Feasibility of extracting a $\Sigma^-$ admixture probability in the neutron-rich $^{10}_{\Lambda}$Li hypernucleus

We examine theoretically production of the neutron-rich $^{10}_{\Lambda}$Li hypernucleus by a double-charge exchange ($\pi^-$, $K^+$) reaction on a $^{10}$B target with distorted-wave impulse approximation calculations. The result shows that the magnitude and shape of the calculated spectrum at 1.20 GeV/c by a one-step mechanism $\pi^-p \to K^+ \Sigma^-$ via $\Sigma^-$ doorways caused by a $\Sigma^-p \leftrightarrow \Lambda n$ coupling can explain the recent experimental data, and the $\Sigma^-$ admixture probability in $^{10}_{\Lambda}$Li is found to be the order of 10$^{-1}$ %. The ($\pi^-$, $K^+$) reaction provides a capability of extracting properties of wave functions with $\Lambda$-$\Sigma$ coupling effects in neutron-rich nuclei, together with the reaction mechanism.