The K d -> Lambda(1405) n reaction with the DAFNE set up and the $\bar{K}NN$ system revisited

The $K^{-}$ induced production of $\mathrm{\Lambda }(1405)$ in the $K^{-} d \to \pi \Sigma n$ reaction is investigated having in mind the conditions of the DAFNE facility at Frascati. We find that the fastest kaons from the decay of the $\varphi$ at DAFNE are well suited to see this resonance if one selects forward going neutrons in the center of mass, which reduce the contribution of single scattering and stress the contribution of the double scattering where the signal of the resonance appears clearer. We take advantage to report briefly on a recent work in which in addition to the $\bar{K}NN$ system with total spin S=0, we find a less bound state (although with equally large width) with S=1, like in the $K^{-}d$ reported in the first part.