eta-nucleon scattering length and effective range

The coupled eta N, pi N system is described by a K-matrix method. The parameters in this model are adjusted to Set an optimal fit to pi N --> pi N, pi N --> eta N, and gamma N --> eta N data in an energy range of about 100 MeV each side of the eta threshold. In the notation T-1 + iq(eta) = 1/a + (r(0)/2) q(eta)(2) + sq(eta)(4) + sq(eta)(4), q(eta) being the momentum in the eta N center of mass, the resulting effective range parameters for eta N scattering are found to be a (fm) = 0.75(4)+ i0.27(3), r(0) (fm) = -1.50(13)-i0.24(4), and s (fm(3)) = -0.10(2)-i0.01(1).