  In this talk we apply the photoproduction framework recently implemented into
the Pythia 8 Monte Carlo event generator to study the potential of
photo-nuclear dijets in ultra-peripheral Pb+Pb collisions at the LHC to further
constrain the nuclear PDFs. These events can be described as $\gamma$A
collisions where the relevant part of the flux of quasi-real photons from
heavy-ions is obtained by using the equivalent photon approximation and cutting
out impact-parameter values which would lead to hadronic interactions between
the beam particles. In particular, we quantify the small-$x$ reach with
different jet kinematics and show how well the values of $x$ derived from
reconstructed jet momenta are correlated with the actual values of partonic
momentum fractions probed in these measurements. Also the contributions from
direct and resolved photons are separately presented. To demonstrate the
potential, we compare the expected experimental uncertainties to the current
nuclear-PDF errors and discuss other theoretical uncertainties including the
uncertainty arising from poorly-constrained photon PDFs. We find that such a
measurement would potentially provide a considerable reduction of the nuclear
PDF uncertainties in a region $10^{-4} \lesssim x \lesssim 10^{-2}$.
