Analysis of the Pion-Nucleus Scattering within the Folding and the Kisslinger Type Potentials

TL;DR

This paper compares folding and Kisslinger-type optical potentials to analyze pion-nucleus elastic scattering data across various nuclei and energies, highlighting the importance of in-medium effects on the elementary pion-nucleon amplitude.

Contribution

It introduces a detailed comparison of folding and Kisslinger optical potentials for pion-nucleus scattering, incorporating in-medium effects on the pion-nucleon interaction parameters.

Findings

Both models agree well with experimental data.

In-medium effects significantly modify pion-nucleon amplitude parameters.

Surface regions of the potentials are consistent between models.

Abstract

Elastic cross sections are calculated and compared with the data on $\pi^{\pm}$ scattering on $^{28}$Si, $^{40}$Ca, $^{58}$Ni, $^{208}$Pb nuclei in the energy range from 130 to 290 MeV. To this end, both the folding optical potential (OP) and the local modified Kisslinger-type OP were calculated, and then the $\pi A$ cross sections were obtained by solving the Klein-Gordon equation to account for the relativization and distortion wave effects. In the folding OPs, the parameters of the elementary $\pi N$ amplitude were fitted when describing the $\pi A$ scattering data, and thus the essential in-medium effect on the parameters of the $\pi N$ amplitude was established since the pion is scattered not on a free but on a bound nuclear nucleon. Fairly good agreement with experimental data was obtained for both models of optical potentials and their forms turn out to be in coincidence in the region of their surfaces.