# On-the-Fly Generation of Differential Resonance Scattering Probability Distribution Functions for Monte Carlo Codes

## Abstract

Current Monte Carlo codes use one of three models: (1) the asymptotic scattering model, (2) the free gas scattering model, or (3) the S(α,β) model, depending on the neutron energy and the specific Monte Carlo code. This thesis addresses the consequences of using the free gas scattering model, which assumes that the neutron interacts with atoms in thermal motion in a monatomic gas in thermal equilibrium at material temperature, T. Most importantly, the free gas model assumes the scattering cross section is constant over the neutron energy range, which is usually a good approximation for light nuclei, but not for heavy nuclei where the scattering cross section may have several resonances in the epithermal region. Several researchers in the field have shown that the exact resonance scattering model is temperaturedependent, and neglecting the resonances in the lower epithermal range can under-predict resonance absorption due to the upscattering phenomenon mentioned above, leading to an over-prediction of keff by several hundred pcm. Existing methods to address this issue involve changing the neutron weights or implementing an extra rejection scheme in the free gas sampling scheme, and these all involve performing the collision analysis in the center-of-mass frame, followed by a conversion backmore »

- Authors:

- Univ. of Michigan, Ann Arbor, MI (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1394437

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Nuclear Science and Engineering

- Additional Journal Information:
- Journal Volume: 187; Journal Issue: 1; Journal ID: ISSN 0029-5639

- Publisher:
- American Nuclear Society - Taylor & Francis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; Resonance upscattering; Monte Carlo; free gas scattering model

### Citation Formats

```
Davidson, Eva E., and Martin, William R.
```*On-the-Fly Generation of Differential Resonance Scattering Probability Distribution Functions for Monte Carlo Codes*. United States: N. p., 2017.
Web. doi:10.1080/00295639.2017.1294931.

```
Davidson, Eva E., & Martin, William R.
```*On-the-Fly Generation of Differential Resonance Scattering Probability Distribution Functions for Monte Carlo Codes*. United States. doi:10.1080/00295639.2017.1294931.

```
Davidson, Eva E., and Martin, William R. Fri .
"On-the-Fly Generation of Differential Resonance Scattering Probability Distribution Functions for Monte Carlo Codes". United States.
doi:10.1080/00295639.2017.1294931. https://www.osti.gov/servlets/purl/1394437.
```

```
@article{osti_1394437,
```

title = {On-the-Fly Generation of Differential Resonance Scattering Probability Distribution Functions for Monte Carlo Codes},

author = {Davidson, Eva E. and Martin, William R.},

abstractNote = {Current Monte Carlo codes use one of three models: (1) the asymptotic scattering model, (2) the free gas scattering model, or (3) the S(α,β) model, depending on the neutron energy and the specific Monte Carlo code. This thesis addresses the consequences of using the free gas scattering model, which assumes that the neutron interacts with atoms in thermal motion in a monatomic gas in thermal equilibrium at material temperature, T. Most importantly, the free gas model assumes the scattering cross section is constant over the neutron energy range, which is usually a good approximation for light nuclei, but not for heavy nuclei where the scattering cross section may have several resonances in the epithermal region. Several researchers in the field have shown that the exact resonance scattering model is temperaturedependent, and neglecting the resonances in the lower epithermal range can under-predict resonance absorption due to the upscattering phenomenon mentioned above, leading to an over-prediction of keff by several hundred pcm. Existing methods to address this issue involve changing the neutron weights or implementing an extra rejection scheme in the free gas sampling scheme, and these all involve performing the collision analysis in the center-of-mass frame, followed by a conversion back to the laboratory frame to continue the random walk of the neutron. The goal of this paper was to develop a sampling methodology that (1) accounted for the energydependent scattering cross sections in the collision analysis and (2) was performed in the laboratory frame,avoiding the conversion to the center-of-mass frame. The energy dependence of the scattering cross section was modeled with even-ordered polynomials (2nd and 4th order) to approximate the scattering cross section in Blackshaw’s equations for the moments of the differential scattering PDFs. These moments were used to sample the outgoing neutron speed and angle in the laboratory frame on-the-fly during the random walk of the neutron. Results for criticality studies on fuel pin and fuel assembly calculations using methods developed in this dissertation showed very close comparison to results using the reference Dopplerbroadened rejection correction (DBRC) scheme.},

doi = {10.1080/00295639.2017.1294931},

journal = {Nuclear Science and Engineering},

number = 1,

volume = 187,

place = {United States},

year = {Fri May 26 00:00:00 EDT 2017},

month = {Fri May 26 00:00:00 EDT 2017}

}