Determination of Uranium Series Activity before Secular Equilibrium Is Established

Timely achievement of uranium series' secular equilibrium is not always feasible. Our objective is to mathematically justify methods for early uranium series gamma spectroscopy measurements that can accurately predict naturally occurring radioactive material equilibrium activities long before equilibrium is established. It was believed that, regardless of prior Rn escape, after sealing a sample for a few hours the activities of Rn, Ra, and U could theoretically be determined with a single measurement of both Pb and Bi. However, when accounting for error, this theory did not work as expected (CV = 14.0 in Ra simulation). A similar approach published by Li et al. in 2015 proved to be much more reliable with the error considered, using Pb activities measured at two different times gave significantly improved results when tested the same way (CV = 0.29 in Ra simulation). Because both Pb and Bi activities are typically available when using gamma spectrometry, we combine these approaches and further increased the accuracy of the calculated activities (CV = 0.21 in Ra simulation).