Energy Distribution of Slow Neutrons Scattered from Solids

The sharp dependence on energy of the cadmium cross section for neutrons of energies near 0.35 ev has been used to investigate the energy distribution of 0.35-ev neutrons scattered through 90^∘{} by lead, aluminum, diamond, and graphite. The transmission of the scattered neutrons by cadmium filters was measured as a function of cadmium thickness and compared with cadmium transmissions calculated for an Einstein crystal model. In all cases agreement was obtained. For lead and aluminum at room temperature the simpler model of a gas of free atoms gave equally good agreement, a well-known behavior at high energies, but here applying when the temperature and neutron energy were only moderately greater than the Einstein temperature and much less than the binding energy. Theoretical formulas for the partial differential scattering cross sections for the two models are given in convenient form.