  Using the general notion of cross section fluctuations in hadron--nucleus
scattering at high energies, we derive an expression for the cross section of
incoherent $J/\psi$ photoproduction on heavy nuclei $d\sigma_{\gamma A \to
J/\psi Y}/dt$, which includes both elastic $d\sigma_{\gamma p \to J/\psi p}/dt$
and proton-dissociation $d\sigma_{\gamma p \to J/\psi Y}/dt$ photoproduction on
target nucleons. We find that with good accuracy, $d\sigma_{\gamma A \to J/\psi
Y}/dt$ can be expressed as a product of the sum of the $d\sigma_{\gamma p \to
J/\psi p}/dt$ and $d\sigma_{\gamma p \to J/\psi Y}/dt$ cross sections, which
have been measured at HERA, and the common nuclear shadowing factor, which is
calculated using the leading twist nuclear shadowing model. Our prediction for
the cross section of incoherent $J/\psi$ photoproduction in Pb-Pb UPCs at
$\sqrt{s_{NN}}=2.76$ TeV and $y=0$, $d\sigma_{AA \to J/\psi
AY}(y=0)/dy=0.59-1.24$ mb, agrees within significant theoretical uncertainties
with the data of the ALICE collaboration.

High Energy Physics - Phenomenology;Nuclear Experiment