We develop the formalism for coherent two pion photoproduction in nuclei and perform actual calculations of cross sections for π−π+ and π0π0 photoproduction on 12C. We find that due to the isospin symmetry the cross section for π0π0 production is very small and has a maximum when the pions propagate together. However, the kinematical region where the energies and polar angles of the two π0 mesons are equal and their relative azimuthal angle ϕ=1800 is forbidden. Conversely in the π−π+ production the pions prefer to have a relative azimuthal angle 1800 and the production of the pions propagating together is suppressed. The dominant one-body mechanism in both channels is related to the excitation of the Δ isobar. Hence the reaction can serve as a source of information about Δ's properties in nucleus. We have found that the reaction is sensitive to effects of the pion and Δ renormalization in the nuclear medium, similar to those found in the coherent (γ,π0) reaction, but magnified because of the presence of the two pions.
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