Final state interaction effects in η photoproduction on two - and three - body nuclei

The role of final state interaction in η photoproduction on a deuteron as well as on three-body nuclei is investigated within few-body scattering theory. Deviation of the theory from the available experimental results is briefly discussed. 1. Incoherent η photoproduction on a deuteron Photoproduction of η mesons on the deuteron near threshold is strongly influenced by final state interaction (FSI). The main reason for the importance of FSI is a strong mismatch between a large momentum transfer and a minimal kinetic energy in the final ηNN system, which on the other hand can effectively be balanced by the interaction between the final particles. Furthermore, an appreciable attraction in the ηNN system generates a virtual pole in the three-body scattering amplitude [ 1], which in turn leads to a strong rise of the cross section just above threshold in agreement with experimental results [ 2]. The calculation was performed using a separable representation of the driving ηN and NN scattering amplitudes as described in detail in [ 1]. For the ηN interaction an isobar ansatz of [ 3] was used with inclusion of S 11 (1535) only. The corresponding parameters were adjusted such that the ηN scattering length a ηN = (0.5 + i0.32) fm, which we consider as an approximate average of the scattering lengths provided by modern ηN analyses, is reproduced and that at the same time a good description is provided of the processes πN → πN, π − p → ηn, and πN → ππN. The NN-interaction was considered only in the dominant s wave scattering states. We have used the version BEST3 for 1 S 0 and correspondingly BEST4 for the triplet states. The separable representation allows one to reduce the three-body problem to a set of integral equation in one variable only, whose structure is analogous to the usual Lippmann-Schwinger equation for two coupled channels (η + d) and (N + N *). The resulting inclusive cross section for γd → ηX (X = {np, d}) is shown by the solid curve in Fig. 1. As one can see, although the three-body calculation leads to a sizeable improvement as compared to the impulse approximation (dashed line), a quantitative agreement with the data is not yet achieved. A possible reason for this disagreement could be the neglect of πNN configurations in the calculation. The contribution of the