Program - Brookhaven National Laboratory

sensitivity/uncertainty methodology that identifies the improved accuracy of nuclear data needed for computation
of responses within their design tolerances. Because the cost of measuring and evaluating improved
nuclear data is automatically optimized by this method, its application is expected to increase the effectiveness
of nuclear data efforts. Our cost-minimization method combines differential and integral nuclear data
measurements into a unified framework for the first time. Furthermore, it is directly applicable to thermal
and intermediate neutron energy systems because it addresses the implicit neutron resonance self-shielding
effects that are essential to accurate modeling of thermal and intermediate systems. Details of the inverse
sensitivity/uncertainty methodology and its application will be demonstrated in the full paper. Notice:
This abstract has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the U.S.
Department of Energy. The United States Government retains and the publisher, by accepting the article
for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable,
world-wide license to publish or reproduce the published form of this manuscript, or allow others to
do so, for United States Government purposes. The U.S. Department of Energy Nuclear Criticality Safety
Program sponsored the work that is presented in this paper.
[1] SCALE: A Comprehensive Modeling and Simulation Suite for Nuclear Safety Analysis and Design,
ORNL/TM-2005/39, Version 6.1, Oak Ridge National Laboratory, Oak Ridge, Tennessee, June 2011.
Available from Radiation Safety Information Computational Center at Oak Ridge National Laboratory as
CCC-785.
RC 4 11:40 AM
Generation of an S(α,β) Covariance Matrix by Monte Carlo Sampling of the Phonon
Frequency Spectrum
Jesse C. Holmes, Ayman I. Hawari
Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695 USA
Formats and procedures are currently established for representing covariance data in ENDF library files
for many neutron reaction types. However, no standard exists for thermal neutron scattering cross section
covariance data. These cross sections depend on the material dynamic structure factors, or S(α,β). The
structure factors are a function of the phonon frequency spectrum, or density of states (DOS). Published
ENDF thermal libraries are commonly produced by modeling codes, such as NJOY/LEAPR, which utilize
the DOS as the fundamental input and directly output S(α,β) in ENDF format. To calculate covariances
for the computed S(α,β) data, information about uncertainties in the DOS is required. The DOS is itself
a PDF of available energy transfer quanta and can be determined by several methods. This work uses
Hellmann-Feynman forces and lattice dynamics in the harmonic approximation to construct a dynamical
matrix for natural silicon in α-quartz. The DOS is produced by randomly sampling wave-vectors (and their
associated phonon frequency eigenvalues) in the first Brillouin zone [1]. By analysis of this methodology,
the DOS can be parameterized pointwise into a set of random variables with a multivariate-PDF describing
feature uncertainties in energy and in relative magnitude. This allows Monte Carlo generation of a set
of perturbed spectra which can be sampled to produce the S(α,β) covariance matrix. With appropriate
sensitivity matrices, the S(α,β) covariance matrix can be propagated to generate covariance matrices for
integrated cross sections, secondary energy distributions, and coupled energy-angle distributions.
Corresponding author: Ayman I. Hawari
[1] B. D. Hehr and A. I. Hawari, ”Calculation of the Thermal Neutron Scattering Cross Sections of α-
Quartz (SiO2),” PHYSOR-2008: International Conference on the Physics of Reactors, Nuclear Power: A
Sustainable Resource, Interlaken, Switzerland (2008).
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