Elastic scattering of 800 MeV/c pions by¹²C has been studied in the diffraction model with a view to determine pion optical potential by the method of inversion. Finding an earlier diffraction model analysis to be deficient in some respects, we propose a Glauber model based parametrization for the elasticS-matrix and show that it provides an exceedingly good fit to the pion-carbon data. The proposed elasticS-matrix gives a closed expression for the pion-¹²C optical potential by the method of inversion in the high energy approximation.

Phenomenological analysis of the $\pi^{-}- ^{12}C$ elastic scattering differential cross-section at 400, 486, 500, 584, 663, 672 and 766 MeV is presented. The analysis is made in the diffraction model framework using the recently proposed parametrization of the phase-shift function. Good description of the experimental data is achieved at all energies. Microscopic interpretation of the parameters of the phase-shift function is provided in terms of Helm's model density parameters.