Probabilistic Sequencing for Compton Imaging using the General Klein-Nishina Cross-Section

For a three-dimensional pixelated position-sensitive Cadmium Zinc Telluride detector, the order of interactions for each recorded full-deposition gamma-ray must be determined using the energy deposition and position of each interaction. Sequence reconstruction is necessary for Compton imaging and is often done via the probabilistic method. After making changes in GEometry ANd Tracking 4 (GEANT4), simulations show that using the general Klein-Nishina (KN) cross-section in the probabilistic method, instead of the conventionally used unpolarized KN cross-section, yields improvement when determining the order of interactions for a gamma-ray originating from a polarized or unpolarized source. For a 511 keV polarized source, the most sequencing improvement was seen for gamma-rays undergoing a scatter of $\left(\theta=90^{\circ}, \phi=90^{\circ}\right.$). The method using the general KN cross-section sequenced 4.83% more events correctly compared to the method using the unpolarized KN cross-section, for 3-interaction events, and 2.23% more events for 4-interaction events. For an 511 keV unpolarized source, the most improvement was also seen in the same scattering geometry, with an improvement of 2.05% for 3-interaction events. There was improvement in other scattering geometries for both source polarizations, however not as much as expected. Simulation is being revised to look for errors and the sequencing algorithm runtime is being optimized to get statistical uncertainties. Currently this work shows a way to improve the probabilistic method of sequence reconstruction by considering a gamma-ray’s initial and final polarization for each scatter. Improvements in sequence reconstruction for polarized sources would aid in Positron Emission Tomography and imaging polarized objects in high-energy astrophysics.