Multiple scattering and transport of neutrons

The collision term in the quantum-mechanical transport equation of neutrons derived by Osborn et al. (1965) is reformulated with the aid of the S-matrix theory of scattering, and the usual transport equation is generalized to include the effect of multiple scattering of neutrons. It is shown that the random phase approximation is no longer necessary by virtue of the adiabatic switching off of interactions.

A semi-quantitative analysis of the effect of multiple scattering is made on the basis of the free gas model, and it is concluded that the validity of the usual transport equation depends on the spatial resolution, the energy of the neutron under consideration and the energy spectrum of all neutrons. The usual transport equation is not valid for a very cold neutron (of energy below 00001 cV), and not generally valid for a cold neutron when the energy spectrum of the neutrons is softer than a Maxwellian. It is also inapplicable to a neutron of any energy when the spatial resolution is not much less than the mean free path of the neutron.