The STAR Collaboration reports on the photoproduction of $\pi^+\pi^-$ pairs
in gold-gold collisions at a center-of-mass energy of 200 GeV/nucleon-pair.
These pion pairs are produced when a nearly-real photon emitted by one ion
scatters from the other ion.
We fit the $\pi^+\pi^-$ invariant mass spectrum with a combination of $\rho$
and $\omega$ resonances and a direct $\pi^+\pi^-$ continuum. This is the first
observation of the $\omega$ in ultra-peripheral collisions, and the first
measurement of $\rho-\omega$ interference at energies where photoproduction is
dominated by Pomeron exchange. The $\omega$ amplitude is consistent with the
measured $\gamma p\rightarrow \omega p$ cross section, a classical Glauber
calculation and the $\omega\rightarrow\pi^+\pi^-$ branching ratio. The $\omega$
phase angle is similar to that observed at much lower energies, showing that
the $\rho-\omega$ phase difference does not depend significantly on photon
The $\rho^0$ differential cross section $d\sigma/dt$ exhibits a clear
diffraction pattern, compatible with scattering from a gold nucleus, with 2
minima visible. The positions of the diffractive minima agree better with the
predictions of a quantum Glauber calculation that does not include nuclear
shadowing than with a calculation that does include shadowing.