A new search for production of correlated e+e- pairs in the alpha decay of 241Am has been carried out deep underground at the Gran Sasso National Laboratory of the I.N.F.N. by using pairs of NaI(Tl) detectors of the DAMA/LIBRA set-up. The experimental data show an excess of double coincidences of events with energy around 511 keV in faced pairs of detectors, which are not explained by known side reactions. This measured excess gives a relative activity lambda = (4.70 pm 0.63) times 10^{-9} for the Internal Pair Production (IPP) with respect to alpha decay of 241Am; this value is of the same order of magnitude as previous determinations. In a conservative approach the upper limit lambda < 5.5 times 10^{-9} (90% C.L.) can be derived. It is worth noting that this is the first result on IPP obtained in an underground experiment, and that the lambda value obtained in the present work is independent on the live-time estimate.
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