The response of the X and Gamma Imaging Spectrometer (XGIS) instrument onboard the Transient High Energy Sky and Early Universe Surveyor (THESEUS) mission, selected by ESA for an assessment phase in the framework of the Cosmic Vision M5 launch opportunity, has been extensively modeled with a Monte Carlo Geant-4 based software. In this paper, the expected sources of background in the Low Earth Orbit foreseen for THESEUS are described (e.g. diffuse photon backgrounds, cosmic-ray populations, Earth albedo emission) and the simulated on-board background environment and its effects on the instrumental performance is shown.
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