Neutron isotopic density differences deduced from 0.8 GeV polarized proton elastic scattering

Abstract

The microscopic spin-independent proton-nucleus optical potential defined by Kerman, McManus, and Thaler is used to analyze recent 0.8 GeV polarized proton elastic scattering data from $^{40,48}\mathrm{Ca}$, $^{58,64}\mathrm{Ni}$, $^{116,124}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$. Second-order effects due to target nucleon correlations are included in both the central and spin-orbit parts of the proton-nucleus optical potential. Electromagnetic corrections to the proton density which arise from the electric and magnetic form factors of the neutron, and from the magnetic form factor of the proton, are also calculated. A discussion is presented regarding uncertainties in the nucleon-nucleon amplitudes used in construction of the potential, and also discrete ambiguities which arise from fitting the limited set of nucleon-nucleon data available near 1 GeV are examined. Approximately model-independent forms are assumed for the target neutron density distributions, thereby allowing the statistical and model-dependence errors to be estimated. Neutron density and rms radii are deduced and compared to Hartree-Fock predictions, with good agreement found for most of the seven nuclei studied. Because of the uncertainty in the proton-nucleon amplitudes, neutron density and radius differences are considered more reliable than individual absolute values. Owing to the inclusion of certain second-o\ifmmode \acute{r}\else \'{r}\fi{}der terms discussed here, an accurate determination of these differences is obtained.