Nankai Univ, Dept Phys, Tianjin 300071, Peoples R China
; Chinese Acad Sci, Inst High Energy Phys, Beijing 100039, Peoples R China
; China Ctr Adv Sci & Technol, World Lab, Beijing 100080, Peoples R China
The eta-nucleon (eta N) interactions are deduced from the heavy-baryon chiral perturbation theory to the next-to-leading-order terms. Combining the relativistic mean-field theory for nucleon system, we have studied the in-medium properties of the eta meson. We find that all the elastic-scattering eta N interactions come from the next-to-leading-order terms. The eta N sigma term is found to be about 280 +/- 130 MeV. The off-shell terms are also important to the in-medium properties of the eta meson. On application of the latest determination of the eta N scattering length, the ratio of the eta-meson effective mass to its vacuum value is near 0.84 +/- 0.015, whereas the optical potential is about -(83 +/- 5) MeV, at the normal nuclear density.