  We systematically analyze nuclear reaction data that are sensitive to nuclear
size, namely, proton-nucleus total reaction cross sections and differential
elastic cross sections, using a phenomenological black-sphere approximation of
nuclei that we are developing. In this framework, the radius of the black
sphere is found to be a useful length scale that simultaneously accounts for
the observed proton-nucleus total reaction cross section and first diffraction
peak in the proton elastic differential cross section. This framework is
expected to be applicable to any kind of projectile that is strongly attenuated
in the nucleus. On the basis of a cross-section formula constructed within this
framework, we find that a less familiar $A^{1/6}$ dependence plays a crucial
role in describing the energy dependence of proton-nucleus total reaction cross
sections.
