Rescattering corrections to the coherent photoproduction ofπ0onHe4,C12, andO16at low energies

Coherent photoproduction of ${\pi }^0$ on ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ is studied in the energy region $E_{\gamma }=200\mathrm{}-400$ MeV, with particular emphasis on the questions: where is rescattering important, what structure does it have, and what approximate scheme can be applied for calculating it? For this purpose, the second-order scattering term has been calculated in a model which incorporates the Fresnel correction to the Glauber theory, and takes into account the spin and the charge exchange effects. It is noted that near the threshold the correction would be very small. However, where rescattering is important, the spin and charge exchange effects and also Fresnel corrections are found to be important. This means that only in specific cases will a distorted-wave approach or a Glauber expansion provide the correct higher-order contributions for these reactions.