Measurement of the $^{99}$Tc $β$ spectrum with Silicon Drift Detectors
The need for reliable calculations of Nuclear Matrix Elements is compelling for the next generation of neutrinoless double-beta decay experiments. This requires nuclear models to be validated against experimental data, such as non-unique forbidden $β$ decays, which have been found sensitive to details in nuclear calculations, most importantly to the renormalization of the axial and vector currents. %, parametrized as a quenching of $g_A$ and $g_V$. We report here a measurement of the 2$^{nd}$ forbidden $^{99}$Tc $β$ spectrum performed for the first time with Silicon Drift Detectors, state-of-the-art semiconductor detectors for low-energy spectroscopy. We designed a novel hybrid spectrometer using a LYSO crystal read by a SiPM to precisely calibrate our main detector and to accurately measure the background. We then compared our measured spectrum with one obtained using cryogenic calorimeters, as well as with predictions from the Realistic Shell Model. Starting from Realistic Shell Model calculations performed with Bare decay operators, we carried out a Bayesian analysis to extract the average quenching factors required to reproduce both the measured spectral shape and the experimental half-life, obtaining $q_{g_A}=0.40(1)$ and $q_{g_V}=0.47(1)$. These values quantify the average renormalization of the axial and vector currents, respectively, and were compared with those predicted by RSM calculations employing Effective decay operators, thereby providing a benchmark for assessing the ability of the model to describe the second-forbidden $β$ decay of $^{99}\mathrm{Tc}$. More broadly, this comparison tests the reliability of the theoretical framework also used to predict $0νββ$ nuclear matrix elements.