Formula for proton-nucleus reaction cross section at intermediate   energies and its application
  We construct a formula for proton-nucleus total reaction cross section as a function of the mass and neutron excess of the target nucleus and the proton incident energy. We deduce the dependence of the cross section on the mass number and the proton incident energy from a simple argument involving the proton optical depth within the framework of a black sphere approximation of nuclei, while we describe the neutron excess dependence by introducing the density derivative of the symmetry energy, L, on the basis of a radius formula constructed from macroscopic nuclear models. We find that the cross section formula can reproduce the energy dependence of the cross section measured for stable nuclei without introducing any adjustable energy dependent parameter. We finally discuss whether or not the reaction cross section is affected by an extremely low density tail of the neutron distribution for halo nuclei. 
Kei Iida, Akihisa Kohama, and Kazuhiro Oyamatsu