  The inclusive production of the $\psi$(2S) charmonium state was studied as a
function of centrality in p-Pb collisions at the nucleon-nucleon center of mass
energy $\sqrt{s_{\rm NN}}$ = 5.02 TeV at the CERN LHC. The measurement was
performed with the ALICE detector in the center of mass rapidity ranges
$-4.46<y_{\rm cms}<-2.96$ and $2.03<y_{\rm cms}<3.53$, down to zero transverse
momentum, by reconstructing the $\psi$(2S) decay to a muon pair. The $\psi$(2S)
production cross section $\sigma_{\psi(\rm 2S)}$ is presented as a function of
the collision centrality, which is estimated through the energy deposited in
forward rapidity calorimeters. The relative strength of nuclear effects on the
$\psi$(2S) and on the corresponding 1S charmonium state J/$\psi$ is then
studied by means of the double ratio of cross sections $[\sigma_{\psi(\rm
2S)}/\sigma_{\rm J/\psi}]_{\rm pPb}/[\sigma_{\psi(\rm 2S)}/\sigma_{\rm
J/\psi}]_{\rm pp}$ between p-Pb and pp collisions, and by the values of the
nuclear modification factors for the two charmonium states. The results show a
large suppression of $\psi$(2S) production relative to the J/$\psi$ at backward
(negative) rapidity, corresponding to the flight direction of the Pb-nucleus,
while at forward (positive) rapidity the suppressions of the two states are
comparable. Finally, comparisons to results from lower energy experiments and
to available theoretical models are presented.
