The analysis of the slowing down of a neutron pulse leads to a detailed analogy between the decay of a pulse in the fast regime versus the decay in the thermal energy region. It is found that the slope, α, of log N(t) versus log(t) depends on the system buckling, B2. An “α versus B2” curve exists that is analogous to the “λ versus B2” curve for thermal systems. Other analogies between fast and thermal time decay are discussed. These analogies exist despite the fact that no time eigenvalue exists for this slowing down problem.