Total and differential cross sections of the dp -> He-3 eta reaction at excess energies between 1 and 15 MeV

New high precision total and differential cross sections are reported for the dp -> He-3 eta reaction close to threshold. The measurements were performed using the magnetic spectrometer ANKE, which is an internal fixed target facility at the COSY cooler synchrotron. The data were taken for deuteron beam momenta between 3.14641 GeV/c and 3.20416 GeV/c, which corresponds to the range in excess energy Q for this reaction between 1.14MeV and 15.01 MeV. The normalization was established through the measurement in parallel of deuteronproton elastic scattering and this was checked through the study of the dp -> He-3 pi(0) reaction. The previously indicated possible change of sign of the slope of the differential cross sections near the production threshold, which could be explained by a rapid variation of the s- and p-wave interference term, is not confirmed by the new data. The energy dependence of the total cross section and the 90 degrees slope parameter are well explained by describing the final state interaction in terms of a complex Jost function and the results are significant in the discussion of eta-mesic nuclei. In combination with recently published WASA-at-COSY data [P. Adlarson et al., Phys. Lett. B 782, 297 (2018)], a smooth variation of the slope parameter is achieved up to an excess energy of 80.9MeV.