AgReO4 microcalorimeters are planned to be used again in the next generation of calorimetric neutrino mass experiments with sensitivity down to 0.2 eV. The understanding and characterization of all possible sources of systematic uncertainties is crucial. In this work we focus on two of these sources, which have been studied in the 10 detectors of the Milano AgReO4 array experiment (MIBETA): a) the solid-state Beta Environmental Fine Structure (BEFS) observed for the first time in AgReO4; b) the detector energy response for internal beta events, which has been investigated with a dedicated measurement using a 44Ti gamma source. The possible effects on neutrino mass experiments due to the incomplete understanding of these two aspects are discussed.
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