Dealing with discontinuities in half-life measurements

This case study investigates a half-life experiment that reveals a single step-like discontinuity in counting efficiency across repeated activity measurements. Plausible causes for this discrepancy may involve a sudden change in geometrical conditions or a modification in the electronic pulse processing. The primary objective is to assess whether a more precise determination of the half-life can be achieved through a combined fit of the decay constant and two amplitudes over the entire decay curve, as opposed to deriving a mean value from two independent fits on distinct sections of the decay curve. It answers the question whether accuracy is gained by fitting a single half-life value to several decay curves simultaneously. The analysis employs both rigorous and approximate uncertainty formulas for least-squares fits, alongside a methodology based on empirical decomposition of residuals.