We investigate the interaction of an antikaon ($K^{-}$) with the ${}^6\mathrm{Li}$ nucleus, described as an $\alpha +d$ cluster system. The study aims to explore the formation of the $\mathrm{\Lambda }\left(1405\right)$ resonance through the $K^{-}d$ subsystem in the presence of a spectator $\alpha$ particle. In the absence of dedicated experimental data for this reaction, particular attention is given to providing quantitative predictions for the manifestation of the $\mathrm{\Lambda }\left(1405\right)$ structure in low-energy $\overline{K}N$ dynamics within a light nuclear environment. Employing different models of the $\overline{K}N-\pi \mathrm{\Sigma }$ interaction, we calculate the $\pi \mathrm{\Sigma }n$ invariant-mass spectra and the $\alpha$-particle missing-mass spectra, thereby identifying robust features of the $\mathrm{\Lambda }\left(1405\right)$ signal and offering guidance for future experimental investigations.

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• Breakup reactions
• Few-body systems
• Meson & hyperon induced nuclear reactions
• Nuclear forces
• Nuclear reactions
• Particle interactions
• QCD in nuclear reactions