Aimed at progress in 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 propose a new algorithm that can identify whether the gamma rays escape from the detectors or not, in addition to the scattering order determination. This algorithm also corrects incoming gamma-ray energies for escape events. The developed algorithm is based on the maximum likelihood method, and we present a general formalism of likelihood functions describing physical interactions inside the detector. We also introduce several approximations in the calculation of the likelihood functions for efficient computation. For validation, we have applied the algorithm 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 mission, and have confirmed that it works successfully for up to 8-hit events. The proposed algorithm can be used for next-generation MeV gamma-ray missions featured by large-volume detectors, e.g., GRAMS and AMEGO.
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