Λ-Nucleon Scattering and the Pion-Hyperon Coupling Constants

Using the prescription laid down by Brueckner and Watson, we have calculated the pion contribution to the hyperon-nucleon potentials for both even and odd Σ parity. The coupled Schr\"odinger equations are solved numerically taking into account the ΛΣ mass difference. Fitting the Λ-nucleon scattering lengths, as obtained from the hyperfragment data, we have determined the coupling constants. When we use the same core (xc=0.35 μ^-1) in all channels and fNN²=0.08125, we find f_ΛΣ²=f_ΣΣ²=0.0841 for the even Σ-parity case and f_ΣΣ²=0.0225 (f_ΣΣ<0) and g_ΛΣ²=0.578 for the odd Σ-parity case. The rationalized pseudovector coupling constant we denote by f and the rationalized scalar coupling constant by g. For these coupling constants and cores, we have calculated the cross sections for Λ-nucleon scattering below Σ threshold. The results suggest the presence of attractive spin-orbit potentials.