Elastic Scattering of Low-Energy Pions and Muons from Lead

Abstract

The small-angle (13°-40°) part of the elastic differential cross section for the scattering of low-energy ($T_{\pi }\sim 100$ MeV) positive and negative pions from natural lead was measured. The same quantity was also measured for the scattering of low-energy muons from lead. The muon-lead data were used to determine the rms charge radius of the lead nucleus. Assuming a Fermi shape for the charge density with a skin thickness of 2.21 fm, the result was ${{〈r^2〉}_{\mathrm{ch}}}^{\frac{1}{2}}=5.50\mathrm{}\pm 0.06$ fm. The ${\pi }^{\pm }-\mathrm{P}\mathrm{b}$ data, taken in the region of large Coulomb nuclear interference, were compared with predictions of the pion-nucleus optical model according to Watson and Kisslinger. Excellent fits to the data were obtained by treating the model phenomenologically; however, the best-fit optical-model parameters were not in agreement with the values computed from experimental pion-nucleon phase shifts. Since the ${\pi }^{\pm }-\mathrm{P}\mathrm{b}$ elastic cross sections are sensitive to the neutron density distribution, a determination of the rms neutron-matter radius could be made. Assuming a Fermi shape for the neutron-matter density, with a skin thickness of 2.21 fm, the result was ${{〈r^2〉}_{\mathrm{n}.\mathrm{m}.\mathrm{}}}^{\frac{1}{2}}={5.45}_{-0.25\mathrm{}}^{+0.13\mathrm{}}$ fm.