Elastic and inelastic differential cross sections and analyzing powers are presented for the scattering of 650 MeV protons from ${}_{}{}^{206,207,208}{}_{}{}^{}\mathrm{Pb}$. Five phenomenological optical potential sets with comparable ${\mathrm{\chi }}^2$ values are obtained. The volume integrals and root-mean-square (rms) radii of these potential sets are compared with those expected from the impulse approximation. The agreement is close for the imaginary, but not the real central potentials. The potential rms radii are ∼3% smaller than those from the impulse approximation indicating a ‘‘shrinking’’ of the effective nuclear density. The inelastic data for ${}_{}{}^{206,208}{}_{}{}^{}\mathrm{Pb}$ are analyzed using collective transition densities. The results are then compared with electromagnetic matrix elements to obtain neutron-proton transition matrix element ratios. These are in fairly good agreement with earlier determinations and indicate large core polarization contributions to the low-lying ‘‘two neutron hole’’ states in ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$.

• Received 19 September 1994

DOI:https://doi.org/10.1103/PhysRevC.52.291