On the exact theory of the slowing-down of neutrons in an infinite homogeneous medium

Abstract

The object of this paper is to study the stationary energy distribution of neutrons slowed down in an infinite homogeneous absorbing medium. In particular, by confining the discussion to the field of the real variable, the following two problems will be considered: 1) The existence, for any scattering and capture law, of a formally exact solution of the Boltzmann equation; 2) The asymptotic behavior of this solution. By assuming a constant scattering cross-section, some details are given for the three practical cases of slowing down : without capture, with constant capture and with l/v-capture. For the last case, curves representing the exact solution evaluated numerically are shown.