Electromagnetic field in nuclear matter and nuclei are studied. In the nuclear matter, because the expectation value of the electric charge density operator is not zero, different in vacuum, the U(1) local gauge symmetry of electric charge is spontaneously broken, and consequently, the photon gains an effective mass through the Higgs mechanism. An alternative way to study the effective mass of photon is to calculate the self-energy of photon perturbatively. It shows that the effective mass of photon is about 5.42 MeV in the symmetric nuclear matter at the saturation density ρ0 = 0.16 fm -3 and about 2.0 MeV at the surface of 238U. It seems that the two-body decay of a massive photon causes the sharp lines of electron–positron pairs in the low energy heavy ion collision experiments of 238 U + 232 Th .