similar values generated using MCNP5. To best present comparisons with the Monte Carlo
results (since Monte Carlo statistical errors were lowest (<3% relative) along the central axis),
we consider a slice through the central axis of the model. It is important to note that even with
the use of volumetric "mesh tallies" that yield global fluxes across a grid spanning the Monte
Carlo geometry, the statistical uncertainty associated with each mesh tally site, particularly those
distal or off-axis from the source region, can routinely exceed 40% or more, limiting their utility
in practical applications.
Figure 2-10 shows that for this particular problem, the relative differences in scalar fluxes
between all deterministic solutions and the Monte Carlo reference increased adjacent to the
gamma source. Also, for this problem, deterministic results using BUGLE-96 and CEPXS
demonstrated good results in this water phantom, and results were within the statistical
uncertainty of the Monte Carlo method. Subsequent investigation of these solutions could not
attribute this behavior to grid density, quadrature, or anisotropic scattering order. We did
determine that the relative fluxes of the Monte Carlo results (converged to <3% relative error),
particularly near the source, were strongly dependent upon the precise method by which the
geometric volume tallies were defined, and this could easily account for the differences
computed near the source. On the other hand, cross section libraries such as CEPXS provide
flexibility in defining energy group width not available in BUGLE-96. In general, differences
can be attributed to the energy group structure of the libraries. Results here demonstrate the
importance of library benchmarking exercises for specific problem applications. This may also
suggest that in some cases the use of an equivalent surface source fluence prescribed on the
entering phantom surface may be more practical to implement for dosimetry in the phantom,
discussed in the next section.