Abstract
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.
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