  In this work, we present an updated model for nuclear $\pi^0$
photoproduction, which incorporates pion second-order rescattering on
intermediate excited nuclear states. Our approach is based on the distorted
wave impulse approximation in momentum space. The many-body medium effects are
incorporated in the complex effective $\Delta$ self-energy, employing the
results of the recently developed second-order pion-nucleus scattering
potential. The experimental data for ${}^{12}$C and ${}^{40}$Ca are
successfully described without the need to fit the model parameters of the
photoproduction amplitude as a result of incorporating the second-order part of
nuclear photoproduction potential, which involves intermediate nucleon
spin-flip and charge exchange.
