The 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 get an optimal fit to pi N -> pi N, pi N -> eta N and gamma N -> eta N data in an energy range of about 100MeV each side of the eta threshold. In the notation T^(-1)+iq_(eta) = 1/a + (r_0)/2 q^2_(eta) + s q^4_(eta), 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)