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The inclusive production of the J/$\psi$ and $\psi$(2S) charmonium states isstudied as a function of centrality in p-Pb collisions at a centre-of-massenergy per nucleon pair $\sqrt{s_{\rm NN}} = 8.16$ TeV at the LHC. Themeasurement is performed in the dimuon decay channel with the ALICE apparatusin the centre-of-mass rapidity intervals $-4.46 < y_{\rm cms} < -2.96$(Pb-going direction) and $2.03 < y_{\rm cms} < 3.53$ (p-going direction), downto zero transverse momentum ($p_{\rm T}$). The J/$\psi$ and $\psi$(2S)production cross sections are evaluated as a function of the collisioncentrality, estimated through the energy deposited in the zero degreecalorimeter located in the Pb-going direction. The $p_{\rm T}$-differentialJ/$\psi$ production cross section is measured at backward and forward rapidityfor several centrality classes, together with the corresponding average$\langle p_{\rm T} \rangle$ and $\langle p^{2}_{\rm T} \rangle$ values. Thenuclear effects affecting the production of both charmonium states are studiedusing the nuclear modification factor. In the p-going direction, a suppressionof the production of both charmonium states is observed, which seems toincrease from peripheral to central collisions. In the Pb-going direction,however, the centrality dependence is different for the two states: the nuclearmodification factor of the J/$\psi$ increases from below unity in peripheralcollisions to above unity in central collisions, while for the $\psi$(2S) itstays below or consistent with unity for all centralities with no significantcentrality dependence. The results are compared with measurements in p-Pbcollisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV and no significant dependence onthe energy of the collision is observed. Finally, the results are compared withtheoretical models implementing various nuclear matter effects.

Centrality dependence of J/$\psi$ and $\psi$(2S) production and nuclear modification in p-Pb collisions at $\sqrt{s_{\rm NN}} =$ 8.16 TeV