We investigate several Pb$(n,ngamma$) and Ge$(n,ngamma$) reactions. We measure $gamma$-ray production from Pb$(n,ngamma$) reactions that can be a significant background for double-beta decay experiments which use lead as a massive inner shield. Particularly worrisome for Ge-based double-beta decay experiments are the 2041-keV and 3062-keV $gamma$ rays produced via Pb$(n,ngamma$). The former is very close to the ^{76}Ge double-beta decay endpoint energy and the latter has a double escape peak energy near the endpoint. Excitation $gamma$-ray lines from Ge$(n,ngamma$) reactions are also observed. We consider the contribution of such backgrounds and their impact on the sensitivity of next-generation searches for neutrinoless double-beta decay using enriched germanium detectors.
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