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Asymptotic giant branch stars are responsible for the production of most of the heavy isotopes beyond Sr observed in the solar system. Among them, isotopes shielded from the $r$-process contribution by their stable isobars are defined as $s$-only nuclei. For a long time the abundance of ${}^{204}\mathrm{Pb}$, the heaviest $s$-only isotope, has been a topic of debate because state-of-the-art stellar models appeared to systematically underestimate its solar abundance. Besides the impact of uncertainties from stellar models and galactic chemical evolution simulations, this discrepancy was further obscured by rather divergent theoretical estimates for the neutron capture cross section of its radioactive precursor in the neutron-capture flow, ${}^{204}\mathrm{Tl}$( $t_{1/2}=3.78\mathrm{yr}$), and by the lack of experimental data on this reaction. We present the first ever neutron capture measurement on ${}^{204}\mathrm{Tl}$, conducted at the CERN neutron time-of-flight facility n_TOF, employing a sample of only 9 mg of ${}^{204}\mathrm{Tl}$produced at the Institute Laue Langevin high flux reactor. By complementing our new results with semiempirical calculations we obtained, at the $s$-process temperatures of $kT\approx 8\mathrm{keV}$and $kT\approx 30\mathrm{keV}$, Maxwellian-averaged cross sections (MACS) of 580(168) mb and 260(90) mb, respectively. These figures are about 3% lower and 20% higher than the corresponding values widely used in astrophysical calculations, which were based only on theoretical calculations. By using the new ${}^{204}\mathrm{Tl}$MACS, the uncertainty arising from the ${}^{204}\mathrm{Tl}(\mathrm{n},\gamma )$cross section on the $s$-process abundance of ${}^{204}\mathrm{Pb}$has been reduced from $\sim 30\%$down to $+8\%/-6\%$, and the $s$-process calculations are in agreement with the latest solar system abundance of ${}^{204}\mathrm{Pb}$reported by K. Lodders in 2021. Published by the American Physical Society2024 

Abstract Gridded monthly rainfall estimates can be used for a number of research applications, including hydrologic modeling and weather forecasting. Automated interpolation algorithms, such as the “autoKrige” function in R, can produce gridded rainfall estimates that validate well but produce unrealistic spatial patterns. In this work, an optimized geostatistical kriging approach is used to interpolate relative rainfall anomalies, which are then combined with long-term means to develop the gridded estimates. The optimization consists of the following: 1) determining the most appropriate offset (constant) to use when log-transforming data; 2) eliminating poor quality data prior to interpolation; 3) detecting erroneous maps using a machine learning algorithm; and 4) selecting the most appropriate parameterization scheme for fitting the model used in the interpolation. Results of this effort include a 30-yr (1990–2019), high-resolution (250-m) gridded monthly rainfall time series for the state of Hawai‘i. Leave-one-out cross validation (LOOCV) is performed using an extensive network of 622 observation stations. LOOCV results are in good agreement with observations (R²= 0.78; MAE = 55 mm month⁻¹; 1.4%); however, predictions can underestimate high rainfall observations (bias = 34 mm month⁻¹; −1%) due to a well-known smoothing effect that occurs with kriging. This research highlights the fact that validation statistics should not be the sole source of error assessment and that default parameterizations for automated interpolation may need to be modified to produce realistic gridded rainfall surfaces. Data products can be accessed through the Hawai‘i Data Climate Portal (HCDP;http://www.hawaii.edu/climate-data-portal). Significance StatementA new method is developed to map rainfall in Hawai‘i using an optimized geostatistical kriging approach. A machine learning technique is used to detect erroneous rainfall maps and several conditions are implemented to select the optimal parameterization scheme for fitting the model used in the kriging interpolation. A key finding is that optimization of the interpolation approach is necessary because maps may validate well but have unrealistic spatial patterns. This approach demonstrates how, with a moderate amount of data, a low-level machine learning algorithm can be trained to evaluate and classify an unrealistic map output.