np → ηd near threshold and the s-wave ηN amplitude

We calculate the process np -> eta d near threshold using a separable potential model of the coupled eta N - pi N - pi pi N subystems, and a relativistic three-body calculation for the eta d scattering amplitude. The pi pi N channels are represented by an effective sigma N channel, and we compare the case where the sigma and pi masses are related by m(sigma) = 2m(pi) and no width is considered, to another where the mass and width of the sigma-meson are taken from pi pi scattering data. The np -> eta d cross-section can be well described up to about 60 MeV by models where the real part of the eta N scattering length lies between 0.4 <= Re(a(eta)N) <= 0.6 fm which allows us to determine the s-wave eta N scattering amplitude for -60 <= E <= 60 MeV.