Diffusion length calculations in water

Abstract

An extensive series of calculations have been performed to determine the asymptotic neutron energy spectra and diffusion lengths in water poisoned by absorbers like boron, cadmium and gadolinium at different concentrations. The effect of chemical binding has been studied by comparing the results obtained by using the well-known Nelkin model of water with the free-gas model for hydrogen. Diffusion theory has been used in making the calculations; however, to test the validity of the diffusion approximation, in a few cases we have also made some transport theory calculations and compared the two results. We find that even for fairly large absorptions (i.e. for $\text{κ}\text{Σ}{}_{\mathrm{<mtext>min</mtext>}}\text{≈ 0·7–0·8}$) diffusion theory gives results which compare well with those obtained by using transport theory.