Heterogeneity effect on neutron shielding in borated concrete and Monte Carlo-based cross section homogenization method for particle dispersed media

A Monte Carlo-based radiation transport calculation method to treat media containing randomly and uniformly dispersed spherical particles was developed by Shmakov et al. The method (hereinafter referred to as "SLD method") formulates effective homogenized cross sections for particle dispersed media. This paper discusses the applicability of the SLD method to neutron shielding in an ordinary concrete and a low-activation concrete containing small B₄C particles. If the absorber particles are not small enough, the heterogeneity effect needs to be treated for accurate dose or activation estimations. The direct heterogeneous representation of the small particles requires long computing time. The use of the SLD method could considerably reduce the computational burdens without reducing its accuracy. The heterogeneity effect on neutron shielding is significant below 10 eV. The homogeneous calculation underestimates the neutron absorption rate of ²³Na by 11% in the ordinary concrete and of ¹⁵¹Eu by 14% in the low-activation concrete containing 14-μm-diameter B₄C particles. MCNP 4C calculations with the SLD method agree very well with the direct heterogeneous calculations. The SLD method improves the figure of merit by a factor of 100 with respect to the direct heterogeneous calculation. (author)