Neutron slowing down in a detector with absorption

In a recent paper, a simple analytical model to describe the statistics of the number of scattering collisions undergone by fast neutrons as they slow down until they are absorbed was presented. In that study, it was assumed that the moderator was infinite and homogeneous and accounted for scattering and absorption by a single nuclear species. In the present paper, that methodology is extended to the more realistic case of neutron slowing down in a homogeneous mixture. The formulas are derived and evaluated numerically, and the results are found to be in very good agreement with corresponding Monte Carlo simulations. The average value of the number of collisions that a neutron undergoes before being captured is computed. The results for a capture-gated detector composed of hydrogen, carbon, and boron are discussed.