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$Ξ$-nucleus potential for $Ξ^-$ quasifree production in the $^9$Be($K^-$, $K^+$) reaction

We study phenomenologically a $Ξ^-$ production spectrum of the $^9$Be($K^-$, $K^+$) reaction at 1.8 GeV/$c$ within the distorted-wave impulse approximation using the optimal Fermi-averaged $K^- p \to K^+ Ξ^-$ amplitude. We attempt to clarify properties of a $Ξ$-nucleus potential for $Ξ^-$-$^8$Li, comparing the calculated spectrum with the data of the BNL-E906 experiment. The results show a weak attraction in the $Ξ$-nucleus potential for $Ξ^-$-$^8$Li, which can sufficiently explain the data in the $Ξ^-$ quasifree region. The strength of $V_0^Ξ=$ $-17 \pm 6$ MeV is favored within the Woods-Saxon potential, accompanied by the reasonable absorption of $W_0^Ξ=$ $-5$ MeV for $Ξ^-p \to Ξ^0n$, $ΛΛ$ transitions in nuclear medium. It is difficult to determine the value of $W_0^Ξ$ from the data due to the insufficient resolution of 14.7 MeV FWHM. The energy dependence of the Fermi-averaged $K^- p \to K^+ Ξ^-$ amplitude is also confirmed by this analysis, and its importance in the nuclear ($K^-$, $K^+$) reaction is emphasized.