Neutron transport in plane geometry with general anisotropic, energy-dependent scattering

Journal Article · Sat Oct 01 04:00:00 EDT 1977 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.523173· OSTI ID:7316090

Gibbs, A G; Larsen, E W

We consider the neutron transport equation in plane geometry with a general energy-dependent anisotropic scattering kernel. We construct the solution of the subcritical half-space albedo problem as a contour integral around the positive half of the spectrum of a reduced transport operator K. The integrand involves the boundary data and two operators which provide the Wiener--Hopf factorization of a third operator contained in (lambdaI-K)/sup -1/. Bounds are obtained for the location of the spectrum of K in the complex plane. We also obtain representations of the solutions of the Milne problem and of the full-space and half-space problems with sources. Various simplifications of the general theory, which occur for particular scattering models, are discussed as an illustration of the results.

• Research Organization: Battelle, Pacific Northwest Laboratory, Richland, Washington 99352
• OSTI ID: 7316090
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 18:10; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

654003* -- Radiation & Shielding Physics-- Neutron Interactions with Matter
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANALYTICAL SOLUTION
EQUATIONS
INTEGRAL EQUATIONS
MILNE PROBLEM
NEUTRON TRANSPORT THEORY
SCATTERING
TRANSPORT THEORY