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Diffusion Parameters for Thermal Neutrons

R. Kladnik.

Nuclear Science and Engineering

Volume 17 / Number 2 / October 1963 / Pages 185-191


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The stationary velocity-dependent transport equation for an infinite homogeneous source-free medium is solved by expanding the solution into a power series of the eigenvalues κ = 1/L. The integral equations, obtained by equating terms with the same κ0m, have been solved numerically on the IBM 704 computer using the iteration procedure. The monatomic gaseous model for the scattering process has been used assuming scattering cross section to be independent of the relative velocity and the absorption cross section to follow the 1/v law. A general expression for the diffusion coefficient in the absorbing medium has been obtained whereas the diffusion length L is obtained as the only positive real root of an algebraic equation whose order depends on the degree of the approximation. A comparison between the calculated and measured values of the diffusion length in poisoned water shows that water can be described roughly as a monatomic gas with A = 1.9 and ls(∞) = 0.40 cm. An empirical formula for the effective temperature of the neutron velocity distribution is evaluated.

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