Physics of ultra-peripheral collisions with ALICE at the LHC

The photoproduction of vector mesons in ultra-peripheral colli- sions (UPC) is a powerful tool to probe the nuclear gluon distribution (Pb-Pb collisions) and the gluon structure function in the proton (p-Pb collisions). The first measurements of coherent photoproduced J /ψ and ψ (2S) in Pb-Pb collisions at √ s NN =2 . 76 TeV, performed with the ALICE detector, are reported and compared to STARLIGHT and QCD based models, in order to investigate nuclear gluon shad- owing. The first results of the measurement of exclusive J /ψ photoproduction off protons in p-Pb collisions at √ s NN =5 . 02 TeV performed by the ALICE Collabora- tion are also mentioned