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

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.