Reaction planes, polarization planes and scattering planes in γ -ray linear polarization events

The relative angles between reaction planes, polarization planes and scattering planes are determined, for laboratory based $\gamma$-ray linear polarization events. The coordinates of the relevant Compton scattering events and photo-electric absorption events are also determined. The results were checked using modelling calculations to determine the statistical averages of the Klein–Nishina formula for a hypothetical compact polarimeter consisting of four closely packed cuboid detectors. The cuboids and their spacing were designed to have the same solid angle correction factors as those of a composite 'clover' EUROGAM detector. The linear polarization sensitivities obtained from these calculations compared reasonably with those which have been measured experimentally at 197, 415, 423, 847 and 1369 keV for the composite 'clover' EUROGAM detector, giving confidence in the geometric results. It is shown that the electronic thresholds set on polarimeter detectors are critical in maximizing linear polarization sensitivities and statistics at incident $\gamma$-ray energies around 200 keV. The modelling calculations show that linear polarization sensitivities, for cuboid detectors, do not follow the same energy dependence as the Klein–Nishina formula for point detectors.