800 MeV protons as probes of neutron transition densities

Angular distribution data for 800 MeV ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(p, p^{\prime })$ (2.61 MeV, $3^{-}$) are analyzed to determine the sensitivity of the analysis to the neutron component of the transition density. The analysis employs the first order Kerman, McManus, and Thaler optical potential model (distorted wave Born approximation together with the impulse approximation). The total error in the multipole moment of the deduced transition density, $M_n\mathrm{}\left(E3\mathrm{}\right)\mathrm{}$, is computed based on uncertainties in (1) the elastic and inelastic scattering data, (2) the geometry of the transition density, (3) the nucleon-nucleon amplitudes, (4) the proton transition density, (5) correlation corrections, and (6) medium modifications to the effective interactions. Under the presumption of an accurate theoretical model, the minimal uncertainty in $M_n\mathrm{}\left(E3\mathrm{}\right)\mathrm{}$ is ±8.5%. Such accuracy permits meaningful comparisons with results from nuclear structure theory.