Total and differential cross sections for the dp --> 3He eta reaction have been measured near threshold for 3He center-of-mass momenta in the range from 17.1 MeV/c to 87.5 MeV/c. The data were taken during a slow ramping of the COSY internal deuteron beam scattered on a proton target detecting the 3He ejectiles with the COSY-11 facility. The forward-backward asymmetries of the differential cross sections deviate clearly from zero for center-of-mass momenta above 50 MeV/c indicating the presence of higher partial waves in the final state. Below 50 MeV/c center-of-mass momenta a fit of the final state enhancement factor to the data of the total cross sections results in the 3He eta scattering length of a = |2.9 +/- 0.6| + i (3.2 +/- 0.4) fm.
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