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Discrimination of $Σ$-nucleus potentials in the angular distribution of elastic scattering of $Σ^-$ hyperons from nuclei

We theoretically investigate the elastic scattering of 50-MeV $Σ^-$ hyperons from $^{28}$Si and $^{208}$Pb in order to clarify the radial distribution of $Σ$-nucleus (optical) potentials. The angular distributions of differential cross sections are calculated using several potentials that can explain experimental data of the $Σ^-$ atomic X-ray and ($π^-$, $K^+$) 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.