  We resolve a long standing question regarding the suitable effective
diffusion coefficient of the spherically-symmetric transport equation, which is
valid at long times. To that end, we generalize a transport solution in three
dimensions for homogeneous media, to include general collisional properties,
including birth-death events and linearly anisotropic scattering. This is done
by introducing an exact scaling law relating the Green function of the
pure-scattering case with the general collision case, which is verified using
deterministic and Monte-Carlo simulations. Importantly, the effective diffusion
coefficient is identified by inspecting the transport solution at long times.
