We discuss production of $J/\psi$ and $e^+ e^-$ pairs in semicentral and peripheral collisions of heavy ions at high energies. We focus on photoproduction mechanism. We present explanation of results of the ALICE collaboration for low transverse momentum production of $J/\psi$ as well as results obtained by the STAR collaboration for $e^+ e^-$ production, also at low transverse momenta. We conclude that such effects are important also in this new corner (semi-central processes) of the phase space.