$\Xi^-$ hyperon and hypernuclear production in the $(K^-,K^+)$ reaction on nucleon and nuclei in a field theoretical model
We investigate the production of a cascade hyperon ($\Xi$) and bound $\Xi^-$ hypernuclei in the $(K^-,K^+)$ reaction on proton and nuclear targets, respectively, within a covariant effective Lagrangian model. The $K^+\Xi^-$ production vertex is described by excitation, propagation and decay of $\Lambda$ and $\Sigma$ resonance states in the initial collision of a $K^-$ meson with a free or bound proton in the incident channel. The parameters of the resonance vertices are taken from previous studies and SU(3) symmetry considerations. The model is able to provide a good description of the available data on total and differential cross sections for the $p(K^-, K^+)\Xi^-$ reaction. The same mechanism was used to describe the hypernuclear production reactions $^{12}$C$(K^-,K^+)^{12}{/!/!/!_{/Xi^-}}$Be and $^{28}$Si$(K^-,K^+)^{28}{/!/!/!_{\Xi^-}}$Mg, where $\Xi$ bound state spinors calculated within a phenomenological model have been employed. Both the elementary and hypernuclear production cross sections are dominated by the contributions from the $\Lambda$(1520) intermediate resonant state. The beam momentum dependence of the $0^\circ$ differential cross sections for the formation of the $\Xi$ hypernuclei is found to be remarkably different from what has been observed previously in the impulse approximation model calculations