Constraining r-process nucleosynthesis via enhanced accuracy neutron-capture experiments

The isotopic abundances of r-process elements in the solar system are traditionally derived as residuals from the subtraction of s-process contributions from total solar abundances. However, the uncertainties in s-process nucleosynthesis – particularly those arising from Maxwellian Averaged Cross Sections (MACS) – propagate directly into the r-process residuals, affecting their reliability. Building upon the seminal work of Goriely (1999), who introduced a multi-event s-process model to quantify these uncertainties, we revisit the problem using a simplified yet effective approach. By assuming that the relative uncertainty in s-process isotopic abundances scales linearly with the MACS uncertainties from data libraries (KADoNiS), we identify a subset of isotopes for which the r-process residuals remain significantly uncertain. Using updated solar abundances (Lodders 2025) and s-process contributions from Bisterzo et al. (2014), we present a short list of isotopes that are prime candidates for improved (n,g) measurements at CERN n_TOF in the near future. Our analysis provides a practical framework for prioritizing future experimental efforts that will profit from upgrades and enhancements of the n_TOF facility. It also highlights the need to revisit key neutron-capture cross sections to refine our understanding of the r-process isotopic abundance pattern, commonly used as a benchmark in stellar models of explosive nucleosynthesis.

💡 Research Summary

The paper addresses a fundamental problem in nuclear astrophysics: the reliability of r‑process residual abundances derived from solar system material. Traditionally, the r‑process contribution to each isotope is obtained by subtracting the s‑process component from the total solar abundance. However, the s‑process component itself depends on neutron‑capture reaction rates, most notably the Maxwellian‑averaged cross sections (MACS) that are used in stellar nucleosynthesis calculations. Uncertainties in these MACS values therefore propagate directly into the r‑process residuals, limiting the precision with which we can test r‑process models and constrain astrophysical sites such as neutron‑star mergers or core‑collapse supernovae.

Building on Goriely’s (1999) multi‑event s‑process framework, the authors propose a simplified yet practical method to estimate how MACS uncertainties affect r‑process residuals. They assume a linear relationship between the relative uncertainty of an s‑process isotopic abundance (ΔNs/Ns) and the relative uncertainty of its MACS (Δσ/⟨σ⟩). This assumption is justified for the main s‑process in low‑ and intermediate‑mass AGB stars (mass number A≈90–200), where the product Ns·⟨σ⟩ remains approximately constant under equilibrium conditions. By adopting this linear scaling, the authors avoid the need for full network calculations while still identifying the isotopes most vulnerable to nuclear data uncertainties.

Three primary data sources are combined: (i) MACS values and uncertainties from the KADoNiS v1.0 database, (ii) updated solar abundances from Lodders (2025), and (iii) s‑process contributions from the galactic chemical evolution study of Bisterzo et al. (2014). The r‑process residual for each isotope is calculated as Nr = N⊙ – Ns, where N⊙ is the solar abundance and Ns the s‑process contribution. The propagated uncertainty is approximated as ΔNr ≈ Ns·(Δσ/⟨σ⟩), effectively treating MACS uncertainties as the dominant source of error because solar abundance uncertainties are typically only 1–3 %, whereas MACS uncertainties range from 10 % to well over 50 % for many isotopes.

Two selection criteria are applied to flag high‑priority isotopes for new (n,γ) measurements at the CERN n_TOF facility: (1) the MACS relative uncertainty must be ≥10 %, and (2) the resulting relative uncertainty in the r‑process residual must be ≥20 %. Seven isotopes satisfy both criteria: 97 Mo, 99 Ru, 122 Sn, 139 La, 168 Er, 184 W, and 200 Hg. For each, the paper provides the r‑process residual abundance (Nr), the absolute uncertainty (ΔNr), and the relative uncertainties of both Nr and the MACS.

The authors discuss each candidate in detail. 97 Mo is a mixed s‑ and r‑process isotope contributing about 47 % of the solar Mo inventory via the s‑process; its MACS uncertainty (≈15 %) leads to a 27 % uncertainty in its r‑process residual. No direct (n,γ) measurement exists, but a high‑resolution experiment at n_TOF could reduce the MACS uncertainty to 4–5 %, dramatically improving the residual. 99 Ru is the decay product of the key branching point nucleus 99 Tc. Although KADoNiS lists a 15 % MACS uncertainty, the value is purely theoretical and likely underestimated; the branching also depends on temperature‑dependent β‑decay rates of 99 Tc, which can vary by factors of 5–10. A precise measurement of 99 Ru (n,γ) would cut the MACS uncertainty to ~5 % and bring the r‑process residual uncertainty down to ~6 %, while also refining s‑process branching diagnostics. The remaining isotopes lie near neutron magic numbers or branching points, making them crucial for both s‑ and r‑process modeling; their current MACS uncertainties (10–12 %) translate into r‑process residual uncertainties ranging from 20 % to over 50 %.

From an experimental perspective, the paper highlights recent upgrades to the n_TOF facility (LS3) and the use of C6D6 liquid scintillation detectors combined with the Pulse‑Height Weighting Technique (PHWT). Monte‑Carlo‑based weighting functions tailored to each sample‑detector geometry enable reaction‑yield determinations with ≤2 % accuracy, as demonstrated in recent measurements of 96 Mo. The authors argue that similar precision can be achieved for the seven priority isotopes, provided enriched samples are available (e.g., natural Ru contains 12.8 % 99 Ru, facilitating target preparation).

In conclusion, the study provides a clear, data‑driven roadmap for prioritizing neutron‑capture experiments that will most effectively reduce uncertainties in r‑process residual abundances. By focusing on MACS uncertainties that dominate the error budget, the proposed measurements at n_TOF will simultaneously sharpen s‑process models (through better constraints on neutron densities, temperatures, and 13 C‑pocket structures) and improve the benchmark r‑process abundance pattern used in astrophysical simulations. The authors suggest that future work should extend the linear uncertainty propagation to include correlated uncertainties, temperature‑dependent β‑decay rates, and full network calculations, thereby refining the prioritization further and ensuring that the next generation of nuclear data fully supports the quest to unravel the origins of the heaviest elements.