  Cross sections for the coherent photoproduction of $\rho^{0}$ vector mesons
in ultra-peripheral Pb-Pb collisions at $ \sqrt{s_{\mathrm{NN}}}= 5.02$ TeV are
reported. The measurements, which rely on the $\pi^+\pi^-$ decay channel, are
presented in three regions of rapidity covering the range $|y|<0.8$. For each
rapidity interval, cross sections are shown for different nuclear-breakup
classes defined according to the presence of neutrons measured in the
zero-degree calorimeters. The results are compared with predictions based on
different models of nuclear shadowing. Finally, the observation of a coherently
produced resonance-like structure with a mass around 1.7 GeV/$c^2$ and a width
of about 140 MeV/$c^2$ is reported and compared with similar observations from
other experiments.
