Extracting the photoproduction cross sections off the neutron, via the {gamma}n{yields}{pi}{sup -}p reaction, from deuteron data with final-state interaction effects
The incoherent pion photoproduction reaction {gamma}d {yields} {pi}{sup -}pp is considered theoretically in a wide energy region E{sub th}{<=}E{sub {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 {yields} {pi}{sup -}p reaction cross sections beyond the impulse approximation for {gamma}d {yields} {pi}{sup -}pp. For the elementary {gamma}N {yields} {pi}N, N N {yields} N N, and {pi}N {yields} {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 {yields} {pi}{sup -}pp) are compared with existing data. The procedure used to extract information on the differential cross section d{sigma} /d{Omega}({gamma}n {yields} {pi}{sup -}p) on the neutron from the deuteron data using the FSI correction factor R is discussed. The calculations for R versus {pi}{sup -}p center-of-mass (CM) angle {theta}{sub 1} of the outgoing pion are performed at different photon-beam energies with kinematic cuts for a ''quasifree'' process {gamma}n {yields} {pi}{sup -}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}{sub 1}{approx}0: this region narrows as the photon energy increases. At larger angles, the effect is small (|R - 1|<<1) and agrees with estimations of FSI in the Glauber approach.