  The first measurement of the coherent photoproduction of $\rho^{0}$ vector
mesons in ultra-peripheral Xe-Xe collisions at $\sqrt{s_{\mathrm{\rm NN}}}=
5.44$ TeV is presented. This result, together with previous HERA $\gamma$p data
and $\gamma$-Pb measurements from ALICE, describes the atomic number ($A$)
dependence of this process, which is particularly sensitive to nuclear
shadowing effects and to the approach to the black-disc limit of QCD at a
semi-hard scale. The cross section of the ${\rm Xe}+{\rm Xe} \to \rho^{0} +
{\rm Xe}+{\rm Xe}$ process, measured at midrapidity through the decay channel
$\rho^{0}\to\pi^+\pi^-$, is found to be ${\rm d}\sigma/{\rm d}y=131.5\pm 5.6
{\rm (stat.)} ^{+17.5}_{-16.9} {\rm (syst.)}$ mb. The ratio of the continuum to
resonant contributions for the production of pion pairs is also measured. In
addition, the fraction of events accompanied by electromagnetic dissociation of
either one or both colliding nuclei is reported. The dependence on $A$ of cross
section for the coherent $\rho^{0}$ photoproduction at a centre-of-mass energy
per nucleon of the $\gamma A$ system of $W_{\gamma A,n}= 65$ GeV is found to be
consistent with a power-law behaviour $\sigma (\gamma A\rightarrow \rho^{0} A)
\propto A^{\alpha}$ with a slope $\alpha = 0.96 \pm 0.02 {\rm (syst.)}$. This
slope signals important shadowing effects, but it is still far from the
behaviour expected in the black-disc limit.
