. Note that the blue and black lines agree within $\approx 20$%. See text for details.
• Figure 4: Matching of experimental Monte-Carlo rates (red) to TALYS results (green) at high temperatures. The top and bottom panels depict the situation where the TALYS rates at the matching temperature, $T^{\text{ETER}}_{\text{match}}$ (vertical dashed line), are larger and smaller, respectively, than the median experimental rate. In either case, the TALYS prediction at the highest temperature, 10 GK, is adopted at face value, with an assumed uncertainty of a factor of 10. The matched rates and their uncertainties (blue) beyond $T^{\text{ETER}}_{\text{match}}$ are found from connecting the experimental rates at $T^{\text{ETER}}_{\text{match}}$ to the TALYS results at 10 GK, according to Equation (\ref{['eq:match1']}). All rates depicted here refer to laboratory rates (i.e., assuming that the target is in its ground state).