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3.2.2 Magnetic Trapping of Ultra Cold Neutrons and Determination of the Mean Lifetime of the Neutron

Kevin J. Coakley, Grace L. Yang

Statistical Engineering Division, ITL

Bradley K. Alpert

Mathematical and Computational Sciences Division, ITL

M.S.Dewey, D.Gilliam

Ionizing Radiation Division, PL

Researchers from Harvard University, Los Alamos National Laboratory, University of Washington, University of Berlin, and NIST plan to produce and confine polarized Ultra Cold Neutrons (UCN) in a magnetic trap. Based on this new technology, the neutron lifetime will be determined at a precision up to 100 times better than the current value. Along with other experimental data, a measurement of the mean lifetime of the neutron allows one to test the consistency of the standard model of electroweak interactions. Further, the mean lifetime of the neutron is an important parameter in astrophysical theories. Statistical and computational work has focused on optimal experimental design and dynamical studies of marginally trapped neutrons.

Optimal Estimation. There will be many run cycles of a two stage experiment. In the first stage of each run, neutrons from the NIST Cold Neutron Research Facility are guided into a superfluid 4He bath where they dissipate almost all their energy by inelastic scattering. These UCN are confined in a magnetic trap. After filling the trap to some level, the neutron beam is blocked and decay events, as well as background events, are recorded. Denote the duration of each stage as Tfill and Tdecay. Two algorithms for estimating the mean lifetime are compared. In one method, the event time data is summarized as a histogram. The time endpoints of the histogram are selected so that the expected number of counts per bin contributed by the decay process, is constant. In the second method, the lifetime is estimated from the complete sequence of event times. The histogram method yields a less variable estimate of the mean lifetime. The optimal strategy for time allocation is found by minimizing the asymptotic variance of the lifetime (estimated from the pooled histogram data from all cycles) as a function Tfill and Tdecay, given knowledge of the filling rate of the trap and parameters which characterize the background process. The validity of the asymptotic approximation is demonstrated in Monte Carlo experiments.

Marginally Trapped Neutrons. Neutrons with sufficiently high energy escape the trap, but not immediately. These ``marginally trapped" neutrons may decay before escaping. In a Monte Carlo study, many trajectories are simulated. For each trajectory, we compute the escape time. Beyond about six seconds of elapsed time, we find that escape times can not be predicted in a numerically stable manner.


Figure 12: The approximate mean lifetime of the neutron is $\tau~\approx~890~ s$. During the fill stage of each run cycle, the expected number of confined neutrons grows as

\begin{displaymath}\lambda_{fill} * \tau ( 1 - exp( - T_{fill} / \tau ) )

where $\lambda_{fill}$ is the rate at which neutrons enter the trap, $\tau$ is the mean lifetime of the neutron and Tfill is the duration of the fill stage. We express the asymptotic standard error of the mean lifetime, estimated from data pooled from all run cycles, as

{ \sigma_{{ \hat{\tau}^{pool}} } } { \tau } ~\approx~
0.001 \sqrt{ \frac{T^{*} } { T_{total}} }

where the duration of the entire experiment is Ttotal. Above, log10(T*) is plotted as a function of Tfill, Tdecayfor the case where $\lambda_{fill}~=~25,000/\tau$and the background is a stationary Poisson process with intensity rate equal to $1000/\tau$.

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Date created: 7/20/2001
Last updated: 7/20/2001
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