  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 $5.42MeV$
in the symmetric nuclear matter at the saturation density $\rho_0 =
0.16fm^{-3}$ and about $2.0MeV$ at the surface of ${}^{238}U$. 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
${}^{238}U+{}^{232}Th$ .
