Ultra-Peripheral Collisions at ALICE, Looking inside lead ions

There are several different predictions for the behaviour of the gluon distribution in nuclei at small Bjorken-$x$ and experimental data are needed to chose among them. This is achieved by measuring the cross section of processes specially sensitive to this parton distribution. This work focuses on ultra-peripheral collisions of lead-lead nuclei producing a $\rm{J/\psi}$ meson. The main task is to calculate the rapidity and |t| dependence of the cross section, where the |t| is the square of the momentum transferred between the incoming and outgoing target nucleus. ALICE data from the Run 2 period, specifically from the year 2018, are used in this thesis. The results proof the existence of nuclear shadowing effects, and put new constraints on available theoretical models in the form of a more precise measurement and in this context the newly measured dependence of the cross section on |t|.