Rare Earth Element Nucleosynthesis in Collapsars: Sensitivity to (n, γ) Reaction Rates of Unstable Isotopes during Secondary i- and s-processes

The secondary i- and s-processes that follow the r-process in collapsar outflows, characterized by low electron fraction Y_e and decelerated expansion, can serve as a major source of rare earth element production. We systematically evaluated the contributions of the r-, i-, and s-processes to the production of rare earth elements in collapsar outflows. A sensitivity analysis of nucleosynthesis yields with respect to (n, γ) reaction rates involving unstable nuclei near the line of stability highlights dozens of key reactions critical for the synthesis of thulium (Z = 69) and lutetium (Z = 71). These specific (n, γ) reactions, however, have a negligible impact on the yields predicted in magnetohydrodynamically driven jets or binary neutron star mergers. Our nucleosynthesis models indicate that collapsars can produce elevated Tm/Eu and Lu/Eu abundance ratios, potentially serving as observational signatures distinguishing collapsar nucleosynthesis from others. The robustness of these predictions, however, is highly sensitive to uncertainties in the relevant nuclear reaction rates. We therefore emphasize the need for precise future experimental measurements of the (n, γ) cross sections for key unstable nuclei. Reducing these nuclear-physics uncertainties will allow collapsar models to predict Tm/Eu and Lu/Eu ratios with greater confidence, thereby improving our interpretation of observed abundances in r-process-enhanced metal-poor stars.