Response of G-NUMEN LaBr$_3$(Ce) detectors to high counting rates

The G-NUMEN array is the future gamma spectrometer of the NUMEN experiment (Nuclear Matrix Element for the Neutrinoless double beta decay), to be installed around the object point of the MAGNEX magnetic spectrometer at the INFN-LNS laboratory. This project aims at exploring Double Charge Exchange (DCE) reactions in order to obtain crucial information about the neutrinoless double beta decay ($0\nu\beta\beta$). The primary objective of the G-NUMEN array is to detect the gamma rays emitted from the deexcitation of the excited states populated via DCE reactions with good energy resolution and detection efficiency, amidst a background composed of transitions from competing reaction channels with far higher cross sections. To achieve this, the G-NUMEN signals will be processed in coincidence with those generated by the detection of the reaction ejectiles in the MAGNEX Focal Plane Detector(FPD). Under the expected experimental conditions, G-NUMEN detectors will operate at high counting rates, of the order of hundreds of kHz per detector, while maintaining excellent energy and timing resolutions. The complete array will consist of over 100 LaBr$_3$(Ce) scintillators. Initial tests have been conducted on the first detectors of the array, allowing for the determination of their performance at high rates.