Estimating Mean Lifetime from Partially Observed Events in Nuclear Physics

Juha Karvanen,Salme Kärkkäinen,Jan Sarén,Mikko Niilo‐Rämä

doi:10.1111/rssc.12519

Abstract

Abstract The mean lifetime is an important characteristic of particles to be identified in nuclear physics. State-of-the-art particle detectors can identify the arrivals of single radioactive nuclei as well as their subsequent radioactive decays (departures). Challenges arise when the arrivals and departures are unmatched and the departures are only partially observed. An inefficient solution is to run experiments where the arrival rate is set very low to allow for the matching of arrivals and departures. We propose an estimation method that works for a wide range of arrival rates. The method combines an initial estimator and a numerical bias correction technique. Simulations and examples based on data on the alpha decays of Lutetium isotope 155 demonstrate that the method produces unbiased estimates regardless of the arrival rate. As a practical benefit, the estimation method enables the use of all data collected in the particle detector, which will lead to more accurate estimates and, in some cases, to shorter experiments.

Highlights

Radioactive decay is the textbook example of a Poisson process in time (Cox & Lewis, 1966)
The mean lifetime is an important characteristic of particles to be identified in nuclear physics since it is sensitive to the structure of underlying quantum mechanical states
Radioactive species are produced continuously and decays are measured simultaneously. This is enabled by state-of-the-art particle detectors and data- acquisition systems which can identify the arrivals of single radioactive nuclei to a detector as well as their subsequent radioactive decays (Lazarus et al, 2001; Page et al, 2003)

Summary

Introduction

Radioactive decay is the textbook example of a Poisson process in time (Cox & Lewis, 1966). The mean lifetime is an important characteristic of particles to be identified in nuclear physics since it is sensitive to the structure of underlying quantum mechanical states. A large change in nuclear structure from the initial to the final state causes a radioactive alpha decay longer than predicted by a simple model (Geiger & Nuttall, 1911). Radioactive species are produced continuously and decays are measured simultaneously. This is enabled by state-of-the-art particle detectors and data- acquisition systems which can identify the arrivals of single radioactive nuclei to a detector as well as their subsequent radioactive decays (Lazarus et al, 2001; Page et al, 2003). If the arrival rate is low and the mean lifetime is short, we are able to say with a high probability that a certain arrival and departure form a pair because only one departure has been observed between two consecutive arrivals

Objectives

Methods

Conclusion