The formulas derived from the synthetic model which were presented in the preceding paper are here applied to the evaluation of partial and total cross sections at thermal neutron energies for the commonly used moderators ${\mathrm{H}}_2$O, ${\mathrm{D}}_2$O, and ${\mathrm{C}}_6$${\mathrm{H}}_6$. The results of our analytical expressions for the scattering kernels ${\sigma }_0$($E_0$,E) and ${\sigma }_1$($E_0$,E) are compared with standard code calculations for well-separated incident neutron energies $E_0$. The related integral quantities, total cross section σ($E_0$), and average cosine of the scattering angle 〈cosθ($E_0$)〉, respectively, are also compared with experimental data and results from other theories. Within the framework of neutron diffusion theory, transport coefficients are readily evaluated using the model expressions and they are compared with available information over a wide range of temperatures.

• Received 7 November 1986

DOI:https://doi.org/10.1103/PhysRevA.36.5594