  This theoretical research aims to examine areas of the Compton cross section
of entangled annihilation photons for the purpose of testing for possible break
down of theory, which could have consequences for predicted optimal
capabilities of Compton PET systems.We provide maps of the cross section for
entangled annihilation photons for experimental verification.We introduce a
strategy to derive cross sections in a relatively straight forward manner for
the Compton scattering of a hypothetical separable, mixed and entangled states.
To understand the effect that entanglement has on the cross section for
annihilation photons, we derive the cross section so that it is expressed in
terms of the cross section of a hypothetical separable state and of a
hypothetical forbidden maximally entangled state.We find lobe-like structures
in the cross section which are regions where entanglement has the greatest
effect.We also find that mixed states do not reproduce the cross section for
annihilation photons, contrary to a recent investigation which reported
otherwise.We review the motivation and method of the most precise Compton
scattering experiment for annihilation photons, in order to resolve conflicting
reports regarding the extent to which the cross section itself has been
experimentally verified.
