Photoproduction of neutral pseudoscalar mesons $\pi^0,\eta(547)$ and $\eta'(958)$ in the Coulomb field of an atomic nucleus is studied using a model which describes the Primakoff and nuclear parts of the production amplitude. At high energies the nuclear background is dominated by the exchange of $C$-parity odd Regge trajectories. In the coherent production the isospin filtering makes the $\omega(782)$ a dominant trajectory. The calculations are in agreement with $\pi^0$ data from JLAB provided the photon shadowing and final state interactions of mesons are taken into account. The kinematic conditions which allow to study the Primakoff effect in $\eta$ and $\eta'$ photoproduction off nuclei are further discussed. We also give predictions for the higher energies available at the JLAB upgrade.Comment: 15 pages, 14 figures, discussion added, final version to be published in Phys. Rev.
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