Conservation of Neutrons in Time-Dependent Slowing Down

The time-dependent slowing down of neutrons in noncapturing media depends in an important way on how the energy-dependent mean-free-time between scatterings behaves as E → 0. For example, if the mean-free-time decreases, i.e., ν∑_s increases, as any positive power of E, the integrated density of neutrons does not remain constant in time. This anomalous behavior is discussed, noting both analogies in other physical processes and early references to the phenomenon of “nonconservation.” The analysis uses some unfamiliar solutions for slowing down in hydrogen, when the cross section has power-law variation; however, the general discussion is not limited to the equal mass case.