Optimal Proton Trapping in a Neutron Lifetime Experiment
| dc.creator | Coakley, Kevin J. | |
| dc.date | 2006-12-05 | |
| dc.date | 2007-03-28 | |
| dc.date.accessioned | 2026-07-07T11:24:07Z | |
| dc.date.available | 2026-07-07T11:24:07Z | |
| dc.description | In a neutron lifetime experiment conducted at the National Institute of Standards and Technology, protons produced by neutron decay events are confined in a Penning trap. In each run of the experiment, there is a trapping stage of duration $τ$. After the trapping stage, protons are purged from the trap. A proton detector provides incomplete information because it goes dead after detecting the first of any purged protons. Further, there is a dead time $δ$ between the end of the trapping stage in one run and the beginning of the next trapping stage in the next run. Based on the fraction of runs where a proton is detected, I estimate the trapping rate $λ$ by the method of maximum likelihood. I show that the expected value of the maximum likelihood estimate is infinite. To obtain a maximum likelihood estimate with a finite expected value and a well-defined and finite variance, I restrict attention to a subsample of all realizations of the data. This subsample excludes an exceedingly rare realization that yields an infinite-valued estimate of $λ$. I present asymptotically valid formulas for the bias, root-mean-square prediction error, and standard deviation of the maximum likelihood estimate of $λ$ for this subsample. Based on nominal values of $λ$ and the dead time $δ$, I determine the optimal duration of the trapping stage $τ$ by minimizing the root-mean-square prediction error of the estimate. | |
| dc.description | 21 pages, 4 figures This is a revised version of "Optimal Proton Trapping". Based on a review, some aspects of the techical argument were refined | |
| dc.identifier | https://arxiv.org/abs/physics/0612036 | |
| dc.identifier | http://arxiv.org/abs/physics/0612036 | |
| dc.identifier | Nucl.Instrum.Meth.A577:702-707,2007 | |
| dc.identifier | doi:10.1016/j.nima.2007.04.172 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/195126 | |
| dc.subject | Data Analysis, Statistics and Probability | |
| dc.subject | Instrumentation and Detectors | |
| dc.title | Optimal Proton Trapping in a Neutron Lifetime Experiment | |
| dc.type | text |