Total cross sections for the quasi-free pn --> pn eta reaction in the range from the kinematical threshold up to 20 MeV excess energy have been determined. At threshold they exceed corresponding cross sections for the pp --> pp eta reaction by a factor of about three in contrast to the factor of six established for higher excess energies. To large extent, the observed decrease of the ratio sigma(pn --> pn eta)/sigma(pp --> pp eta) towards threshold may be assigned to the different energy dependence of the proton-proton and proton-neutron final state interactions. The experiment has been conducted using a proton beam of the cooler synchrotron COSY and a cluster jet deuteron target. The proton-neutron reactions were tagged by the spectator proton whose momentum was measured for each event. Protons and neutron outgoing from the pn --> pn eta reaction have been registered by means of the COSY-11 facility, an apparatus dedicated for threshold meson production.
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