  We review our recent results for double-scattering mechanism in the exclusive
$AA \to AA \rho^0\rho^0$ reaction in ultrarelativistic ultraperipheral heavy
ion collisions. The cross section for single and double-$\rho^0$ production is
calculated in the impact parameter space equivalent photon approximation. We
compare the results of our calculation with the STAR and ALICE Collaboration
results on one $\rho^0(770)$ meson and four-charged-pion production.
