Pion nucleus potential from scattering data and a test of charge symmetry

Abstract

A modified form of the inverse scattering method of Newton and Sabatier is applied to generate local complex potentials for the scattering of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ on zero spin and zero isospin nuclei. The phase shifts and inelasticity parameters, used as inputs, are extracted from a partial wave analysis of the elastic differential cross-section data by parametrizing the nuclear amplitude. Analytic mapping techniques are used to get a better accuracy in the phase shift analysis. The nuclear parts of the inversion potentials for ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ scattering on ${}^{4}\mathrm{He}$ are compared as a possible test of charge symmetry breaking. The method has been repeated for several incident pion energies below the (3,3) resonance threshold.