Neutron lifetime experiments using magnetically trapped neutrons: optimal background correction strategies

In the first stage of each run of a neutron lifetime experiment, a magnetic trap is filled with neutrons. In the second stage of each run, decay events plus background events are observed. In a separate experiment, background is measured. The mean lifetime is estimated by fitting a two parameter exponential model to the background-corrected data. For two models of the background signal, I determine the optimal ratio of the number of “background-only” measurements to the number of primary “neutron decay plus background” measurements. Further, for each run, I determine the optimal allocation of time for filling and for observing decay events. For the case where the background consists of an activated material (aluminum) plus a stationary Poisson process, the asymptotic standard error of the lifetime estimate computed from the background-corrected data is lower than the asymptotic standard error computed from the uncorrected data. For the case where the background is a stationary Poisson process, background correction is desirable provided that the background intensity is sufficiently small compared to the rate at which neutrons enter the trap.