${\Xi }^{-}$ emission probabilities at $(K^{-},K^{+})$ reaction points and the $\Xi N$ interaction

Abstract

${\Xi }^{-}$ escaping and scattering probabilities in the $(K^{-},K^{+})$ reaction with nuclear targets is investigated on the basis of the eikonal approximation. Calculations are performed using the $S=-2$ sector of the Nijmegen model-D interaction, whose hard core radii are treated phenomenologically. %The ${\Xi }^{-}N$, ${\Xi }^{-}p$ and ${\Xi }^{-}n$ elastic cross sections are The ${\Xi }^{-}N$ elastic cross sections are derived from the ${}^9$Be$(K^{-},K^{+})$ data of the BNL-E906 experiment, which is useful to determine the hard-core radii in $P$-states. The $\Xi$ single-particle potential energy is investigated with the G-matrix calculation in nuclear matter, which is sensitive to the hard-core radii in $S$-states. The important constraint for the $\Xi N$ interaction is obtained by combining the two analyses.

Comments: 10 pages, 3 figures