Statistical planning for a neutron lifetime experiment using magnetically trapped neutrons

At the NIST Cold Neutron Research Facility, a two-stage experiment will be repeated many times. During the first stage of each run cycle, ultracold neutrons will be produced and confined in a magnetic trap filled with superfluid 4He. Ultracold neutrons will result when cold (8.9 إ) neutrons undergo inelastic scattering in the superfluid helium. After filling the trap to a desired level, decay events will be recorded as a function of time. Detection is possible because the charged particles created by neutron decay generate detectable scintillations in the helium. In addition to neutron decay events, background events will be recorded. I model the background as a stationary Poisson process. By Monte Carlo methods, I study the performance of two nonlinear algorithms for estimating the mean lifetime of the neutron. In one method, the event time data are summarized as a histogram where the bin widths vary. I select the time endpoints of the bins so that the expected number of counts per bin contributed by the decay process is approximately constant. In the second method, the lifetime is estimated from the complete sequence of event times. The histogram method yields a less variable estimate than does the complete data estimation method. The allocation of time between the fill and decay stages affects the precision of the estimate. To get the optimal time allocation, I minimize the asymptotic variance of the estimated mean lifetime (estimated from the pooled histogram data from all cycles) given knowledge of the rate at which neutrons enter the trap and parameters which characterize the background. The mean lifetime estimate is biased. I observe bias reduction when estimating the lifetime from data pooled from many cycles (rather than averaging estimates from each of the cycles).