Taking advantage of both the high mass resolution of the COSY-11 detector and the high energy resolution of the low-emittance proton-beam of the Cooler Synchrotron COSY we determine the excitation function for the pp --> pp eta reaction close-to-threshold. Combining these data with previous results we extract the scattering length for the eta-proton potential in free space to be Re(a_{p eta}) = 0+-0.43 fm and Im(a_{p eta}) = 0.37(+0.40)(-0.16) fm.
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