Spatial moments in nonstationary single-velocity problem of transport theory with isotropic scattering. 1. Point instant source

The equations for the moments of the particles distribution in the single-velocity problem on the transport theory in the uniform medium with isotropic scattering are derived. The exact point solutions for five even moments (from the second one to the tenth one) are determined in the analytical and numerical from through the Laplace transformation method. Algorithm for calculating the arbitrary order moments is presented. The convergence by t → ∞ to the diffusion approximation moments is studied and it is established that it is of nonequilibrium character: the higher moments by any t essentially differ from the diffusion ones. The physical causes of such a behaviour of the moments are discussed