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Milne Problem for Thermal Neutrons with Absorption

Jacek Arkuszewski

Nuclear Science and Engineering

Volume 27 / Number 1 / January 1967 / Pages 104-119


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The Wiener-Hopf factorization method has been applied to the energy-dependent Milne problem with simple separable isotropic kernel and absorption of 1/vn type. Extensive numerical calculations for free gas scattering cross sections have been performed and their partial results are presented. Discussion of these results, namely the critical absorption coefficients, discrete space eigenvalues, extrapolation distances, and emergent neutron distributions confirm the earlier assertion of Williams that critical absorption as well as asymptotic spatial parameters depend rather weakly upon the energy exchange mechanism, being more sensitive to the energy dependence of the mean free path. Nelkinapos;s model for water has also been studied, in the form of a separable kernel. The critical absorption as well as discrete spatial eigenvalues for this case appear to be in good agreement with values obtained by Honeck for the full isotropic Nelkin kernel.

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