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The ratio of the proton's elastic electromagnetic form factors was obtained by measuring the transverse and longitudinal polarizations of recoiling protons from the elastic scattering of polarized electrons with unpolarized protons. The ratio of the electric to magnetic form factor is proportional to the ratio of the transverse to longitudinal recoil polarizations. The ratio was measured over a range of four-momentum transfer squared between 0.5 and 3.5 GeV-squared. Simultaneous measurement of transverse and longitudinal polarizations in a polarimeter provides good control of the systematic uncertainty. The results for the ratio of the proton's electric to magnetic form factors show a systematic decrease with increasing four momentum squared, indicating for the first time a marked difference in the spatial distribution of charge and magnetization currents in the proton.

A static analysis of measurements of $^{12}\mathrm{C}$ elastic electron-scattering cross sections demonstrates unambiguously the existence of a form-factor energy dependence beyond that due to Coulomb distortion effects. This energy dependence increases smoothly as a function of momentum transfer and incident energy in the region covered by the experiments (1.0${\mathit{q}}_{\mathrm{eff}}$2.3 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$, 240${\mathit{E}}_{0}$690 MeV). Outside the first diffraction minimum the discrepancies between the form factors deduced from data obtained at different energies are as large as 5%; in the minimum discrepancies as large as 18% have been observed. Including dispersion corrections which are reasonably compatible with this observed energy dependence in the analysis of the data increases the rms charge radius deduced for $^{12}\mathrm{C}$ by 0.007 to 2.478(9), fm, which is in excellent agreement with the value from muonic x-ray studies.

This paper was published online on 20 May 2005 without several of the authors' corrections incorporated. Equation (13) has been replaced. The captions of Figs. 16--18 have also been replaced. Typographical errors on pages 4, 6, 14, 15, 18, 19, 22, and 24 have all been corrected. The paper has been corrected as of 8 June 2005. The text is correct in the printed version of the journal.

We compare the elastic-scattering cross sections for electrons and positrons from {sup 208}Pb and {sup 12}C. The results demonstrate that the electron-nucleus interaction can be described to good accuracy as a single hard-photon exchange process, and validate the theoretical framework used to interpret electron-scattering data in terms of ground-state charge densities of nuclei.

Our investigation of the energy dependence of dispersive effects in elastic electron scattering from {sup 12}C has been extended to a beam energy of 690 MeV. The cross section observed in the minimum of the form factor is larger than that predicted using a static charge density obtained by fitting lower-energy data with the customary phase-shift analysis. This filling-in'' of the minimum at 690 MeV is even larger than that observed previously at 430 MeV. This indicates an increase in the relative strength of higher-order processes in the minimum with an increase of beam energy; the presence of dispersive effects is the most likely explanation for this effect.

The elastic photon scattering cross sections of $^{208}\mathrm{Pb}$ and $^{206}\mathrm{Pb}$ were measured at 90\ifmmode^\circ\else\textdegree\fi{} and 135\ifmmode^\circ\else\textdegree\fi{} in the energy range from 9.5 to 12 MeV with a tagged photon beam whose energy spread was about 125 keV. The $^{206}\mathrm{Pb}$ cross section rises monotonically with energy, and is consistent with a total photon interaction cross section which has a Lorentzian energy dependence with a peak cross section of 650 mb at 13.6 MeV and a width $\ensuremath{\Gamma}\ensuremath{\simeq}3.8$ MeV. The $^{208}\mathrm{Pb}$ scattering cross section is larger and has some rapid variations with energy; there is a narrow extra peak near 10.04 MeV and there are abrupt increases in the cross section just below 10.6 and 11.3 MeV. The relative scattering observed at the two angles indicates that all of the scattering, including the rapid variations with energy, is dominated by dipole interactions. This dipole assignment for the fine structure is important for the proper interpretation of inelastic electron scattering by $^{208}\mathrm{Pb}$. Some of the observed fine structure in inelastic electron scattering must be dipole; the fine structure previously reported as being due to electric quadrupole excitation should be considered as tentative until the correct dipole contributions are included.

A significant energy dependence was observed in the region of the first diffraction minimum of the form factor for elastic electron scattering from /sup 12/C between 238 and 419 (and 431) MeV. This effect might be attributed to dispersive (two-step) processes.

The elastic magnetic form factor of /sup 3/He has been measured up to q/sup 2/ = 32 fm/sup -2/. Few-body theory fails to explain the location of the diffraction minimum unless nonnucleonic degrees of freedom are explicitly introduced.

The ground-state magnetization densities of $^{207}\mathrm{Pb}$ and $^{205}\mathrm{Tl}$ have been studied by 180\ifmmode^\circ\else\textdegree\fi{} elastic electron scattering. The magnetic form factors were found to be quenched substantially relative to the predictions of the independent-particle model. Microscopic calculations indicate that core polarization can account for part of the observed suppression but it is not sufficient to reproduce the data. The quenching observed at high momentum transfers is comparable to that observed in related electron-scattering studies in the lead region, and can be explained in terms of partial occupancy of shell orbits in $^{208}\mathrm{Pb}$.