Calculating Probability Tables for the Unresolved-Resonance Region Using Monte Carlo Methods

A new module, Probability tables for the Unresolved Region using Monte Carlo (PURM), has been developed for the AMPX-2000 cross-section-processing system. PURM uses a Monte Carlo approach to calculate probability tables on an evaluator-defined energy grid in the unresolved-resonance region. For each probability table, PURM samples a Wigner spacing distribution for pairs of resonances surrounding the reference energy (i.e., energy specified in the cross-section evaluation). The resonance distribution is sampled for each spin sequence (i.e., l-J pair), and PURM uses the ₃-statistics test to determine the number of resonances to sample for each spin sequence. For each resonance, PURM samples the resonance widths from a chi-square distribution for a specified number of degrees of freedom. Once the resonance parameters are sampled, PURM calculates the total, capture, fission, and scatter cross sections at the reference energy using the single-level Breit-Wigner formalism with appropriate treatment for temperature effects. Probability tables have been calculated and compared with NJOY. The probability tables and cross-section values that are calculated by PURM and NJOY are in agreement, and the verification studies with NJOY establish the computational capability for generating probability tables using the new AMPX module PURM.