Astrophysical analysis of the measurement of (alpha,gamma) and (alpha,n) cross sections of 169Tm

Reaction cross sections of 169Tm(alpha,gamma)173Lu and 169Tm(alpha,n)172Lu have been measured in the energy range 12.6<=E_alpha<=17.5 MeV and 11.5<=E_alpha<=17.5 MeV, respectively, using the recently introduced method of combining activation with X-ray counting. Improved shielding allowed to measure the (alpha,gamma) to lower energy than previously possible. The combination of (alpha,gamma) and (alpha,n) data made it possible to study the energy dependence of the alpha width. While absolute value and energy dependence are perfectly reproduced by theory at energies above 14 MeV, the observed change in energy dependence at energies below 14 MeV requires a modification of the predicted alpha width. Using an effective, energy-dependent, local optical alpha+nucleus potential it is possible to reproduce the data but the astrophysical rate is still not well constrained at gamma-process temperatures. The additional uncertainty stemming from a possible modification of the compound formation cross section is discussed. Including the remaining uncertainties, the recommended range of astrophysical reaction rate values at 2 GK is higher than the previously used values by factors of 2-37.

💡 Research Summary

The paper presents a comprehensive experimental study of the α‑induced reactions on ^169Tm, namely ^169Tm(α,γ)^173Lu and ^169Tm(α,n)^172Lu, measured over the laboratory α‑particle energy ranges 12.6–17.5 MeV and 11.5–17.5 MeV, respectively. The authors employed a recently developed activation‑with‑X‑ray counting technique, which combines conventional activation analysis with high‑efficiency X‑ray detection. This method offers superior background suppression compared with traditional γ‑ray spectroscopy, allowing the (α,γ) channel to be measured down to lower energies than previously possible. Improved shielding around the detectors further reduced background, enabling reliable cross‑section data even at the lowest energies investigated.

The experimental results reveal that both reaction channels are well reproduced by standard statistical model calculations (e.g., TALYS, NON‑SMOKER) at α‑energies above ≈14 MeV. In this high‑energy regime the absolute cross sections and their energy dependence match the predictions that use the widely adopted global α‑nucleus optical potentials such as McFadden‑Satchler. However, a pronounced deviation appears below 14 MeV: the measured (α,γ) cross sections drop more steeply than the model predicts, and the (α,n) data also lie systematically below the theoretical curves. This discrepancy signals that the global optical potentials overestimate the α‑width (the transmission probability for the incoming α particle) at low energies.

To address the mismatch, the authors constructed an energy‑dependent local optical potential specifically tuned to the low‑energy data. By reducing the α‑width in the sub‑14 MeV region, the modified potential brings the calculated cross sections into agreement with the measurements for both channels. Nevertheless, this potential is calibrated only within the experimentally accessible energy window; extrapolation to the much lower effective α‑energies relevant for the astrophysical γ‑process (≈0.2 MeV in the stellar plasma at T≈2 GK) remains uncertain. Consequently, the astrophysical reaction rates derived from the new potential still carry sizable systematic uncertainties.

A further source of uncertainty discussed in the paper concerns the compound‑formation cross section. Standard Hauser‑Feshbach calculations assume that the formation probability of the compound nucleus depends solely on the entrance‑channel transmission coefficients (i.e., the α‑width). The authors point out that additional nuclear‑structure effects—such as low‑lying resonances, deformation, or clustering—could modify the compound‑formation probability independently of the α‑width. Accounting for such effects would introduce an extra factor of uncertainty into the stellar rates.

Using the locally adjusted optical potential, the authors computed the reaction rate for ^169Tm(α,γ)^173Lu at a temperature of 2 GK. The resulting rate is higher than the previously adopted values by a factor ranging from 2 up to 37, depending on the assumed magnitude of the remaining uncertainties (both from the optical potential and from possible modifications of the compound‑formation cross section). This broad range reflects the limited experimental constraints at the low energies that dominate the stellar rate.

In summary, the study provides the first simultaneous low‑energy measurements of both (α,γ) and (α,n) channels on ^169Tm, demonstrates that the standard global α‑nucleus optical potentials fail to describe the α‑width below 14 MeV, and offers a locally tuned, energy‑dependent potential that reproduces the data. While the new potential improves the reliability of the extrapolated astrophysical rates, the authors emphasize that significant uncertainties remain, especially concerning the extrapolation to γ‑process temperatures and the possible need to adjust the compound‑formation model. Future low‑energy α‑beam experiments, refined nuclear‑structure calculations, and a better theoretical understanding of the compound‑formation process are required to narrow the reaction‑rate uncertainties and to provide more accurate inputs for nucleosynthesis network simulations.