${\Sigma }^{-}$ admixture in the ${}_{\Lambda }^{10}$Li hypernucleus with a repulsive $\Sigma$-nucleus potential

Abstract

${\Sigma }^{-}$ hyperon component of the ${}_{\Lambda }^{10}$Li wave function is studied. The ${\Sigma }^{-}$ admixture is vital for production of neutron-rich $\Lambda$ hypernuclei via mesonic beams. We use a simplified shell model wave function for the $\Lambda$ channel and calculate the ${\Sigma }^{-}$ admixture directly from coupled equations. Probability of the ${\Sigma }^{-}$ admixture for realistic repulsive ${\Sigma }^{-}$-nucleus potentials is less by several times than that for attractive potentials and does not exceed $0.1\%$. We conclude that the cross sections of the ${}^{10}\text{mbox}B({\pi }^{-},K^{+}){}_{\Lambda }^{10}\text{mbox}Li$ reaction measured at KEK cannot be explained by production via ${\Sigma }^{-}$ admixture as a doorway state.