Nucleon charge and magnetization densities from Sachs form factors

Relativistic prescriptions relating Sachs form factors to nucleon charge and magnetization densities are used to fit recent data for both the proton and the neutron. The analysis uses expansions in complete radial bases to minimize model dependence and to estimate the uncertainties in radial densities due to limitation of the range of momentum transfer. We find that the proton charge distribution, fitted to recent recoil-polarization data displaying an almost linear decrease in $G_{\mathrm{Ep}}{/G}_{\mathrm{Mp}}$ for $Q^2\gtrsim 1(\mathrm{GeV}{/c)}^2,$ is significantly broader than its magnetization density. We also find that the magnetization density is broader for the neutron than the proton. The neutron charge form factor is consistent with the Galster parametrization over the available range of $Q^2,$ but the relativistic inversion produces a softer radial density. Discrete ambiguities in the inversion method are analyzed in detail. The method of Mitra and Kumari ensures compatibility with pQCD at large $Q^2$ and is most useful for extrapolating form factors. Although a recent observation that ${\mathrm{QF}}_{2p}{/F}_{1p}$ is approximately constant for $2<\mathrm{}{Q}^2<6\mathrm{}(\mathrm{GeV}{/c)}^2$ appears to be inconsistent with the $Q^{-2}$ scaling expected from quark helicity conservation, our analysis fits these data while remaining consistent with pQCD for large $Q^2.$