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

TL;DR

This paper investigates how medium effects influence $\Xi^-$ hyperon production in the ($K^-$, $K^+$) reaction, highlighting the importance of energy and angular dependencies in the in-medium cross section and their impact on production spectra.

Contribution

It introduces an optimal Fermi-averaging method to accurately account for Fermi motion effects on the in-medium $K^-p o K^+\Xi^-$ reaction in nuclei.

Findings

Strong energy and angular dependence of the in-medium cross section.

Significant impact on the shape and magnitude of $\Xi^-$ production spectra.

Application to $^{12}$C target shows notable medium effects.

Abstract

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