EXA2011

on behalf of the FINUDA Collaboration The presentation deals with the study of the $K_{stop}^{-}A$ $\to$ ${\mathrm{\Sigma }}^{\pm }{\pi }^{\mp }{A}^{\prime }$ reaction, which is studied on light nuclei, $A=$ ${}^{6,7}Li$, ${}^{9}Be$, ${}^{13}C$ and ${}^{16}O$. Final $\mathrm{\Sigma }$'s and $\pi$'s are detected by using the FINUDA spectrometer, which operated at the DA$\mathrm{\Phi }$NE $e^{+}{e}^{-}$ facility (LNF). The ${\mathrm{\Sigma }}^{\pm }$ 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 ${\mathrm{\Sigma }}^{\pm }{\pi }^{\mp }$ 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 ${\mathrm{\Sigma }}^{\pm }$ invariant mass. \\ The ${\mathrm{\Sigma }}^{\pm }{\pi }^{\mp }/K_{stop}^{-}$ 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 ($\gamma ={\mathrm{\Sigma }}^{+}{\pi }^{-}/{\mathrm{\Sigma }}^{-}{\pi }^{+}$) 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 $\overline{K}N$ interaction. \\ The momentum spectra of prompt pions and free sigmas are also discussed as well as the ${\mathrm{\Sigma }}^{\pm }{\pi }^{\mp }$ missing mass behavior. These spectra are discussed in detail rather than the invariant masses. In this case, the ${\mathrm{\Sigma }}^{\pm }{\pi }^{\mp }$ channel is filled by two resonances $\mathrm{\Sigma }(1385)$ and $\mathrm{\Lambda }(1405)$ as well as by the ${\mathrm{\Sigma }}^{\pm }{\pi }^{\mp }$ 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 $$\text{Unknown environment 'thebibliography'}$$