Effective range theory and the low energy hyperon-nucleon interactions

Abstract

The effective range theory is treated in the case of coupled channels where allowance is made for channels with higher l-waves. Also it is shown how to take the Coulomb interaction into account. A shape-independent relation connecting the volume integral of the potential and the scattering length is derived. Applying this to the analyses of the light hyperfragments leads to the estimates of the Λ-nucleon scattering lengths: a 0=− 3.6 +3.6 −1.8 f for S=0 and a 1=−(0.53±0.12)f for S=1 The low energy Σ −-proton reactions are considered. It is shown how one can take account of the kinematical effects due to the mass differences between the members of the same isomultiplet. We have calculated the effective range parameters for three different potentials corresponding to global ( g NN π = g ΣΣπ = g ΛΣπ ) and antiglobal ( g NNπ = − g ΣΣπ = − g ΛΣπ ) symmetry. These are then applied to the Σ −-proton reactions. It is shown that the global symmetry assumption is consistent with the Λ-nucleon scattering lengths, the ratio r R = Σ 0 (Σ 0 + Λ 0) obtained in the Σ −-proton reactions and with the data in the K − absorption in deuterium. Also it is shown that the same data rule out the antiglobal symmetry assumption.