  We point out a significance of ultraperipheral photoproduction of vector
mesons in the Coulomb field of nuclei as a means of measuring the radius of the
neutral vector meson. This new contribution to the production amplitude is very
small compared to the conventional diffractive amplitude, but because of large
impact parameters inherent to the ultraperipheral Coulomb mechanism its impact
on the diffraction slope is substantial. We predict appreciable and strongly
energy dependent increase of the diffraction slope towards very small momentum
transfer.The magnitude of the effect is proportional to the mean radius squared
of the vector meson and is within the reach of high precision photoproduction
experiments, which gives a unique experimental handle on the size of vector
mesons.
