Propagator nonlocalities in nuclear photopion reactions

The coordinate-space distorted-wave impulse approximation approach to ($\gamma , \pi$) and ($\pi , \gamma$) reactions on light nuclei is extended to include the full nonlocality of the pion, nucleon, and isobar propagators that appear in the photoproduction operator. Whereas the introduction of the pionpropagator nonlocality always produces a large effect on the corresponding term of the nuclear photopion amplitude, the other nonlocalities affect mainly the relative phases of the appropriate contributions leaving their magnitude almost unchanged. As a result, in a nucleus like ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, where at low energies one diagram (the contact term) accounts for most of the cross section and the pion-pole term is not very important, there is almost no change compared with the local calculation. On the other hand, in the nuclei ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, where an appreciable interference occurs between the contact and pion-pole diagrams, the nonlocality effect is quite large. Particularly affected is the reaction on the nucleus ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, even at very low energies. Our treatment blends coordinate- and momentum-space techniques and hence allows one to incorporate other effects such as medium corrections or pionnucleon form factors. Comparison with available data is also discussed.