<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Λ</mml:mi></mml:math>-Nucleon Scattering and the Pion-Hyperon Coupling Constants

Abstract

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 $\ensuremath{\Sigma}$ parity. The coupled Schr\"odinger equations are solved numerically taking into account the $\ensuremath{\Lambda}\ensuremath{\Sigma}$ mass difference. Fitting the $\ensuremath{\Lambda}$-nucleon scattering lengths, as obtained from the hyperfragment data, we have determined the coupling constants. When we use the same core (${x}_{c}=0.35$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$) in all channels and ${{f}_{\mathrm{NN}}}^{2}=0.08125$, we find ${{f}_{\ensuremath{\Lambda}\ensuremath{\Sigma}}}^{2}={{f}_{\ensuremath{\Sigma}\ensuremath{\Sigma}}}^{2}=0.0841$ for the even $\ensuremath{\Sigma}$-parity case and ${{f}_{\ensuremath{\Sigma}\ensuremath{\Sigma}}}^{2}=0.0225$ (${f}_{\ensuremath{\Sigma}\ensuremath{\Sigma}}&lt;0$) and ${{g}_{\ensuremath{\Lambda}\ensuremath{\Sigma}}}^{2}=0.578$ for the odd $\ensuremath{\Sigma}$-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 $\ensuremath{\Lambda}$-nucleon scattering below $\ensuremath{\Sigma}$ threshold. The results suggest the presence of attractive spin-orbit potentials.