Determination of neutron and proton multipole matrix elements in ²⁰⁸ Pb from π^- and π⁺ scattering at 180 MeV

New data for elastic and inelastic π⁺ and π^- scattering by ²⁰⁸Pb at 180 MeV are presented. The elastic scattering data were analyzed with a standard Kisslinger potential in a coordinate space (p- space) calculation using the free π-N amplitudes to calculate the potential coefficients. Momentum-space (p-space) calculations were also performed using the free N amplitudes to calculate on-shell matrix elements and the Landau-Tabakin model for the off-shell. The same ground-state proton and neutron densities were used in these two spaces and the fits are good. The distorted-wave impulse approximation calculations in both spaces, with the same collective model transition densities, reproduce the inelastic differential cross sections quite well. The proton and neutron transition multipole matrix elements and their ratios were calculated from the deformation parameters extracted from fits to inelastic scattering data. It is found that the ratios calculated in these two spaces are quite close to each other and close to those found in a comparison of (e,e') and (p,p') experiments, while the absolute value of matrix elements found in the p-space calculations are ∼15-20 % smaller than those from the r-space calculations. The r-space proton matrix elements are generally in good agreement with those obtained from electron scattering. The effects of the pion-nucleon interactions and form factors used in these calculations were investigated.