$\Sigma^-$ hyperon component of the $^{10}_\Lambda$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 $^{10}\mbox{B}(\pi^-,K^+){}^{10}_\Lambda\mbox{Li}$ reaction

measured at KEK cannot be explained by production via $\Sigma^-$ admixture as a doorway

state.

**Document number: ** 2014-1/885

**Authors: **D.E.Lanskoy, A.Sinyakova

**Email: ** lanskoy@sinp.msu.ru