A Simple Calculation of the Time Dependence of the Second Spatial Moment

Consider one-speed neutron transport in an infinite medium. Let a neutron be released from the origin at time zero. In a recent paper, a probabilistic argument was used to derive an exact expression, for an arbitrary scattering law, giving the neutron’s mean square distance from the origin as a function of time. This result can be derived in a much simpler manner by merely forming the appropriate spatial and angular moments of the transport equation.