$Σ^-$ admixture in the $^{10}_Λ$Li hypernucleus with a repulsive $Σ$-nucleus potential

$Σ^-$ hyperon component of the $^{10}_Λ$Li wave function is studied. The $Σ^-$ admixture is vital for production of neutron-rich $Λ$ hypernuclei via mesonic beams. We use a simplified shell model wave function for the $Λ$ channel and calculate the $Σ^-$ admixture directly from coupled equations. Probability of the $Σ^-$ admixture for realistic repulsive $Σ^-$-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 $^{10}\mbox{B}(π^-,K^+){}^{10}_Λ\mbox{Li}$ reaction measured at KEK cannot be explained by production via $Σ^-$ admixture as a doorway state.

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