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Home / Publications / Journals / Nuclear Science and Engineering / Volume 187 / Number 1

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

Eva E. Davidson, William R. Martin

Nuclear Science and Engineering / Volume 187 / Number 1 / July 2017 / Pages 1-26

Technical Paper /

Received:July 7, 2016
Accepted:January 7, 2017
Published:July 3, 2017

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 paper 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 temperature dependent, and neglecting the resonances in the lower epithermal range can underpredict resonance absorption due to the upscattering phenomenon mentioned above, leading to an overprediction 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 (CM) 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 energy-dependent scattering cross sections in the collision analysis and (2) was performed in the laboratory frame, avoiding the conversion to the CM frame. The energy dependence of the scattering cross section was modeled with even-ordered polynomials (second and fourth order) to approximate the scattering cross section in Blackshaw’s equations for the moments of the differential scattering probability distribution functions. 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 paper showed very close comparison to results using the reference Doppler-broadened rejection correction scheme.

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