The collision, scattering, and absorption differential cross sections for t
wo-photon Compton scattering in both the forward and backward hemispheres h
ave been measured as a function of independent final photon energy for 0.66
2 MeV incident gamma photons as produced by an 8-Ci Cs-137 radioactive sour
ce. The two simultaneously emitted photons in this process are detected in
coincidence using two NaI(TI) scintillation spectrometers and 30 nsec timin
g electronics: Many systematic effects contributing to true events have bee
n taken into account. The differential cross-section values agree with the
theory within experimental estimated error. [S1050-2947(99)03912-8].