Coherent two pion photoproduction on 12C

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 Ø = 180° is forbidden. Conversely in the π⁻π⁺ production the pions prefer to have a relative azimuthal angle 180° 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.