Coherent photoproduction of two neutral pseudoscalar mesons on light nuclei

Coherent photoproduction of ${\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ and ${\ensuremath{\pi}}^{0}\ensuremath{\eta}$ on nuclei with $A\ensuremath{\le}7$ is systematically studied in the energy region from the threshold to the laboratory photon energy ${E}_{\ensuremath{\gamma}}=2$ GeV. The amplitude of photoproduction on nuclei is derived in the impulse approximation taking account of certain processes responsible for the meson-nucleus final-state interaction. For the first time, the unified microscopic approach is used to calculate effects such as rescattering of the $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\pi}N$ and $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\eta}N$ pions from spectator nucleons, photoproduction of ${\ensuremath{\pi}}^{+/\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ and ${\ensuremath{\pi}}^{+/\ensuremath{-}}{\ensuremath{\pi}}^{0}\ensuremath{\eta}$, and the follow-on absorption of ${\ensuremath{\pi}}^{+/\ensuremath{-}}$ by spectator nucleons, as well as three-body $\ensuremath{\pi}\text{\ensuremath{-}}NN$ and $\ensuremath{\eta}\text{\ensuremath{-}}NN$ interaction among effects being responsible for the meson-nucleus final-state interaction. Direct calculation shows total cross sections of ${\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ and ${\ensuremath{\pi}}^{0}\ensuremath{\eta}$ photoproduction to be strongly dependent both on the target nucleus isospin, and the target nucleus model.