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We study phenomenologically inclusive spectra of the $^6$Li($\pi^-$, $K^+$)reaction at 1.2 GeV/$c$ within a distorted-wave impulse approximation with theoptimal Fermi-averaging $\pi^- p \to K^+ \Sigma^-$ $t$ matrix. We attempt toclarify the property of a $\Sigma$-nucleus potential for $\Sigma^-$-$^5$He bycomparing the calculated spectra with the data of the J-PARC E10 experiment.The result shows that the repulsive and absorptive components of the$\Sigma^-$-$^5$He potential provide the ability to explain the data of thecontinuum spectra in $\Sigma$ and $\Lambda$ regions; the strengths of $V_\Sigma\simeq$ +30 MeV and $W_\Sigma \simeq$ $-$26 MeV are favored within theWoods-Saxon potential, consistent with analyses for heavier nuclei. Effects ofthe size and potential range for $\Sigma^-$-$^5$He in the neutron excess of$(N-Z)/(N+Z)=$ 0.2 are also discussed.

Repulsion and absorption of the $\Sigma$-nucleus potential for $\Sigma^-$-$^5$He in the $^6$Li($\pi^-$, $K^+$) reaction