Search for tri-nucleon decays of 76Ge in GERDA

Abstract

We search for tri-nucleon decays of ${}^{76}$Ge in the dataset from the GERmanium Detector Array (GERDA) experiment. Decays that populate excited levels of the daughter nucleus above the threshold for particle emission lead to disintegration and are not considered. The ppp-, ppn-, and pnn-decays lead to ${}^{73}$Cu, ${}^{73}$Zn, and ${}^{73}$Ga nuclei, respectively. These nuclei are unstable and eventually proceed by the beta decay of ${}^{73}$Ga to ${}^{73}$Ge (stable). We search for the ${}^{73}$Ga decay exploiting the fact that it dominantly populates the 66.7 keV ${}^{73m}$Ga state with half-life of 0.5 s. The nnn-decays of ${}^{76}$Ge that proceed via ${}^{73m}$Ge are also included in our analysis. We find no signal candidate and place a limit on the sum of the decay widths of the inclusive tri-nucleon decays that corresponds to a lower lifetime limit of 1.2$\times$10${}^{26}$ yr (90% credible interval). This result improves previous limits for tri-nucleon decays by one to three orders of magnitude.

Fig. 1

Scheme of the potential channels for tri-nucleon decay of ${}^{76}$Ge including the beta decays for the unstable daughter nuclei along with their half lives, beta decay Q values and neutron thresholds (all energies in keV and not to scale). Also shown are the metastable levels of ${}^{73}$Ge with energies of 66.7 keV and 13.3 keV and half lives of 0.499 s and 2.95 $\mathrm{\mu }$s, respectively. Figure adapted from [4]

Fig. 2

Cross sections of the GERDA experimental apparatus and an enlarged view of the central part (right), the germanium detector array enclosed by the LAr veto system [7]

Fig. 3

Energy levels of ${}^{73}$Ge populated by ${}^{73}$Ga beta decay [14]; see [4] for an update of some branching ratios, e.g. 5.9% to the 66.7 keV level. The ground state of ${}^{73}$Ge is never directly populated

Fig. 4

Simulated waveform of the decay of the 66.7 keV metastable state in ${}^{73}$Ge to the ground state via the intermediate 13.3 keV state. Details of the response of the amplifier to the signal are omitted

Fig. 5

Monte Carlo energy spectrum corresponding to $E_1$, the energy of the ${}^{73}$Ga decay to ${}^{73}$Ge and the subsequent gamma transition to its metastable state. The step at about 300 keV can be explained by the level scheme of ${}^{73}$Ge: 6% of ${}^{73}$Ga decays directly populate the metastable state. 78.6% of decays will populate a state at 364 keV which can transition to the metastable state releasing  297 keV which accounts for the step

Fig. 6

Monte Carlo energy spectrum corresponding to $E_2$, the energy released in the decay of the 66.7 keV metastable state of ${}^{73}$Ge. Approximately 99% of entries are contained within the peak at 66.7 keV

Fig. 7

Energy cut optimisation plot showing the background rejection, the signal survival fractions and the performance metric as a function of the energy threshold |$E_1-E_2$|. The signal efficiency for the optimum is 87% with 93% background rejection at an energy difference threshold of 204 keV. The metric curve is the product of the signal and background curves

Fig. 8

Risetime optimisation plot for BEGe detectors. The signal efficiency for the optimum is 91% with 93% background rejection at a time difference threshold of 500 ns. The other detector types exhibit similar performance

Fig. 9

GERDA energy spectrum from 20 keV to 1600 keV before any analysis cuts. The contributions from ${}^{39}$Ar, two neutrino double beta (2$\nu \beta \beta$) decay and ${}^{40,42}$K are indicated. Bottom: Surviving $E_2$ events after applying our search procedure with energy, rise time and LAr veto cuts. The region of interest (ROI) is indicated. The expected number of accidental events up to 1600 keV is about 2