Effect of the knock-on electrons in the calorimetric mode of an underground muon detector

Calibrating underground detectors necessitates careful consideration of the passage of penetrating particles through matter. In muon detectors based on plastic scintillators, like the Underground Muon Detector of the Pierre Auger Observatory, the energy deposition within the plastic is significantly influenced by the generation of delta (knock-on) electrons in the surrounding ground as muons pass through. In this study, we analyzed the energy deposition by various particles impacting a 2.3 m deep underground detector and assessed its effect on the reconstruction of muon density in extensive air showers induced by energetic nuclei. Our results reveal that calibrating the calorimetric mode of these detectors using individual vertical muons introduces a reconstruction bias of up to 20% for proton showers with energies of 1017.5 eV. This bias arises from an increased energy deposition per muon, particularly near the shower axis, where more energetic muons are generated and, therefore, more knock-on electrons are produced.