[en] The asymptotic distribution of neutrons from a pulsed, high energy source in an infinite moderator has been obtained earlier in a 'diffusion' approximation. In that paper the cross section was assumed to be constant over the whole energy region and the time derivative of the first moment was disregarded. Here, first, an analytic expression is obtained for the density in a P₁ -approximation. However, the result is very complicated, and it is shown that an asymptotic solution can be found in a simpler way. By taking into account the low hydrogen scattering cross section at the source energy it follows that the space dependence of the distribution is less than that obtained earlier. The importance of keeping the time derivative of the first moment is further shown in a perturbation approximation