Extracting the photoproduction cross section off the neutron gn-->pi-p from deuteron data with FSI effects

The incoherent pion photoproduction reaction gamma d -> pi(-) pp is considered theoretically in a wide energy region E-th <= E-gamma <= 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 -> pi(-) p reaction cross sections beyond the impulse approximation for gamma d -> pi(-) pp. For the elementary gamma N -> pi N, NN -> NN, and pi N -> 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 -> pi pp) are compared with existing data. The procedure used to extract information on the differential cross section d sigma/d Omega(gamma n -> 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 -> pi(-) p. The results show a sizable FSI effect R not equal 1 from the S-wave part of pp-FSI at small angles close to theta(1) similar to 0: this region narrows as the photon energy increases. At larger angles, the effect is small (vertical bar R - 1 vertical bar << 1) and agrees with estimations of FSI in the Glauber approach.