# Estimating the mass variance in neutron multiplicity counting $-$ A comparison of approaches

## Abstract

In the standard practice of neutron multiplicity counting, the first three sampled factorial moments of the event triggered neutron count distribution are used to quantify the three main neutron source terms: the spontaneous fissile material effective mass, the relative (α,n) production and the induced fission source responsible for multiplication. This study compares three methods to quantify the statistical uncertainty of the estimated mass: the bootstrap method, propagation of variance through moments, and statistical analysis of cycle data method. Each of the three methods was implemented on a set of four different NMC measurements, held at the JRC-laboratory in Ispra, Italy, sampling four different Pu samples in a standard Plutonium Scrap Multiplicity Counter (PSMC) well counter.

- Authors:

- Nuclear Research Center Negev (NRCN), Beer Sheva (Israel)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Inst. of Transuranium Elements, Ispra (Italy). Nuclear Security Unit

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA). Office of Nonproliferation Research and Development (NA-22)

- OSTI Identifier:
- 1392875

- Report Number(s):
- LA-UR-17-22890

Journal ID: ISSN 0168-9002; TRN: US1702589

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment

- Additional Journal Information:
- Journal Volume: 875; Journal Issue: C; Journal ID: ISSN 0168-9002

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; Neutron Multiplicity Counting, Passive neutron interrogation, Uncertainty Quantification.

### Citation Formats

```
Dubi, C., Croft, S., Favalli, A., Ocherashvili, A., and Pedersen, B. Estimating the mass variance in neutron multiplicity counting $-$ A comparison of approaches. United States: N. p., 2017.
Web. doi:10.1016/j.nima.2017.08.036.
```

```
Dubi, C., Croft, S., Favalli, A., Ocherashvili, A., & Pedersen, B. Estimating the mass variance in neutron multiplicity counting $-$ A comparison of approaches. United States. doi:10.1016/j.nima.2017.08.036.
```

```
Dubi, C., Croft, S., Favalli, A., Ocherashvili, A., and Pedersen, B. Thu .
"Estimating the mass variance in neutron multiplicity counting $-$ A comparison of approaches". United States. doi:10.1016/j.nima.2017.08.036. https://www.osti.gov/servlets/purl/1392875.
```

```
@article{osti_1392875,
```

title = {Estimating the mass variance in neutron multiplicity counting $-$ A comparison of approaches},

author = {Dubi, C. and Croft, S. and Favalli, A. and Ocherashvili, A. and Pedersen, B.},

abstractNote = {In the standard practice of neutron multiplicity counting, the first three sampled factorial moments of the event triggered neutron count distribution are used to quantify the three main neutron source terms: the spontaneous fissile material effective mass, the relative (α,n) production and the induced fission source responsible for multiplication. This study compares three methods to quantify the statistical uncertainty of the estimated mass: the bootstrap method, propagation of variance through moments, and statistical analysis of cycle data method. Each of the three methods was implemented on a set of four different NMC measurements, held at the JRC-laboratory in Ispra, Italy, sampling four different Pu samples in a standard Plutonium Scrap Multiplicity Counter (PSMC) well counter.},

doi = {10.1016/j.nima.2017.08.036},

journal = {Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment},

number = C,

volume = 875,

place = {United States},

year = {2017},

month = {9}

}

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