  We calculate total and differential cross sections for $J/\psi$
photoproduction in ultrarelativistic lead-lead collisions at the LHC energy
$\sqrt{s_{NN}}=2.76$ TeV. We use a simple model based on vector dominance
picture and multiple scattering of the hadronic ($c \bar c$) state in a cold
nucleus. In our analysis we use Glauber formulae for calculating
$\sigma_{tot,J/\psi Pb}$ which is a building block of our model. For
semi-central collisions a modification of the photon flux is necessary. We
discuss how to effectively correct photon fluxes for geometry effects. We try
to estimate the cross sections for different centrality bins and for $J/\psi$
mesons emitted in forward rapidity range ($2.5<y<4$) corresponding to the ALICE
experimental results.
  We discuss similar analysis for dilepton production in ultrarelativistic
heavy-ion collisions at very low pair transverse momenta, $P_T\leq 0.15$\,GeV.
We investigate the interplay of thermal radiation with photon annihilation
processes, $\gamma \gamma \to l^+ l^-$, due to the coherent electromagnetic
fields of the colliding nuclei. For the thermal radiation, we employ the
emission from the QGP and hadronic phases with in-medium vector spectral
functions. We first verify that the combination of photon fusion, thermal
radiation and final-state hadron decays gives a fair description of the
low-$P_T$ invariant-mass as well as $P_T$ distributions as measured recently by
the STAR collaboration in $\sqrt{s_{NN}}$=200\,GeV Au+Au collisions for
different centralities. The coherent contribution dominates in peripheral
collisions, while thermal radiation shows a significantly stronger increase
with centrality. We also provide predictions for the ALICE experiment at the
LHC. The resulting excitation function reveals a nontrivial interplay of
photoproduction and thermal radiation.
