Empirical decomposition and error propagation of medium-term instabilities in half-life determinations

Abstract

A least-squares fit of exponential functions to a measured radioactive decay rate curve provides an estimate of the half-life and its statistical uncertainty in the assumption that all deviations from the theoretical curve are purely of a random nature. The result may be biased and the error underestimated as soon as the experiment suffers instabilities that exceed the duration of individual measurements. Contrary to long-term systematic errors, medium-frequency cyclic perturbations may be observable as autocorrelated structures in the residuals. In this work, an empirical decomposition algorithm is used to separate medium-frequency effects from the random statistical component in the fit residuals, such that custom error propagation factors can be calculated. A theoretical study of error propagation is made for sine and square wave perturbations. The empirical decomposition method is demonstrated on a synthetic spectrum, a time series of solar neutrino detection rates, and two experimental decay curves of 134Cs measured in an ionisation chamber.