Error analysis of large-time approximations for decay chains

Consider a radioactive decay chain X1 → ⋯ → Xn→ and let Nn(t) be the amount of Xn at time t. This paper establishes error bounds for large-time approximations to Nn(t) that include and generalize the transient equilibrium approximations and other known approximations. The error bounds allow one to find the range of t for which these approximations can be used with a given degree of precision.