Polarization constraints on gamma-ray event circles in compton scatter instruments

A number of researchers are developing novel Compton scatter instruments, designed to track γ-ray interactions within their detector volume with high spatial and spectral resolution. Many of these instruments are designed as Compton imagers, where the initial photon direction can be determined through the Compton scatter formula to within an event circle on the sky for astronomy, or an event cone for near-field imaging. If the γ-ray scatters more than once before photoabsorption in the instrument, it is possible to use the polarization-dependent Klein–Nishina differential cross-section to constrain the probability density of the initial photon direction along the event circle. Here we derive this probability density, which will improve the imaging capabilities and sensitivities of Compton imagers.