  In $\rho^0$ photoproduction in ultra-peripheral heavy ion collisions, either
ion can be the photon emitter or the target. The two possibilities are
indistinguishable, and they should be able to interfere, reducing $rho^0$
production at low transverse momentum, $p_T<\hbar/< b>$, where $<b>$ is the
median impact parameter.
  The two $\rho^0$ production points are separated by $<b> \approx 18-46$ fm,
while the $\rho^0$ decay before travelling 1 fm. The two decay points are well
separated in space-time, so the decays proceed independently and any
interference must involve the final state $\pi^+\pi^-$. This requires a
non-local wave function.
