Computation of Temperature-Dependent Legendre Moments of a Double-Differential Elastic Cross Section

Conference · Sat Jan 01 04:00:00 EST 2011

OSTI ID:1018597

Arbanas, Goran ^[1]; Dunn, Michael E ^[1]; Larson, Nancy M ^[1]; Leal, Luiz C ^[1]; Williams, Mark L ^[1]; Becker, B. ^[2]; Dagan, R ^[3]

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1. ORNL
2. Rensselaer Polytechnic Institute (RPI)
3. Institut fur Neutronenphysik und Reaktortechnik

A general expression for temperature-dependent Legendre moments of a double-differential elastic scattering cross section was derived by Ouisloumen and Sanchez [Nucl. Sci. Eng. 107, 189-200 (1991)]. Attempts to compute this expression are hindered by the three-fold nested integral, limiting their practical application to just the zeroth Legendre moment of an isotropic scattering. It is shown that the two innermost integrals could be evaluated analytically to all orders of Legendre moments, and for anisotropic scattering, by a recursive application of the integration by parts method. For this method to work, the anisotropic angular distribution in the center of mass is expressed as an expansion in Legendre polynomials. The first several Legendre moments of elastic scattering of neutrons on U-238 are computed at T=1000 K at incoming energy 6.5 eV for isotropic scattering in the center of mass frame. Legendre moments of the anisotropic angular distribution given via Blatt-Biedenharn coefficients are computed at ~1 keV. The results are in agreement with those computed by the Monte Carlo method.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: NNSA USDOE - National Nuclear Security Administration (NNSA)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1018597
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR DISTRIBUTION
CROSS SECTIONS
Doppler
ELASTIC SCATTERING
LEGENDRE POLYNOMIALS
MONTE CARLO METHOD
NEUTRONS
SCATTERING
broadening
differential
elastic
resonance
scattering