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In-situ gamma-ray background measurements for next generation CDEX experiment in the China Jinping Underground Laboratory

In-situ $γ$-ray measurements were performed using a portable high purity germanium spectrometer in Hall-C at the second phase of the China Jinping Underground Laboratory (CJPL-II) to characterise the environmental radioactivity background below 3 MeV and provide ambient $γ$-ray background parameters for next generation of China Dark Matter Experiment (CDEX). The integral count rate of the spectrum was 46.8 cps in the energy range of 60 to 2700 keV. Detection efficiencies of the spectrometer corresponding to concrete walls and surrounding air were obtained from numerical calculation and Monte Carlo simulation, respectively. The radioactivity concentrations of the walls in the Hall-C were calculated to be ${6.8\pm1.5}$ Bq/kg for ${^{238}}$U, ${5.4\pm0.6}$ Bq/kg for ${^{232}}$Th, ${81.9\pm14.4}$ Bq/kg for ${^{40}}$K. Based on the measurement results, the expected background rates from these primordial radionuclides of future CDEX experiment were simulated in unit of counts per keV per ton per year (cpkty) for the energy ranges of 2 to 4 keV and around 2 MeV. The total background level from primordial radionuclides with decay products in secular equilibrium are ${7.0 \times 10^{-2}}$ and ${3.1 \times 10^{-3}}$ cpkty for energy ranges of 2 keV to 4 keV and around 2 MeV, respectively.