Discrimination of $\mathrm{\Sigma }$-nucleus potentials in the angular distribution of elastic scattering of ${\mathrm{\Sigma }}^{-}$ hyperons from nuclei

We theoretically investigate the elastic scattering of 50-MeV ${\mathrm{\Sigma }}^{-}$ hyperons from ${}^{28}$Si and ${}^{208}$Pb in order to clarify the radial distribution of $\mathrm{\Sigma }$-nucleus (optical) potentials. The angular distributions of differential cross sections are calculated using several potentials that can explain experimental data of the ${\mathrm{\Sigma }}^{-}$ atomic X-ray and (${\pi }^{-}$, $K^{+}$) reaction spectra simultaneously. The magnitude and oscillation pattern of the angular distributions are understood by the use of nearside/farside decompositions of their scattering amplitudes. It is shown that the resultant angular distributions can considerably discriminate among the radial distributions of the potentials that have a repulsion inside the nuclear surface and an attraction outside the nucleus with a sizable absorption.