Physics-based method for generating probability table using random-matrix approach

TL;DR

This work presents a GOE-S-matrix based method to generate probability tables for neutron-induced cross sections in the unresolved resonance region, addressing the unitarity and interference shortcomings of traditional approaches. By constructing the scattering matrix from a GOE Hamiltonian and channel couplings, the method yields cross sections and NJOY-like probability tables without assuming fixed resonance distributions. Convergence analyses show that using a modest level count and a central energy range provides results close to evaluated data, with RMSPE decreasing as the ladder count increases and reaching about 1% at high ladder counts. The approach offers a physically grounded, unitarity-preserving alternative to SLBW for URR data, with implications for uncertainty quantification and reactor physics calculations.

Abstract

We develop a new method for generating probability tables based on a solid theoretical foundation. The fluctuating cross sections are calculated using the GOE-$S$-matrix model, in which the Gaussian Orthogonal Ensemble (GOE) is incorporated into the calculation of the scattering ($S$) matrix. The calculated cross sections are then converted into the probability tables in the same manner as in NJOY. Using $^{238}$U and $^{239}$Pu as target nuclei, we determine the optimal model parameters based on the convergence behavior of the average cross sections. The statistical uncertainty of the probability tables is examined as a function of the number of ladders. We demonstrate that the probability tables calculated at 0 K are qualitatively comparable with those calculated using the conventional single-level Breit-Wigner formalism, albeit we observe some local differences due to requisite unitality for the $S$ matrix.

Figures (9)

• Figure 1: Schematic illustration of the cross section (left) and the probability table generated from the corresponding cross section (right)
• Figure 2: The eigenvalue distribution of 0.1 million realizations of a $10\times10$ GOE.
• Figure 3: Average total (top) and capture (bottom) cross sections for $^{238}$U as a function of $L$.
• Figure 4: Average total (top), capture (middle), and fission (bottom) cross sections for $^{239}$Pu as a function of $L$.
• Figure 5: The probability (top) and cumulative probability (bottom) as functions of the average cross sections for $^{238}$U at an incident neutron energy of 20 keV. The results for elastic scattering are scaled by a factor of 10 along the $x$-axis.