A New Method for Generating Probability Tables in the Unresolved Resonance Region
Abstract
One new method for constructing probability tables in the unresolved resonance region (URR) has been developed. This new methodology is an extensive modification of the singlelevel BreitWigner (SLBW) pseudoresonance pair sequence method commonly used to generate probability tables in the URR. The new method uses a Monte Carlo process to generate many pseudoresonance sequences by first sampling the average resonance parameter data in the URR and then converting the sampled resonance parameters to the more robust Rmatrix limited (RML) format. Furthermore, for each sampled set of pseudoresonance sequences, the temperaturedependent cross sections are reconstructed on a small grid around the energy of reference using the ReichMoore formalism and the LealHwang Doppler broadening methodology. We then use the effective cross sections calculated at the energies of reference to construct probability tables in the URR. The RML crosssection reconstruction algorithm has been rigorously tested for a variety of isotopes, including ^{16}O, ^{19}F, ^{35}Cl, ^{56}Fe, ^{63}Cu, and ^{65}Cu. The new URR method also produced normalized crosssection factor probability tables for ^{238}U that were found to be in agreement with current standards. The modified ^{238}U probability tables were shown to produce results in excellent agreement with several standard benchmarks, including the IEUMETFAST007 (BIG TEN),more »
 Authors:
 Georgia Inst. of Technology, Atlanta, GA (United States). Dept. of Nuclear and Radiological Engineering; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Reactor and Nuclear Systems Division
 Intitute for Radiological Protection (IRSN), Paris (France)
 Georgia Inst. of Technology, Atlanta, GA (United States). Dept. of Nuclear and Radiological Engineering
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Reactor and Nuclear Systems Division
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1361302
 Grant/Contract Number:
 AC0500OR22725
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Nuclear Science and Engineering
 Additional Journal Information:
 Journal Volume: 186; Journal Issue: 2; Journal ID: ISSN 00295639
 Publisher:
 American Nuclear Society  Taylor & Francis
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 97 MATHEMATICS AND COMPUTING; Unresolved resonance region; nuclear data processing; neutron cross sections
Citation Formats
Holcomb, Andrew M., Leal, Luiz C., Rahnema, Farzad, and Wiarda, Dorothea. A New Method for Generating Probability Tables in the Unresolved Resonance Region. United States: N. p., 2017.
Web. doi:10.1080/00295639.2016.1273632.
Holcomb, Andrew M., Leal, Luiz C., Rahnema, Farzad, & Wiarda, Dorothea. A New Method for Generating Probability Tables in the Unresolved Resonance Region. United States. doi:10.1080/00295639.2016.1273632.
Holcomb, Andrew M., Leal, Luiz C., Rahnema, Farzad, and Wiarda, Dorothea. Tue .
"A New Method for Generating Probability Tables in the Unresolved Resonance Region". United States.
doi:10.1080/00295639.2016.1273632. https://www.osti.gov/servlets/purl/1361302.
@article{osti_1361302,
title = {A New Method for Generating Probability Tables in the Unresolved Resonance Region},
author = {Holcomb, Andrew M. and Leal, Luiz C. and Rahnema, Farzad and Wiarda, Dorothea},
abstractNote = {One new method for constructing probability tables in the unresolved resonance region (URR) has been developed. This new methodology is an extensive modification of the singlelevel BreitWigner (SLBW) pseudoresonance pair sequence method commonly used to generate probability tables in the URR. The new method uses a Monte Carlo process to generate many pseudoresonance sequences by first sampling the average resonance parameter data in the URR and then converting the sampled resonance parameters to the more robust Rmatrix limited (RML) format. Furthermore, for each sampled set of pseudoresonance sequences, the temperaturedependent cross sections are reconstructed on a small grid around the energy of reference using the ReichMoore formalism and the LealHwang Doppler broadening methodology. We then use the effective cross sections calculated at the energies of reference to construct probability tables in the URR. The RML crosssection reconstruction algorithm has been rigorously tested for a variety of isotopes, including 16O, 19F, 35Cl, 56Fe, 63Cu, and 65Cu. The new URR method also produced normalized crosssection factor probability tables for 238U that were found to be in agreement with current standards. The modified 238U probability tables were shown to produce results in excellent agreement with several standard benchmarks, including the IEUMETFAST007 (BIG TEN), IEUMETFAST003, and IEUCOMPFAST004 benchmarks.},
doi = {10.1080/00295639.2016.1273632},
journal = {Nuclear Science and Engineering},
number = 2,
volume = 186,
place = {United States},
year = {Tue Apr 18 00:00:00 EDT 2017},
month = {Tue Apr 18 00:00:00 EDT 2017}
}

URR (Unresolved Resonance Region) computer code: A code to calculate resonance neutron crosssection probability tables, Bondarenko selfshielding factors, and selfindication ratios for fissile and fertile nuclides
The URR computer code has been developed to calculate crosssection probability tables, Bondarenko selfshielding factors, and self indication ratios for fertile and fissile isotopes in the unresolved resonance region. Monte Carlo methods are utilized to select appropriate resonance parameters and to compute the cross sections at the desired reference energy. The neutron cross sections are calculated by the singlelevel BreitWigner formalism with s, p, and dwave contributions. The crosssection probability tables are constructed by sampling the Doppler broadened crosssection. The various shelfshielded factors are computed numerically as Lebesgue integrals over the crosssection probability tables. 6 refs. 
URR (Unresolved Resonance Region) computer code: A code to calculate resonance neutron crosssection probability tables, Bondarenko selfshielding factors, and selfindication ratios for fissile and fertile nuclides
The URR computer code has been developed to calculate crosssection probability tables, Bondarenko selfshielding factors, and selfindication ratios for fertile and fissile isotopes in the unresolved resonance region. Monte Carlo methods are utilized to select appropriate resonance parameters and to compute the cross sections at the desired reference energy. The neutron cross sections are calculated by the singlelevel BreitWigner formalism with s, p, and dwave contributions. The crosssection probability tables are constructed by sampling by Doppler broadened crosssections. The various selfshielding factors are computer numerically as Lebesgue integrals over the crosssection probability tables. 
Fitting multiband probability tables to the unresolved resonance region
An alternate procedure for the generation of cross section probability tables, which is based upon an entirely different principle than the Probability Table method, has been developed by D.E. Cullen and is applicable to any cross section energy range where there is sufficient structure in the cross sections. When this multiband method is adapted to the unresolved resonance range, the multiband parameters are determined from moments of the unresolved selfshielded cross sections assuming a Bondarenko form for the selfshielding across individual resonance sequences. The procedure is described. (WHK)