  The $\pi^0 \gamma$ invariant mass distribution spectra in the $ (\gamma,
\pi^0\gamma) $ reaction were measured by TAPS/ELSA collaboration to look for
the hadron parameters of the $\omega$ meson in Nb nucleus. We study the
mechanism for this reaction, where we consider that the elementary reaction in
Nb nucleus proceeds as $ \gamma N \to \omega N; ~ \omega \to \pi^0\gamma $. The
$\omega$ meson photoproduction amplitude for this reaction is extracted from
the measured four momentum transfer distribution in the $ \gamma p \to \omega p
$ reaction. The propagation of the $\omega$ meson and the distorted wave
function for the $\pi^0$ meson in the final state are described by the eikonal
form. The $\omega$ and $\pi^0$ mesons nucleus optical potentials, appearing in
the $\omega$ meson propagator and $\pi^0$ 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 $\omega$ meson produced in the
nucleus for its momentum greater than 200 MeV. It occurs since the $\omega$
meson dominantly decays outside the nucleus. The dependence of the cross
section on the final state interaction is also investigated. The broadening of
the $\omega$ meson mass distribution spectra is shown to occur due to the large
resolution width associated with the detector used in the experiment.
