Neutron slowing down and transport in a medium of constant cross section. I. Spatial moments

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Abstract
Some aspects of the problem of neutron slowing down and transport have been investigated in an infinite medium consisting of a single nuclide scattering elastically and isotropically without absorption and with energy‐independent cross sections. The method of singular eigenfunctions has been applied to the Boltzmann equation governing the Laplace transform (with respect to the lethargy variable) of the neutron flux. Formulas have been obtained for the lethargy dependent spatial moments of the scalar flux applicable in the limit of large lethargy. In deriving these formulas, use has been made of the well‐known connection between the spatial moments of the Laplace‐transformed scalar flux and the moments of the flux in the ’’eigenvalue space.’’ The calculations have been greatly aided by the construction of a closed general expression for these ’’eigenvalue space’’ moments. Extensive use has also been made of the methods of combinatorial analysis and of computer evaluation, via FORMAC, of complicated sequences of manipulations. It has been possible to obtain for materials of any atomic weight explicit corrections to the age theory formulas for the spatial moments M2n(u), of the scalar flux, valid through terms of order of u−5. Higher order correction terms could be obtained at the expense of additional computer time. The evaluation of the coefficients of the powers of n, as explicit functions of the nuclear mass, represent the end product of this investigation.