Resonance absorption of neutrons in an infinite homogeneous medium

Abstract

We consider the problem of the slowing down of neutrons in an infinite homogeneous medium with strong resonance absorption and uniformly distributed neutron sources.

The solution of the adjoint equation gives the probability that a neutron of energy E escapes resonance capture during the process of moderation down to a certain limiting energy. The solutions of the original and the adjoint problem enable one to use a perturbation functional to take into account the influence of Doppler broadening of the resonance level in the resonance integral.

The methods developed are applied to the calculation of the collision density and the resonance integrals for the first level of ²³⁸U (E₀ = 6·7 eV) in pure uranium and in UO₂.