The nuclei that constitute a crystalline lattice, oscillate relative to each other with a very low energy that is not sufficient to penetrate through the Coulomb barriers separating them. An additional energy, which is needed to tunnel through the barrier and fuse, can be supplied by external electromagnetic waves (X-rays or the synchrotron radiation). Exposing to the X-rays the solid compound LiD (lithium-deuteride) for the duration of 111 hours, we have detected 88 events of the nuclear fusion d + 6 Li → 8 Be * . Our theoretical estimate agrees with what we observed. One of possible applications of the phenomenon we found, could be the measurements of the rates of various nuclear reactions (not necessarily fusion) at extremely low energies inaccessible in accelerator experiments.