Photoproduction of light vector mesons in Xe-Xe ultraperipheral collisions at the LHC and the nuclear density of Xe-129

We make predictions for cross sections of $rho$ and $phi$ vector meson photoproduction in ultraperipheral Xe-Xe collisions at $sqrt{s_{NN}}=5.44$ TeV. Analyzing the momentum transfer distribution of $rho$ mesons in this process, we explore the feasibility of extracting the nuclear density of $^{129}$Xe, which is needed in searches for dark matter with Xenon-based detectors.