I investigate the elastic electron scattering off nuclei far from the
stability line. The effects of the neutron and proton skins and halos on the
differential cross sections are explored. Examples are given for the charge
distribution in Sn isotopes and its relation to the neutron skin. The neutron
halo in 11Li and the proton halo in 8B are also investigated.
Particular interest is paid to the inverse scattering problem and its
dependence on the experimental precision. These studies are of particular
interest for the upcoming electron ion colliders at the GSI and RIKEN
facilities.Comment: 27 pages, 9 figures, accepted for publication in J. Phys.