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Luminosity determination within the ALICE experiment is based on the measurement, in van der Meer scans, of the cross sections for visible processes involving one or more detectors (visible cross sections). In 2015 and 2018, the Large Hadron Collider provided Pb–Pb collisions at a centre-of-mass energy per nucleon pair of √s_NN= 5.02 TeV. Two visible cross sections, associated with particle detection in the Zero Degree Calorimeter (ZDC) and in the V0 detector, were measured in a van der Meer scan.This article describes the experimental set-up and the analysis procedure, and presents the measurement results. The analysis involves a comprehensive study of beam-related effects and an improved fitting procedure, compared to previous ALICE studies, for the extraction of the visible cross section. The resulting uncertainty of both the ZDC-based and the V0-based luminosity measurement for the full sample is 2.5%. The inelastic cross section for hadronic interactions in Pb–Pb collisions at √s_NN= 5.02 TeV, obtained by efficiency correction of the V0-based visible cross section, was measured to be 7.67 ± 0.25 b, in agreement with predictions using the Glauber model.

The production of the$\psi (2S)$charmonium state was measured with ALICE in Pb-Pb collisions at$\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$, in the dimuon decay channel. A significant signal was observed for the first time at LHC energies down to zero transverse momentum, at forward rapidity ($2.5<y<4$). The measurement of the ratio of the inclusive production cross sections of the$\psi (2S)$and$\mathrm{J}/\psi$resonances is reported as a function of the centrality of the collisions and of transverse momentum, in the region$p_T<12\mathrm{GeV}/c$. The results are compared with the corresponding measurements in$pp$collisions, by forming the double ratio$[{\sigma }^{\psi (2S)}/{\sigma }^{J/\psi }{]}_{\mathrm{Pb}\text{−}\mathrm{Pb}}/[{\sigma }^{\psi (2S)}/{\sigma }^{J/\psi }{]}_{pp}$. It is found that in Pb-Pb collisions the$\psi (2S)$is suppressed by a factor of$\sim 2$with respect to the$J/\psi$. The$\psi (2S)$nuclear modification factor$R_{\mathrm{AA}}$was also obtained as a function of both centrality and$p_T$. The results show that the$\psi (2S)$resonance yield is strongly suppressed in Pb-Pb collisions, by a factor of up to$\sim 3$with respect to$pp$. Comparisons of cross section ratios with previous Super Proton Synchrotron findings by the NA50 experiment and of$R_{\mathrm{AA}}$with higher-$p_T$results at LHC energy are also reported. These results and the corresponding comparisons with calculations of transport and statistical models address questions on the presence and properties of charmonium states in the quark-gluon plasma formed in nuclear collisions at the LHC.