EXA2011

on behalf of the FINUDA Collaboration The presentation deals with the study of the $K^-_{stop} A$ $\rightarrow$ $\Sigma^\pm\pi^\mp A'$ reaction, which is studied on light nuclei, $A=$ $^{6,7}Li$, $^9Be$, $^{13}C$ and $^{16}O$. Final $\Sigma$'s and $\pi$'s are detected by using the FINUDA spectrometer, which operated at the DA$\Phi$NE $e^+e^-$ facility (LNF). The $\Sigma^\pm$ hyperons are reconstructed via the $n \pi^\pm$ decay with the neutrons detected by TOFONE, a large volume plastic scintillator array. The two final $\pi^\pm$ mesons are reconstructed by means of the tracking device of FINUDA, which consists of 5 position sensitive layers. Final $\Sigma^\pm \pi^\mp$ pairs are selected by requiring a proper topology for the $n \pi^\pm$ correlated pairs, where the $n \pi^\pm$ pairs are requested to have $\Sigma^\pm$ invariant mass. \\ The $\Sigma^\pm \pi^\mp/ K^-_{stop}$ emission rates are reported as a function of $A$. These rates are discussed in comparison with previous experimental findings \cite{katz} \cite{vander-velde} and with the existing theoretical issues \cite{staronski} \cite{ohnishi}. They are also used to calculate the $\gamma$ ratio ($\gamma=\Sigma^+\pi^-/\Sigma^-\pi^+$) which strongly increases when the kaon is absorbed on an in-medium proton instead of a free proton. This effect is closely related to the sub-threshold behavior of the $\bar{K}N$ interaction. \\ The momentum spectra of prompt pions and free sigmas are also discussed as well as the $\Sigma^\pm \pi^\mp$ missing mass behavior. These spectra are discussed in detail rather than the invariant masses. In this case, the $\Sigma^\pm \pi^\mp$ channel is filled by two resonances $\Sigma(1385)$ and $\Lambda(1405)$ as well as by the $\Sigma^\pm \pi^\mp$ quasi-free reaction whose phase space develops in the same region as the two resonances \cite{oset}.\\ PACS:21.45.-v, 21.80.+a, 25.80.Nv \begin{thebibliography}{9} \bibitem{katz} P.~A.~Katz et al., Phys.\ Rev.\ {\bf D1 } (1970) 1267. \bibitem{vander-velde} C.~Vander Velde-Wilquet et al., Nuovo Cim.\ {\bf A39 } (1977) 538. \bibitem{staronski} L.~R.~Staronski and S.~Wycech, J.\ Phys.\ {\bf G13} (1987) 1361. \bibitem{ohnishi} A.~Ohnishi, Y.~Nara, V.~Koch, Phys.\ Rev.\ {\bf C56 } (1997) 2767. \bibitem{oset} D.~Jido, E.~Oset and T.~Sekihara, Eur.\ Phys.\ Jour.\ {\bf A47} (2011) 42. \end{thebibliography}