  We demonstrate that the matter density distribution in the surface region is
determined well by the use of the relatively low-intensity beams that become
available at the upcoming radioactive beam facilities. Following the method
used in the analyses of electron scattering, we examine how well the density
distribution is determined in a model-independent way by generating pseudo data
and by carefully applying statistical and systematic error analyses. We also
study how the determination becomes deteriorated in the central region of the
density, as the quality of data decreases. Determination of the density
distributions of neutron-rich nuclei is performed by fixing parameters in the
basis functions to the neighboring stable nuclei. The procedure allows that the
knowledge of the density distributions of stable nuclei assists to strengthen
the determination of their unstable isotopes.
