Uncertainties in neutron densities determined from analysis of 0.8 GeV polarized proton scattering from nuclei

The first order, spin-dependent microscopic proton-nucleus optical potential of Kerman, McManus, and Thaler is used to analyze 800 MeV polarized proton elastic differential cross section and analyzing power data for target nuclei ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{116,124}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. Approximately model-independent target neutron density distributions are constructed in order to investigate the uncertainty in the deduced neutron densities resulting from the statistical error and the finite range of momentum transfer in the experimental angular distributions. Numerous other experimental and theoretical sources of error and uncertainty are considered to obtain a realistic estimate of the total error in the deduced neutron densities and their root-mean-square radii. The typical error in the root-mean-square radii is found to be ±0.07 fm. Impressive qualitative agreement is found between the deduced neutron matter densities and the corresponding densities predicted by Hartree-Fock calculations.