Arbitrary Order Statistical Moments of Neutron Energy and Lethargy Across Multiple Collisions During Neutron Moderation Without Absorption

We revisit the classical problem of neutron moderation in an infinite medium without absorption. We consider the multiscattered collision densities F1E,F2E,… denoting the collision densities for neutrons that have undergone 1, 2, ... collisions, and develop a recursive formula that allows for expectation values taken over the density FNE to be alternatively expressed in terms of the preceding density FN−1E. We apply the formula to recursively and efficiently derive the statistical moments for neutron energy and lethargy, up to arbitrary order, across multiple collisions. We also investigate some implications of the derived statistical moments on the problem of estimating the number of collisions required to slow down a neutron.