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

TL;DR

This paper introduces a physics-based approach using random-matrix theory to generate probability tables for nuclear cross sections, providing a theoretically grounded alternative to traditional methods.

Contribution

The authors develop a novel method employing the GOE-$S$-matrix model to calculate and convert cross sections into probability tables, enhancing the theoretical foundation of the process.

Findings

Probability tables at 0 K are qualitatively similar to traditional methods.

Optimal model parameters are determined based on convergence of average cross sections.

Statistical uncertainties depend on the number of ladders used.

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.