## Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions

## Abstract

Here, we solve a simple theoretical model of time evolving fission chains due to Feynman that generalizes and asymptotically approaches the point model theory. The point model theory has been used to analyze thermal neutron counting data. This extension of the theory underlies fast counting data for both neutrons and gamma rays from metal systems. Fast neutron and gamma-ray counting is now possible using liquid scintillator arrays with nanosecond time resolution. For individual fission chains, the differential equations describing three correlated probability distributions are solved: the time-dependent internal neutron population, accumulation of fissions in time, and accumulation of leaked neutrons in time. Explicit analytic formulas are given for correlated moments of the time evolving chain populations. The equations for random time gate fast neutron and gamma-ray counting distributions, due to randomly initiated chains, are presented. Correlated moment equations are given for both random time gate and triggered time gate counting. There are explicit formulas for all correlated moments are given up to triple order, for all combinations of correlated fast neutrons and gamma rays. The nonlinear differential equations for probabilities for time dependent fission chain populations have a remarkably simple Monte Carlo realization. A Monte Carlo code was developed formore »

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1377778

- Report Number(s):
- LLNL-JRNL-658859

Journal ID: ISSN 0029-5639; TRN: US1702573

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Nuclear Science and Engineering

- Additional Journal Information:
- Journal Volume: 181; Journal Issue: 3; Journal ID: ISSN 0029-5639

- Publisher:
- American Nuclear Society - Taylor & Francis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 22 GENERAL STUDIES OF NUCLEAR REACTORS; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Kim, K. S., Nakae, L. F., Prasad, M. K., Snyderman, N. J., and Verbeke, J. M. Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions. United States: N. p., 2015.
Web. doi:10.13182/NSE14-120.
```

```
Kim, K. S., Nakae, L. F., Prasad, M. K., Snyderman, N. J., & Verbeke, J. M. Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions. United States. doi:10.13182/NSE14-120.
```

```
Kim, K. S., Nakae, L. F., Prasad, M. K., Snyderman, N. J., and Verbeke, J. M. Sun .
"Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions". United States. doi:10.13182/NSE14-120. https://www.osti.gov/servlets/purl/1377778.
```

```
@article{osti_1377778,
```

title = {Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions},

author = {Kim, K. S. and Nakae, L. F. and Prasad, M. K. and Snyderman, N. J. and Verbeke, J. M.},

abstractNote = {Here, we solve a simple theoretical model of time evolving fission chains due to Feynman that generalizes and asymptotically approaches the point model theory. The point model theory has been used to analyze thermal neutron counting data. This extension of the theory underlies fast counting data for both neutrons and gamma rays from metal systems. Fast neutron and gamma-ray counting is now possible using liquid scintillator arrays with nanosecond time resolution. For individual fission chains, the differential equations describing three correlated probability distributions are solved: the time-dependent internal neutron population, accumulation of fissions in time, and accumulation of leaked neutrons in time. Explicit analytic formulas are given for correlated moments of the time evolving chain populations. The equations for random time gate fast neutron and gamma-ray counting distributions, due to randomly initiated chains, are presented. Correlated moment equations are given for both random time gate and triggered time gate counting. There are explicit formulas for all correlated moments are given up to triple order, for all combinations of correlated fast neutrons and gamma rays. The nonlinear differential equations for probabilities for time dependent fission chain populations have a remarkably simple Monte Carlo realization. A Monte Carlo code was developed for this theory and is shown to statistically realize the solutions to the fission chain theory probability distributions. Combined with random initiation of chains and detection of external quanta, the Monte Carlo code generates time tagged data for neutron and gamma-ray counting and from these data the counting distributions.},

doi = {10.13182/NSE14-120},

journal = {Nuclear Science and Engineering},

number = 3,

volume = 181,

place = {United States},

year = {2015},

month = {11}

}

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