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Medium effects on $Ξ^-$ production in the nuclear ($K^-$, $K^+$) reaction

We study theoretically medium effects on $Ξ^-$ production in the ($K^-$, $K^+$) reaction, using the optimal Fermi-averaging procedure which describes the Fermi motion of a nucleon on the on-energy-shell $K^-p\to K^+Ξ^-$ reaction condition in nuclei. The result shows the strong energy and angular dependence of the in-medium $K^-p\to K^+Ξ^-$ cross section,which affects significantly the shape and magnitude of the production spectrum for $Ξ^-$ hypernuclear states in the ($K^-$, $K^+$) reaction on a nuclear target.The application to the $Ξ^-$ quasi-free production via the ($K^-$, $K^+$) reaction on a $^{12}$C target is also discussed in a Fermi gas model.