  In ultraperipheral collisions (UPCs) of relativistic nuclei without overlap
of nuclear densities, the two nuclei are excited by the Lorentz-contracted
Coulomb fields of their collision partners. In these UPCs, the typical nuclear
excitation energy is below a few tens of MeV, and a small number of nucleons
are emitted in electromagnetic dissociation (EMD) of primary nuclei, in
contrast to complete nuclear fragmentation in hadronic interactions. The cross
sections of emission of given numbers of neutrons in UPCs of $^{208}$Pb nuclei
at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV were measured with the neutron zero degree
calorimeters (ZDCs) of the ALICE detector at the LHC, exploiting a similar
technique to that used in previous studies performed at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. In addition, the cross sections for the
exclusive emission of one, two, three, four, and five forward neutrons in the
EMD, not accompanied by the emission of forward protons, and thus mostly
corresponding to the production of $^{207,206,205,204,203}$Pb, respectively,
were measured for the first time. The predictions from the available models
describe the measured cross sections well. These cross sections can be used for
evaluating the impact of secondary nuclei on the LHC components, in particular,
on superconducting magnets, and also provide useful input for the design of the
Future Circular Collider (FCC-hh).
