We theoretically investigate $\mathrm{\Lambda }$ production via a ($K^{-}$, ${\pi }^{-}$) reaction on a ${}^6\mathrm{Li}$ target, using the distorted-wave impulse approximation with a Fermi-averaged $K^{-}n\to {\pi }^{-}\mathrm{\Lambda }$ amplitude. We calculate $\mathrm{\Lambda }$ production spectra using the Green's function method for a ${}^5\mathrm{Li}$ nuclear core $+$ $\mathrm{\Lambda }$ system, employing a $\mathrm{\Lambda }$ folding-model potential based on the ${}^5\mathrm{Li}$ nuclear density, which is constructed from $\alpha \text{−}p$ and ${}^3\mathrm{He}\text{−}d$ cluster wave functions. The results show that the calculated spectrum, which includes $\mathrm{\Lambda }$ bound, resonance, and continuum states, agrees well with the experimental data from the ($K^{-}$, ${\pi }^{-}$) reaction at $p_{K^{-}}=790\mathrm{MeV}/c$ ($0^{\circ }$), where substitutional ${(0p,0p^{-1})}_{\mathrm{\Lambda }n}$ and ${(0s,0s^{-1})}_{\mathrm{\Lambda }n}$ configurations dominate in the near-recoilless reactions. A narrow peak corresponds to a high-lying excited state with spin-parity $J^P=1^{+}$ at $E_{\mathrm{\Lambda }}=13.8\mathrm{MeV}$ near the ${}^3\mathrm{He}+d+\mathrm{\Lambda }$ threshold, arising from interference effects between ${}^5\mathrm{Li}(3/2^{+})\otimes {\left(0s_{1/2}\right)}_{\mathrm{\Lambda }}$ and ${}^5\mathrm{Li}(1/2^{+})\otimes {\left(0s_{1/2}\right)}_{\mathrm{\Lambda }}$ components. This study offers a valuable framework for extracting essential information on the structure and production mechanisms of hypernuclear states from experimental data.

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• Meson & hyperon induced nuclear reactions
• Nuclear reactions
• Optical, coupled-channel & distorted wave models