A low-background \(\gamma\) spectrometer named the Gamma spectrometer for Nuclear Activation Studies (GNAS) was developed to detect scarce \(\gamma\) radioactivity, with a special focus on conducting activation experiments in nuclear astrophysics. It consisted of a well-type HPGe detector surrounded by optimized multi-layer shielding, which reduced the laboratory background counting rate by 99.5% and enabled a sensitivity edge as low as 0.044 Bq for the 477.6 KeV \(\gamma\) line of \(\,^{7}{\text{Be}}\) . The near \(4\pi\) geometry of the HPGe detector introduces a severe true coincidence summing (TCS) effect along with its high detection efficiency. To determine the intrinsic detection efficiency and correct for the TCS effect, a Monte Carlo simulation method was developed with the Geant4 toolkit. The detector model was optimized by matching the simulated full energy peak (FEP) statistics with those of a \(\,^{137}\text{Cs}\) monoenergetic source and calibrated \(\,^{{55,57,58}} {\text{Co}}\) sources produced by low-energy proton beam bombardment of natural iron. The intrinsic detection efficiency curve was obtained, and an algorithm for the correction of the TCS effect was programmed using decay data from the ENSDF library and Nuclear Wallet Cards. The GNAS fulfills the requirements of the ongoing activation measurement of proton- and alpha-induced reactions in nuclear astrophysics on the ground and at the Jinping Underground Nuclear Astrophysics (JUNA) facility.
