Total reaction cross sections and the matter density of finite nuclei

A simple model for total reaction cross sections based on the impulse approximation and the use of an eikonal propagator is derived. Semiquantitative approximations are used to demonstrate that total reaction cross sections are determined by the radius at which the profile function is equal to one mean free path for the incident particle. A simple quantitative relation between the density and the profile function is also provided. The model is tested against existing data for proton-nucleus total reaction cross sections for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40,44,48}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ targets at energies from 100 MeV to 1 GeV. The total reaction cross sections are generally found to be in agreement (with several exceptions) with neutron densities determined either theoretically or from other experiments.