We report a novel correlated background in the antineutrino detection using the inverse beta decay reaction. Spontaneous fissions and $(alpha,n)$ reactions in peripheral materials of the antineutrino detector, such as borosilicate glass of photomultipliers, produce fast neutrons and prompt gamma rays. If the shielding from the material to the detector target were not thick enough, neutrons and gammas could enter the target volume and mimic antineutrino signals. This paper revisits the yields and energy spectra of neutrons produced in B$(alpha,n)$N and F$(alpha,n)$Na reactions. A Geant4 based simulation has been carried out using a simplified detector geometry for the present generation reactor neutrino experiments. The background rates in these experiments are estimated. If this background was not taken into account, the value of the neutrino mixing angle $sin^22theta_{13}$ would be underestimated. We recommend that Daya Bay, RENO, Double Chooz, and JUNO, carefully examine the masses and radiopurity levels of detector materials that are close to the target and rich in boron and fluorine.
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