Energy and mass-number dependence of hadron-nucleus total reaction cross   sections
  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. 
Akihisa Kohama, Kei Iida, and Kazuhiro Oyamatsu
nucl-th