Constraining cross sections for unstable $^{153,159}$Gd$(n,\gamma)$ and their astrophysical implications

Neutron capture $(n,\gamma)$ cross sections of Gadolinium (Gd) isotopes are critical to astrophysics research, nuclear reactor designs, and medical applications. However, the available $(n,\gamma)$ data on unstable Gd isotopes are scarce and direct measurement is challenging. In this work, we propose an approach to infer the $(n,\gamma)$ cross sections for unstable $^{153,159}$Gd isotopes by constraining both the $\gamma$-ray strength functions ($\gamma$SFs) and nuclear level densities (NLDs). Specifically, the key $\gamma$SF parameters are adjusted to match the available experimental data, and the NLD parameters are determined by renormalizing microscopic level densities through a Bayesian optimization method. Our approach is verified by comparing our predictions with the experimental $(n,\gamma)$ data for the stable $^{155,157}$Gd isotopes. We then infer the unstable $^{153,159}\text{Gd}(n,\gamma)$ cross sections within the neutron energy range of 0.01--5.0 MeV. The resulting uncertainty is about $30\%$, which is significantly reduced by a factor of 5.5 compared to a large uncertainty of $\sim167\%$ predicted with different nuclear models in TALYS. We further calculate the astrophysical reaction rates for the $^{153,159}\text{Gd}$ isotopes. It is found that the $^{159}\text{Gd}(n,\gamma)$ rate is larger by a factor of $\sim$2.9 than the JINA REACLIB recommendation. This enhancement increases the neutron capture branching ratio at $^{159}$Gd. Consequently, the resulting $^{160}$Gd abundance is increased by a factor of $\sim$2 compared to predictions using the JINA REACLIB rate in $s$-process nucleosynthesis simulations. Our approach is promising for extracting $(n,\gamma)$ data on a wider range of unstable isotopic chains as well as for essential astrophysical reaction network calculations and nuclear science applications.