  We propose to use antiprotons to investigate the sizes of stable and
neutron-rich exotic nuclei by measurements of the $\pbar A$ absorption cross
section along isotopic chains in inverse kinematics. The expected effects are
studied theoretically in a microscopic model. The $\pbar U$ optical potentials
are obtained by folding free space $\pbar N$ scattering amplitudes with HFB
ground state densities and solving the scattering equations by direct
integration. The mass dependence of absorption cross sections is found to
follow closely the nuclear root-mean-square radii. The total absorption cross
section is shown to be a superposition of cross sections describing partial
absorption on neutrons and protons, respectively. Thus measuring the
differential cross sections for absorption on neutrons and protons will give
information on their respective distributions. In neutron-rich nuclei the outer
neutron layer shields the absorption on the protons giving access to
investigations of antiproton-neutron interactions in matter.
