Environmental $\gamma$-Ray Flux in Hall C at LNGS and Its Correlation with Radon Activity

arXiv:2605.09835v2 Announce Type: replace Abstract: We report a comprehensive measurement of the environmental $\gamma$-ray flux in Hall C of the Gran Sasso National Laboratory. A spatial mapping of the radiation was carried out using a high-purity germanium detector mounted on a movable cart and deployed at eight locations within the hall. The detector response function and full-energy-peak efficiencies were determined through Geant4 simulations validated with calibrated $\gamma$-ray sources, with particular attention devoted to the efficiency modeling and associated systematic uncertainties. In the energy range of 57-2800 keV, the average $\gamma$-ray flux is measured to be $(\mathrm{0.46} \pm \mathrm{0.06}_{stat} \pm \mathrm{0.03}_{syst})$ $\mathrm{cm}^{-2}$ $\mathrm{s}^{-1}$. The radon level was monitored for about a month using a radon detector mounted on the same cart, and a clear correlation is observed between the environmental $\gamma$-ray rate and the ambient radon concentration, consistent with the short-lived daughters of $^{222}\mathrm{Rn}$. This result represents the first high-precision and efficiency-corrected mapping of the $\gamma$-ray flux in Hall C, substantially improving its radiological characterization and providing key input for future rare-event experiments operating in this hall.