Photopions from nuclei in the distorted-wave impulse approximation

The formalism for photoproduction of pions from nuclei has been developed in the distorted-wave impulse approximation, taking into account the effect of the change in pion momentum in nuclear medium. Detailed calculations have been done for the reaction ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\gamma , {\pi }^{+}){}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ for photon energies from 170 to 380 MeV, with a view to investigate the effect due to the gradient operator ${\overrightarrow{\nabla }}_{\pi }$ for momentum of the pion and test the sensitivity of the photopion cross sections to the details of the pion-nucleus optical potential. The results clearly establish that the gradient operator increases the cross sections throughout the energy region considered, the increase being small at lower energies. Also with ${\overrightarrow{\nabla }}_{\pi }$, the cross sections are rendered less sensitive to the optical potential. The calculated differential cross sections agree very well with the recent experimental data of Shoda et al. for $\gamma$-ray energy of 200 MeV. However, the cross sections obtained at medium energies are higher when compared to the available experimental data.