  A nonlocal dispersive-optical-model analysis has been carried out for
neutrons and protons in $^{48}$Ca. Elastic-scattering angular distributions,
total and reaction cross sections, single-particle energies, the neutron and
proton numbers, and the charge distribution have been fitted to extract the
neutron and proton self-energies both above and below the Fermi energy. From
the single-particle propagator resulting from these self-energies we have
determined the charge and neutron matter distributions in $^{48}$Ca. A neutron
skin of 0.249$\pm$0.023~fm is deduced. The energy dependence of the total
neutron cross sections is shown to have strong sensitivity to the skin
thickness.
