A deuterium-tritium neutron source is amplified when emitted into a body of material with appreciable (n,2n), (n,3n), and (n,f) cross sections. This amplification is described by a simple theory, approximating the strict integral transport description of the process. The distribution of neutrons in energy, from 14 MeV down to the (n,2n) threshold, is approximated by a generalized slowing down equation, which is similar in form to the infinite medium slowing down equation, and with average collision probabilities taking up the role of scattering fractions. Following a few collisions, the collision source spatial distribution resembles the fundamental mode flux distribution of a critical reactor. The average collision probability for such a source is, in diffusion theory, ∑tr/(∑tr + DB2), where B2 is the geometrical buckling of the system. This yields an expression of the form (αx+βx2)/(l + αx + βx2) for the average collision probability, where x is a representative optical thickness of the system. It has been shown by numerical means that this form for the average collision probability is generally true for centrally peaked sources in variously shaped bare bodies of any optical thickness.