Impact of Decay-Chain Feeding by Long-Lived Heavy Nuclei on Nuclear Cosmochronology

Nuclear cosmochronology provides an independent method for determining the ages of astrophysical objects without relying on Galactic chemical evolution models. Long-lived radioactive actinides synthesized via the rapid neutron-capture process ($r$-process) particularly thorium and uranium serve as ideal chronometric nuclei. However, predicting the initial abundances of these nuclei and their subsequent long-term evolution remains a major source of uncertainty in nuclear cosmochronology. In this work, we investigate the impact of decay-chain feeding from long-lived progenitor nuclei on nuclear cosmochronology and estimate the corresponding age corrections. We develop a self-consistent radioactive decay network that includes all relevant decay pathways and couple it to $r$-process nucleosynthesis calculations. By tracking the long-term evolution of $r$-process nucleosynthesis based on neutron star merger trajectories, the dominant long-lived nuclei shaping the evolution of the chronometric elements Th and U are identified as ${}^{232}$Th, ${}^{235}$U, ${}^{236}$U, ${}^{238}$U, and ${}^{244}$Pu. It is found that delayed feeding substantially modifies the long-term evolution of actinides particularly for ${}^{232}$Th, which receives significant late-time contributions from heavier progenitor nuclei such as ${}^{244}$Pu and ${}^{236}$U. As a consequence, the U/Th and Th/X chronometers exhibit significant sensitivity to delayed feeding from the progenitor nuclei ${}^{244}$Pu and ${}^{236}$U, with age corrections reaching $\sim 5$~Gyr. These results suggest that decay-chain feeding from long-lived progenitor nuclei plays a crucial role in nuclear cosmochronology and should be properly accounted for in age determinations based on actinide chronometers.