Precise Test for the Unitarized Pion Photoproduction Impulse Amplitude in Exclusive Nuclear Reactions

We construct an impulse operator for pion photoproduction from threshold through the $\Delta$ region, suitable for nuclear use, with improved Born dynamics and unitarity. Taking the example of the reaction ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(\gamma ,{\pi }^{+}){}_{}{}^{14}{}_{}{}^{}\mathrm{C}(\mathrm{g}.\mathrm{s}.\mathrm{})$, we demonstrate superior features of the amplitude at different energies. At or near the $\Delta$ resonance, very sizable effects arise both from the unitarity and from the refined treatment of the pionic final-state interaction in the $\Delta$-hole approach.