The background of a High Purity Germanium (HPGe) detector measured in a deep underground laboratory was investigated analytically and by Monte Carlo simulations using the GEANT4 toolkit. Contributions of different background sources to the experimental γ-ray background were determined. Namely, contribution of radionuclides in materials of the detector and around the detector, neutrons produced by (α, n) reactions due to presence of radionuclides in rock and concrete and by spontaneous fission of mainly 238U, and finally, cosmic rays with neutron generation. The simulation, including radionuclides in the material, was in a good agreement with the experiment. At the same time, neutron and muon induced spectra were simulated. The radiation coming from the presence of members of the 238U, and 232Th decay series, and 40K in the detector parts and the laboratory walls contribute to the continuum of the experimental spectrum at the level of around 94%. According to simulations, the contribution of muon events to the experimental energy spectrum was below 1% and it was confirmed that muon induced spectra are about three orders of magnitude lower than the experimental one. The comparison of integral count rates of the experimental spectrum with the simulated spectrum induced by neutrons showed that about 6% of the measured background continuum originated from neutron reactions. Fast neutrons contributed more to the background (at around 65%) than thermal neutrons. Despite only a 6% share of neutron contributions in the total γ-ray background, they contributed mainly to the lower continuum of the spectrum up to 250 keV, which is a region of interest for potential low mass weakly interacting massive particle (WIMP) dark matter interactions. In addition, they interact with the detector and the shield by inelastic scattering and induce unwanted γ-rays. Neutron capture, elastic and inelastic scattering were simulated separately as well. It was found that inelastic scattering is the major contributor to the spectrum induced by neutrons. The effect of neutrons on the background of the HPGe detector operating underground, such as Obelix, is manifested mainly by their contribution to the continuum up to 1 MeV, especially in the lower part up to 500 keV. Thus, neutrons are an important background component in deep underground laboratories, too. Possible detector optimization is also discussed.
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