Low energy ω(\to π^0 γ) meson photoproduction in the nucleus
The $π^0 γ$ invariant mass distribution spectra in the $ (γ, π^0γ) $ reaction were measured by TAPS/ELSA collaboration to look for the hadron parameters of the $ω$ meson in Nb nucleus. We study the mechanism for this reaction, where we consider that the elementary reaction in Nb nucleus proceeds as $ γN \to ωN; ~ ω\to π^0γ$. The $ω$ meson photoproduction amplitude for this reaction is extracted from the measured four momentum transfer distribution in the $ γp \to ωp $ reaction. The propagation of the $ω$ meson and the distorted wave function for the $π^0$ meson in the final state are described by the eikonal form. The $ω$ and $π^0$ mesons nucleus optical potentials, appearing in the $ω$ meson propagator and $π^0$ meson distorted wave function respectively, are estimated using the "$t\varrho$" approximation. The effects of pair correlation and color transparency are also studied. The calculated results do not show medium modification for the $ω$ meson produced in the nucleus for its momentum greater than 200 MeV. It occurs since the $ω$ meson dominantly decays outside the nucleus. The dependence of the cross section on the final state interaction is also investigated. The broadening of the $ω$ meson mass distribution spectra is shown to occur due to the large resolution width associated with the detector used in the experiment.