Coulomb-assisted ${\mathbf{\Sigma }}^{-}$-nucleus bound states in the ($K^{-}$, ${\pi }^{+}$) reaction

Abstract

We study a production of Coulomb-assisted ${\Sigma }^{-}$-nucleus bound states by nuclear ($K^{-}$, ${\pi }^{+}$) reactions within a distorted-wave impulse approximation, so as to examine several types of the $\Sigma$-nucleus potentials that are consistent with the available ${\Sigma }^{-}$ atomic X-ray data and nuclear (${\pi }^{-}$, $K^{+}$) data. We theoretically demonstrate the inclusive ($K^{-}$, ${\pi }^{+}$) spectra of the ${\Sigma }^{-}$ unstable bound states on ${}^{28}$Si, ${}^{58}$Ni, and ${}^{208}$Pb targets at incident $K^{-}$ lab momenta $p_K=400\text{–}800$ MeV/c. The results show that the near-recoilless ($K^{-}$, ${\pi }^{+}$) reaction on the ${}^{58}$Ni target gives a clear candidate to confirm properties of the $\Sigma$-nucleus potentials having a repulsion inside the nuclear surface and an attraction outside the nucleus with a sizable absorption, whereas details of the repulsion of the potential at the nuclear center cannot be determined by the inclusive spectra. This is a promising attempt to extract properties of the $\Sigma$-nucleus potential in the nucleus at forthcoming J-PARC experiments, as a full complement to the analyses of the ${\Sigma }^{-}$ atomic and (${\pi }^{-}$, $K^{+}$) data.