How rapidly and how far do neutrons migrate?

Exact fonnulas are derived for the mean-squared displacements of neutrons from an isotropic point, line, or plane source in an infinite homogeneous medium. These displacements depend on the initial energy Eo of the neutron, the elapsed time t since the birth of the neutron, and the energy E of the neutron at time t. Our results are stated in terms of the solutions of three infinite-medium transport equations - it is not necessary to solve a space-d.ependent transport equation, even though the underlying transport problem is space-dependent. Also, time and energy-dependent diffusion equations are fonnulated, whose diffusion coefficients are chosen so that their solutions exactly preserve certain of the mean-squared displacement properties of the transport equation.