The incoherent pion photoproduction reaction $\gamma d\to {\pi }^{-}pp$ is considered theoretically in a wide energy region $E_{th}\le E_{\gamma }\le 2700$ MeV. The model applied contains the impulse approximation as well as the $NN$ and $\pi N$ final-state-interaction (FSI) amplitudes. The aim of the paper is to study a reliable way for getting the information on elementary $\gamma n\to {\pi }^{-}p$ reaction cross sections beyond the impulse approximation for $\gamma d\to {\pi }^{-}pp$. For the elementary $\gamma N\to \pi N$, $NN\to NN$, and $\pi N\to \pi N$ amplitudes, the results of The George Washington University (GW) Data Analysis Center (DAC) are used. There are no additional theoretical constraints. The calculated cross sections $d\sigma /d\Omega (\gamma d\to {\pi }^{-}pp)$ are compared with existing data. The procedure used to extract information on the differential cross section $d\sigma /d\Omega (\gamma n\to {\pi }^{-}p)$ on the neutron from the deuteron data using the FSI correction factor $R$ is discussed. The calculations for $R$ versus ${\pi }^{-}p$ center-of-mass (CM) angle ${\theta }_1$ of the outgoing pion are performed at different photon-beam energies with kinematic cuts for a “quasifree” process $\gamma n\to {\pi }^{-}p$. The results show a sizable FSI effect $R\ne 1$ from the $S$-wave part of $pp$-FSI at small angles close to ${\theta }_1\sim 0$: this region narrows as the photon energy increases. At larger angles, the effect is small ($|R-1|\ll 1$) and agrees with estimations of FSI in the Glauber approach.

• Received 7 May 2011

DOI:https://doi.org/10.1103/PhysRevC.84.035203