Rare event search experiments using liquid xenon as target and detection medium require ultra-low background levels to fully exploit their physics potential. Cosmic ray induced activation of the detector components and, even more importantly, of the xenon itself during production, transportation and storage at the Earth's surface, might result in the production of radioactive isotopes with long half-lives, with a possible impact on the expected background. We present the first dedicated study on the cosmogenic activation of xenon after 345 days of exposure to cosmic rays at the Jungfraujoch research station at 3470m above sea level, complemented by a study of copper which has been activated simultaneously. We have directly observed the production of 7Be, 101Rh, 125Sb, 126I and 127Xe in xenon, out of which only 125Sb could potentially lead to background for a multi-ton scale dark matter search. The production rates for five out of eight studied radioactive isotopes in copper are in agreement with the only existing dedicated activation measurement, while we observe lower rates for the remaining ones. The specific saturation activities for both samples are also compared to predictions obtained with commonly used software packages, where we observe some underpredictions, especially for xenon activation.
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