Extracting the photoproduction cross section off the neutron $\gamma $n$\to \pi ^{-}$p from deuteron data with FSI effects

The incoherent pion photoproduction $\gamma $d$\to \pi ^{-}$pp is considered theoretically in a wide energy region below 2.7 GeV. The model applied contains the impulse approximation (IA) as well as the NN- and $\pi $N-FSI. The aim of the project is to study a reliable way for getting the information on elementary $\gamma $n$\to \pi ^{-}$p cross section beyond the IA for $\gamma $d$\to \pi ^{-}$pp. For the elementary $\gamma $N$\to \pi $N, NN$\to $NN, and $\pi $N$\to \pi $N amplitudes, the results of the GW DAC are used. There are no additional theoretical constraints. The calculated d$\sigma $/d$\Omega (\gamma $d$\to \pi ^{-}$pp) are compared with existing data. The procedure used to extract information on the d$\sigma $/d$\Omega (\gamma $n$\to \pi ^{-}$p) on the neutron from the deuteron data using the FSI correction factor R is discussed. The results show a sizeable FSI effect R $\ne $ 1 from S-wave part of pp-FSI at small angles close to $\theta _{1}\sim $0: this region narrows as the photon energy increases. At larger angles, the effect is small ($\vert $R-1$\vert <<$1) and agrees with estimations of FSI in the Glauber approach.