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Discrete Eigenvalues of Case Spectrum with Anisotropic Scattering

D. C. Sahni, R. G. Tureci

Nuclear Science and Engineering / Volume 191 / Number 2 / August 2018 / Pages 121-135

Technical Paper /

Received:January 25, 2018
Accepted:April 7, 2018
Published:July 13, 2018

Discrete eigenvalues of a one-speed linear transport equation with anisotropic scattering are studied. It is shown that there is only one pair of real discrete eigenvalues for linear, quadratic, or triplet scattering for a nonmultiplicative medium. For a multiplicative medium there is one imaginary pair of eigenvalues or at most four eigenvalues. These can form one real and one imaginary pair, two imaginary pairs, or a quartet. The range of parameters for these different situations is derived analytically. These are then supported by numerical results that are tabulated in tables for each type of scattering.