dorsal/arxiv
View SchemaOptimal Proton Trapping in a Neutron Lifetime Experiment
| Authors | Kevin J. Coakley |
|---|---|
| Categories | |
| ArXiv ID | physics/0612036 |
| URL | https://arxiv.org/abs/physics/0612036 |
| DOI | 10.1016/j.nima.2007.04.172 |
| Journal | Nucl.Instrum.Meth.A577:702-707,2007 |
Abstract
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 $\tau$. 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 $\delta$ 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 $\lambda$ 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 $\lambda$. I present asymptotically valid formulas for the bias, root-mean-square prediction error, and standard deviation of the maximum likelihood estimate of $\lambda$ for this subsample. Based on nominal values of $\lambda$ and the dead time $\delta$, I determine the optimal duration of the trapping stage $\tau$ by minimizing the root-mean-square prediction error of the estimate.
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"abstract": "In a neutron lifetime experiment conducted at the National Institute of\nStandards and Technology, protons produced by neutron decay events are confined\nin a Penning trap. In each run of the experiment, there is a trapping stage of\nduration $\\tau$. After the trapping stage, protons are purged from the trap. A\nproton detector provides incomplete information because it goes dead after\ndetecting the first of any purged protons. Further, there is a dead time\n$\\delta$ between the end of the trapping stage in one run and the beginning of\nthe next trapping stage in the next run. Based on the fraction of runs where a\nproton is detected, I estimate the trapping rate $\\lambda$ by the method of\nmaximum likelihood. I show that the expected value of the maximum likelihood\nestimate is infinite. To obtain a maximum likelihood estimate with a finite\nexpected value and a well-defined and finite variance, I restrict attention to\na subsample of all realizations of the data. This subsample excludes an\nexceedingly rare realization that yields an infinite-valued estimate of\n$\\lambda$. I present asymptotically valid formulas for the bias,\nroot-mean-square prediction error, and standard deviation of the maximum\nlikelihood estimate of $\\lambda$ for this subsample. Based on nominal values of\n$\\lambda$ and the dead time $\\delta$, I determine the optimal duration of the\ntrapping stage $\\tau$ by minimizing the root-mean-square prediction error of\nthe estimate.",
"arxiv_id": "physics/0612036",
"authors": [
"Kevin J. Coakley"
],
"categories": [
"physics.data-an",
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"doi": "10.1016/j.nima.2007.04.172",
"journal_ref": "Nucl.Instrum.Meth.A577:702-707,2007",
"title": "Optimal Proton Trapping in a Neutron Lifetime Experiment",
"url": "https://arxiv.org/abs/physics/0612036"
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