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We study the production of $Xi^-$-hypernuclei, $^{12}_{Xi^{-}}$Be and $^{28}_{Xi^{-}}$Mg, via the ($K^-,K^+$) reaction within a covariant effective Lagrangian model, employing the bound $Xi^-$ and proton spinors calculated by the latest quark-meson c oupling model. The present treatment yields the $0^circ$ differential cross sections for the formation of simple s-state $Xi^-$ particle-hole states peak at a beam momentum around 1.0 GeV/c with a value in excess of 1 $mu$b.
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