Photoproduction of vector mesons: from ultraperipheral to semi-central heavy ion collisions

We discuss nuclear cross sections for $AA \to AAV$ and $AA \to AAVV$ reactions with one or two vector mesons in the final state. Our analysis is done in the impact parameter space equivalent photon approximation. This approach allows to consider the above processes taking into account distance between colliding nuclei. We consider both ultraperipheral and semi-central collisions. We are a first group which undertook a study of single $J/\psi$ photoproduction for different centrality bins. We show that one can describe new ALICE experimental data by including geometrical effects of collisions in the flux factor. Next, total and differential cross section for double-scattering mechanism in the exclusive $AA \to AAVV$ reaction in ultrarelativistic ultraperipheral heavy ion collisions is presented. In this context we consider double photoproduction and photon-photon processes. Simultaneously, we get very good agreement of our results with STAR (RHIC), CMS and ALICE (LHC) experimental data for single $\rho^0$ and $J/\psi$ vector meson production. A comparison of our predictions for exclusive four charged pions production is also presented.