The Statistics of the Number of Neutron Collisions Prior to Absorption

We propose a simple analytical model to describe the statistics of the number of collisions undergone by fast neutrons during slowing down until they are absorbed. We assume that the moderator is homogeneous and account for scattering and absorption, but we do not consider thermalization. Although the problem cannot be solved in a compact form, a simple recurrent formula provides the solution in a very transparent way. The model can be readily evaluated numerically, and the results are in excellent agreement with the corresponding Monte Carlo simulations. Both the mean number and the variance of the number of collisions are calculated. The results are discussed and compared with the classical case of neutron slowing down to or past a given energy in a moderating medium without absorption.