$\mathrm{\Xi }$-nucleus potential for ${\mathrm{\Xi }}^{-}$ quasifree production in the ${}^9$Be($K^{-}$, $K^{+}$) reaction

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