Statistical approaches to lifetime measurements with restricted observation times

Two generic methods based on frequentism and Bayesianism are presented in this work aiming to adequately estimate decay lifetimes from measured data, while accounting for restricted observation times in the measurements. All the experimental scenarios that can possibly arise from the observation constraints are treated systematically and formulas are derived. The methods are then tested against the decay data of bare isomeric ${}^{94m}\mathrm{Ru}^{44+}$, which were measured using isochronous mass spectrometry with a timing detector at the CSRe in Lanzhou, China. Applying both methods in three distinct scenarios yields six different but consistent lifetime estimates. The deduced values are all in good agreement with a prediction based on the neutral-atom value modified to take the absence of internal conversion into account. Potential applications of such methods are discussed.

Figure 1

Schematic presentation of nine possible scenarios of decay experiments when a restricted observation time is involved. The highlighted four with shade are the current scope of this work. See the text for details.

Figure 2

Degree of modification as a function of the observation time. $g\left(t\right)$ is closer to $f\left(t\right)$ as the observation time gets longer.

Figure 3

Posterior density for the lifetime estimation of the experimental data in the filtering scenario from bare isomeric ${}^{94m}\mathrm{Ru}^{44+}$ decays in the laboratory frame. The dashed line indicates the point estimate, while the shaded region marks the credible interval at $68.3\%$ level. The inset in log-log scale demonstrates the asymptotic inverse-square relationship on $\tau$.

Figure 4

Comparison between six lifetime estimates for the bare isomeric ${}^{94m}\mathrm{Ru}^{44+}$ in the laboratory frame by means of frequentist and Bayesian inferences in three distinct experimental scenarios. The horizontal band indicates the theoretical prediction range.