Neutron Slowing Down and Thermalization

The theory behind the generation of thermal cross sections is presented, concentrating on the phonon expansion method. Examples are given for graphite, water, heavy water, and zirconium hydride. The graphite example demonstrates incoherent inelastic scattering and coherent elastic scattering for crystalline solids. The water example demonstrates incoherent inelastic scattering for liquids with diffusive translations. Heavy water adds a treatment for intermolecular coherence. Zirconium hydride shows the effects of the “Einstein oscillations” of the hydrogen atoms in a cage of zirconium atoms, and it also demonstrates incoherent elastic scattering. Neutron thermalization is introduced using Monte Carlo simulations of several systems, followed by multigroup discrete-ordinates and collision-probability methods. Size effects in thermalization are demonstrated. Steady-state slowing down is discussed by illustrating typical cross-section data, and showing slowing down by elastic scattering, inelastic scattering, and resonance cross sections in the narrow resonance approximation. Intermediate resonance self-shielding effects are introduced using the NJOY flux calculator and the WIMS implementation. The effects of time and space on slowing down are demonstrated using Monte Carlo simulations, and the theoretical basis is summarized.