Reconstruction of multiple Compton scattering events in MeV gamma-ray Compton telescopes towards GRAMS: the physics-based probabilistic model

Aimed at progress in mega-electron volt (MeV) gamma-ray astronomy, which has not yet been well-explored, Compton telescope missions with a variety of detector concepts have been proposed so far. One of the key techniques for these future missions is an event reconstruction algorithm that is able to determine the scattering orders of multiple Compton scattering events and to identify events in which gamma rays escape from the detectors before they deposit all of their energies. We revisit previous event reconstruction methods and propose a modified algorithm based on a probabilistic method. First, we present a general formalism of the probabilistic model of Compton scattering describing physical interactions inside the detector and measurement processes. Then, we also introduce several approximations in the calculation of the probability functions for efficient computation. For validation, the developed algorithm has been applied to simulation data of a Compton telescope using a liquid argon time projection chamber, which is a new type of Compton telescope proposed for the GRAMS project. We have confirmed that it works successfully for up to 8-hit events, including correction of incoming gamma-ray energies for escape events. The proposed algorithm can be used for next-generation MeV gamma-ray missions featured by large-volume detectors, e.g., GRAMS.