Evaluation of cosmogenic Ge-68 background in a high purity germanium detector via a time series fitting method

Ge-68 is a cosmogenic isotope in germanium with a half-life of 270.9 days. Ge-68 and its decay daughter Ga-68 contribute considerable background with energy up to 3 MeV to low background $\gamma$ spectrometers using high purity germanium (HPGe) detectors. In this paper, we evaluated the background of Ge-68 and Ga-68 in a $p$-type coaxial HPGe detector operated at China Jinping underground laboratory (CJPL) via a time series fitting method. Under the assumption that Ge-68 and Ga-68 are in radioactive equilibrium and airborne radon daughters are uniformly distributed in the measurement chamber of the spectrometer, we fit the time series of count rate in 1-3 MeV to calculate the Ge-68 activity, radon daughter concentrations, and the time-invariant background component. A total of 90-day measurement data were used in the analysis, a hypothesis test confirmed a significant Ge-68 signal at 99.64% confidence level. The initial activity of Ge-68 is fitted to be 477.0$\pm 112.4\mu$Bq/kg, corresponding to an integral count rate of 55.9 count/day in the 1-3 MeV range. During the measurement, Ge-68 activity decreased by about 30%, contributing about 62% of the total background in the 1-3 MeV range. Our method also provides an estimation of the variation of airborne radon daughter concentrations in the measurement chamber, which could be used to monitor the performance of radon reduction measures.