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

Abstract

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

Comments: 20 pages, 5 figures. arXiv admin note: text overlap with arXiv:1712.02664