On MCNP Stochastic Volume Estimation Normalization

This paper resolves a perennial point of confusion regarding the source-weighting normalization factor recommended in the MCNP manual () to stochastically estimate the volume of a region within an enclosing inward-directed spherical surface source with radius . The normalization factor arises from the relationship between a sphere’ s mean chord length, its volume, and the values estimated by MCNP track-length tallies. A brief derivation is given that relates these quantities and results in the stated normalization. The correctness of this factor is demonstrated by estimating the volume of a variety of convex and nonconvex volumes. A heuristic demonstration of how biasing the inward-directed source reduces the statistical uncertainty of the stochastic volume estimate is also given, but a rigorous analysis of this improvement is left as future work.