The rare event search experiments using germanium detectors are performed in the underground laboratories to prevent cosmic rays. However, the cosmogenic activation of the cupreous detector components on the ground will generate long half-life radioisotopes and contribute continually to the expected background level. We present a study on the cosmogenic activation of copper after 504 days of exposure at an altitude of 2469.4 m outside the China Jinping Underground Laboratory (CJPL). The specific activities of the cosmogenic nuclides produced in the copper bricks were measured using a low background germanium gamma-ray spectrometer at CJPL. The production rates at sea level, in units of nuclei/kg/day, are 18.6 pm 2.0 for Mn-54, 9.9 pm 1.3 for Co-56, 48.3 pm 5.5 for Co-57, 51.8 pm 2.5 for Co-58 and 39.7 pm 5.7 for Co-60, respectively. Given the expected exposure history of the germanium detectors, a Monte Carlo simulation is conducted to assess the cosmogenic background contributions of the detectors cupreous components.
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