Uncertainties in the eta-Nucleon Scattering Length and Effective Range

The coupled eta-N, pi-N, gamma-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$, pi-N --->eta-N$, gamma-N--->pi-N and gamma-N --->eta-N data in an energy range of about 100MeV or so each side of the eta threshold. The outcome is the appearance of two solutions one which has an eta-nucleon scattering length (a) of about 1.0 fm and a second with a~0.2fm. However, the second solution has an unconventional non-Lorentian form for the T-matrix in the region of the 1535(20)MeV and 1650(30)MeV S-wave pi-N resonances.