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

TL;DR

This paper theoretically analyzes elastic scattering of $\Sigma^-$ hyperons to distinguish different radial distributions of $\Sigma$-nucleus potentials, using angular distribution patterns to identify potential characteristics.

Contribution

It introduces a method to discriminate among $\Sigma$-nucleus potentials with different radial profiles based on angular scattering data.

Findings

Angular distributions vary significantly with different potential radial profiles.

Nearside/farside decomposition helps interpret scattering patterns.

Potential models with repulsion inside and attraction outside the nucleus fit experimental data.

Abstract

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.