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Stochastic Modeling and Estimation in a Neutron Lifetime Experiment



Yang G. L., Kevin Coakley


A team of researchers demonstrated at the National Institute of Standards and Technology Cold Neutron Research Facility for the first time that ultra cold neutrons can be confined in a magnetic trap filled with liquid helium. This technical breakthrough allows a more accurate measurement of the neutron lifetime and helps to answer questions fundamental to physics and astrophysics. In a first generation version of the experiment, the neutron trapping technique was demonstrated. As part of a statistical planning effort, an experimental protocol for data collection and analysis has been under development. The experiment is composed of two stages. In the first stage, ultra cold neutrons are generated and confined in the magnetic trap. In the second stage, decays of the trapped neutrons are recorded. During the first stage, nothing is observable. We do not know the number of neutrons available from the first stage for decay recording during the second stage. Furthermore, neutron lifetimes are only partially observable and are subject to contamination due to the presence of background events. In this presentation, we give an overview of stochastic modeling of lifetime data from such experiment and statistical estimation of mean neutron lifetime. We model a neutron lifetime by a birth and death process. Models are needed to account for a missing or incomplete lifetime and background contamination, and thereby correcting biases in the estimation of the mean neutron lifetime. Our statistical approach unifies many of the existing statistical methods used for studying radioactive decay processes. The problem of lifetime estimation is extensively studied in the survival analysis of patients in biostatistics and reliability analysis in industrial quality control in which lifetime data are subject to censoring, truncation and length-biased (cross-sectional) sampling. In the context of renewal processes, Feller called the length bias a renewal paradox. Neutron lifetimes are subject to similar effects. However, distinct characteristics of neutrons bring out some statistical problems that are rarely encountered in the survival analysis about which we shall discuss.
Proceedings of MATH EVERYWHERE, Milano, 4-6 Sept. 2005


estimation, neutron lifetime, stochastic modeling


Yang G. L., Y. and Coakley, K. (2007), Stochastic Modeling and Estimation in a Neutron Lifetime Experiment, Proceedings of MATH EVERYWHERE, Milano, 4-6 Sept. 2005 (Accessed December 7, 2023)
Created December 31, 2006, Updated October 12, 2021