The search for neutrinoless double beta decay (0νββ) is considered one of the most sensitive ways to determine the nature of the neutrino. However, the sensitivity of future experiments directly depends on the accuracy of nuclear matrix elements (NMEs), which cannot be measured directly. They are calculated within nuclear models, and the uncertainties in these calculations limit the interpretation of results. Forbidden beta decays, especially second-forbidden ones like that of 99Tc, have proven to be stringent tests for such models: their half-lives and spectral shapes depend strongly on nuclear wave functions and the effective renormalization of weak currents. This work joins recent measurements of beta spectra from various isotopes but uses a fundamentally different detector: a silicon drift detector (SDD) instead of cryogenic calorimeters. This approach promises greater experimental flexibility and the possibility of direct background measurement.
The 99Tc source was prepared by sublimation drying: a drop of ammonium pertechnetate solution was deposited on a silicon substrate, frozen at -10°C, and dried under vacuum to obtain a uniform thin layer without large crystals. The source activity was about 10 Bq. The main detector is a silicon drift detector (SDD) with a thickness of 1 mm and an area of 8×8 mm, fabricated at FBK. A scintillating LYSO crystal containing natural lutetium-176 was placed nearby; its decay provides gamma and X-ray lines at energies of 55.8, 201.8, and 306.8 keV. The crystal was read out by a silicon photomultiplier (SiPM). Events in the SDD that coincided in time with a SiPM signal were used to calibrate the energy scale; events without coincidence were attributed to the beta decay of 99Tc. This scheme allowed calibrating the detector during data acquisition without subtracting the calibration source contribution from the spectrum. The measurement lasted six days in a vacuum chamber at a pressure of $10^{-5}$ mbar, with the detector cooled to -10°C to reduce leakage current. To account for spectral distortions (self-absorption in the source, electron backscattering, incomplete charge collection), a detailed simulation of the setup was built in GEANT4 with the Penelope physics package, optimized for low energies. Background was measured separately by replacing the technetium substrate with a clean silicon wafer and was approximated with an analytical model.
After event selection based on pulse rise time (to suppress edge effects), about 180 thousand events entered the analysis. The selection efficiency was found to be nearly energy-independent, as confirmed by the calibration peaks. The measured spectrum was compared with predictions from different models. First, the MetroBeta data obtained with magnetic metallic calorimeters were used as the input spectrum and convolved with the response function of our setup. The agreement was reasonable, although the formal p-value is small (chi-square 477 for 344 degrees of freedom), indicating possible unaccounted systematics in one of the works. Then, comparisons were made with calculations within the realistic shell model (RSM) using 'bare' and 'effective' decay operators, as well as with the phenomenological BetaShape model. Both versions of RSM describe the spectral shape better than BetaShape, with the calculation using 'bare' operators giving better agreement in shape but worse in half-life. This shows that the spectral shape and half-life provide complementary constraints. The final Bayesian analysis with five free parameters (quenching factors for axial and vector currents, source thickness, background amplitude, and Q-value) yielded average quenching factors $q_{gA}$ = 0.40(1) and $q_{gV}$ = 0.47(1). These values indicate significant quenching of both currents compared with 'bare' operators. RSM predictions with effective operators give $q_{gA}$ = 0.81 and $q_{gV}$ = 0.58, which move in the right direction but do not fully reproduce the extracted quenching. The Q-value determined in the fit was 291.6(7) keV, notably lower than the MetroBeta value of 295.82(16) keV. However, a reanalysis with a Gaussian prior on the Q-value from MetroBeta gave $q_{gA}$ = 0.42(1) and $q_{gV}$ = 0.43(1), meaning the conclusions about current quenching remain unchanged. The final fit describes the data well: chi-square 327 for 340 degrees of freedom, p-value around 70%.
The main result is independent confirmation that the renormalization of weak currents must be considered to describe forbidden beta decays, and quantitatively it turns out to be stronger than predicted by the modern realistic shell model with effective operators. This points to the incompleteness of the current theoretical description and provides a benchmark for improving models. Unlike work with cryogenic calorimeters, where the source is embedded in the detector and the background is modeled, here the background is measured directly and calibration is performed without subtracting the calibration source contribution. This approach reduces systematic uncertainties related to background modeling and makes the method attractive for systematic studies of many isotopes. The work also demonstrates that silicon drift detectors operating at room temperature can compete with cryogenic calorimeters in the precision of beta spectral shape measurements.
The method can be extended to other forbidden beta transitions, such as 36Cl and 94Nb, as planned by the ASPECT-BET collaboration. This will allow accumulating statistics across different nuclei and degrees of forbiddenness to identify systematic patterns in weak current renormalization. Further improvements in precision are possible with thinner sources (reducing self-absorption), optimized detector geometry, and longer data acquisition times. It is also important to resolve the discrepancy in the Q-value between this measurement and the MetroBeta data: this could indicate unaccounted systematic effects in one of the experiments. On the theoretical side, more refined calculations of effective operators are needed that would reproduce the extracted quenching without adjustable parameters.
The results directly affect the assessment of the reliability of nuclear matrix elements for neutrinoless double beta decay of 100Mo, which is one of the main candidates for future ton-scale experiments (CUPID, AMoRE). An improved understanding of weak current renormalization will reduce theoretical uncertainties in the sensitivity predictions of these experiments.
Measure the spectra of other forbidden beta decays (36Cl, 94Nb) with the same method and compare the obtained quenching factors with theoretical predictions. Conduct an independent high-precision measurement of the Q-value of 99Tc to clarify the cause of the discrepancy with MetroBeta.
In nuclear physics, the magnitude and origin of the renormalization of axial and vector currents in the nuclear medium remain an open question. This phenomenon is known as 'quenching' and manifests as a systematic underestimation of experimental beta transition probabilities compared with calculations using free nucleons. This work provides new quantitative constraints on quenching for the case of a second-forbidden transition, where the vector current contribution is also significant, which is rare in other channels. Understanding the quenching mechanism is necessary for reliable calculations of nuclear matrix elements not only for double beta decay but also for other weak processes in nuclei.
Technetium-99 is an artificial isotope with a half-life of 211 thousand years. It is produced in significant quantities as a fission product of uranium in nuclear reactors and is one of the main long-lived radionuclides in spent nuclear fuel. Its beta decay leads to ruthenium-99, which is stable.