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The Density Distribution in the Steady-State Diffusion of Neutrons
Phys. Rev. 59, 136 – Published 15 January, 1941
DOI: https://doi.org/10.1103/PhysRev.59.136
Abstract
By carrying the method of Laplace transformations and inversions to its ultimate conclusion, an expression in closed form for the spatial distribution in density of diffusing particles is obtained. This derivation is valid both for the case of incident currents of particles upon the face of a half-infinite medium and for the case of source distributions within that medium. The final expressions are given in terms of a transcendental function and its zeros together with a definite integral, all of which require numerical evaluation. Such numerical calculations have not been performed, since the problem is principally of theoretical interest in the sense that these methods yield for the first time an exact nonseries solution of a well-known, and in this respect, unsolved integral equation. From an experimental point of view it is the ratio of activities at different points within the medium rather than the ratio of particle densities which is of principal interest. These quantities are not the same, and some results for the former based on the exact theory have already been given.
References (5)
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