Derivation of an uncertainty propagation factor for half-life determinations

An analytical equation is derived for the uncertainty propagation factor for a half-life determination from a least-squares fit to equidistant activity measurements performed with identical relative uncertainties. The obtained formula applies to a purely random statistical uncertainty component. It is equivalent to the solution published by Parker in Nucl. Instr. Meth. A 286, 502. A more general equation for weighted least-squares fitting is derived and presented in a compact manner. It is used as a benchmark to verify the applicability of Parker's solution to non-equidistant data with unequal uncertainties.