Search for the in-situ production of 77 Ge in the GERDA neutrinoless double-beta decay experiment

Abstract

The beta decay of $_{}^{77}$ Ge and $_{}^{77\text{m}}$ Ge, both produced by neutron capture on $_{}^{76}$ Ge, is a potential background for Germanium based neutrinoless double-beta decay search experiments such as GERDA or the LEGEND experiment. In this work we present a search for $_{}^{77}$ Ge decays in the full GERDA Phase II data set. A delayed coincidence method was employed to identify the decay of $_{}^{77}$ Ge via the isomeric state of $_{}^{77}$ As ( $9/2^{+}$ , $475\text{keV}$ , $T_{1/2}=114\mu \text{s}$ , $_{}^{77\text{m}}$ As). New digital signal processing methods were employed to select and analyze pile-up signals. No signal was observed, and an upper limit on the production rate of $_{}^{77}$ Ge was set at $<0.216$ nuc/(kg $·$ yr) (90% CL). This corresponds to a total production rate of $_{}^{77}$ Ge and $_{}^{77\text{m}}$ Ge of $<0.38$ nuc/(kg $·$ yr) (90% CL), assuming equal production rates. A previous Monte Carlo study predicted a value for in-situ $_{}^{77}$ Ge and $_{}^{77\text{m}}$ Ge production of (0.21 ± 0.07) nuc/(kg.yr), a prediction that is now further corroborated by our experimental limit. Moreover, tagging the isomeric state of $_{}^{77\text{m}}$ As can be utilised to further suppress the $_{}^{77}$ Ge background. Considering the similar experimental configurations of LEGEND-1000 and GERDA, the cosmogenic background in LEGEND-1000 at LNGS is estimated to remain at a sub-dominant level.

Fig. 1

Simplified decay scheme of $_{}^{77}$Ge and $_{}^{77\text{m}}$Ge into $_{}^{77}$As. $_{}^{77\text{m}}$Ge only populates states $\le 216\text{keV}$ while $_{}^{77}$Ge also populates higher states including the $9/2^{+}$ isomeric state in $_{}^{77}$As with $T_{1/2}=114\mu$s and an excitation energy of $475\text{keV}$. Approximately $16\%$ of $_{}^{77}$Ge decays into this isomeric state, while more than $79\%$ of $_{}^{77}$Ge decays populate states above (not drawn) and can also populate the isomeric state from above. This plot was generated from the values of [7]

Fig. 2

Simulated energy distribution of the delayed gamma emission from the isomeric state in $_{}^{77}$As deposited in a HPGe. The peaks correspond to the full energy deposition of both gammas in the detector at $475\text{keV}$ or the full energy deposition of only one of the gammas in the detector at $211\text{keV}$ or $264\text{keV}$. The energy resolutions of each individual detector derived from the standard GERDA analysis were implemented

Fig. 3

An example of pile-up signal reconstruction. (Top) Example of a pile-up event waveform in the GERDA data stream. (Bottom) The waveform of the example pile-up event after applying a trapezoidal filter. The time difference between the signals is estimated by taking the difference between the triggers. Finally, the signal heights are extracted with a fixed time pick off

Fig. 4

Reconstructed energy spectra for the first and second pulse in a pile-up signal in the calibration data where two signals are contained in the waveform of one event. The red histogram corresponds to the first pulses energies, while the blue histogram corresponds to the second pulses energies. The former distribution was scaled by a factor of 100 to illustrate the differences between the spectra. Both spectra reconstruct the expected $_{}^{208}$Tl gamma lines well. The spectra of the second pulses consistently shows larger resolution and a slight tail to lower energies

Fig. 5

Pile-up signal selection efficiency plotted over the time difference between generated pile-up signals. Our new DSP is sensitive for delayed coincidences starting at time differences $>4.5\mathrm{\mu }$s. Individual events in this range were rejected due to quality cuts. Black: central value. Yellow: 68% uncertainty band

Fig. 6

The distribution of all 8 candidate delayed coincidences after the multiplicity condition plotted dT over $E_{\text{d}}$. The energy windows around the points correspond to the linear combination of the full-width-at-tenth-maximum (FWTM) window (yellow) plus the asymmetric bias window (red). The FWTM window covers about $97\%$ of the gamma peak area. The vertical size of the data is enlarged for better visualization. The blue lines correspond to the gamma energies of the internal transitions from $_{}^{77\text{m}}$As . A delayed coincidence candidate is rejected, if its energy window misses any of the three gamma lines. We found no candidate delayed coincidence that satisfies this condition resulting in $N_{\text{obs}}=0\text{cts}$. The right part shows a projection of the candidates onto dT. The blue line corresponds to the expected distribution for $_{}^{77\text{m}}$As delayed coincidences

Fig. 7

Bayesian update of the simulated production rate using the likelihood of the GERDA data estimated in this analysis