  To combat the risk of nuclear smuggling, radiography systems are deployed at
ports to scan cargo containers for concealed illicit materials. Dual energy
radiography systems enable a rough elemental analysis of cargo containers due
to the $Z$-dependence of photon attenuation, allowing for improved material
detection. This work studies the capabilities for atomic number discrimination
using dual energy MeV systems by considering dual energy $\{6, 4\}$ MeV, $\{10,
6\}$ MeV, and $\{10, 4\}$ MeV bremsstrahlung beams. Results of this analysis
show that two different pure materials can sometimes produce identical
transparency measurements, leading to a fundamental ambiguity when
differentiating between materials of different atomic numbers. Previous
literature has observed this property, but the extent of the limitation is
poorly understood and the cause of the degeneracy is generally inadequately
explained. This non-uniqueness property stems from competition between
photoelectric absorption and pair production and is present even in systems
with perfect resolution and zero statistical noise. These findings are
validated through Monte Carlo transparency simulations. Results of this study
show that currently deployed commercial radiographic systems are fundamentally
incapable of distinguishing between high-$Z$ nuclear materials and
miscellaneous mid-$Z$ cargo contents.
