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