Complete Glauber calculations for proton-nucleus inelastic cross sections

We perform a parameter-free calculation for the high-energy proton-nucleus scattering based on the Glauber theory. A complete evaluation of the so-called Glauber amplitude is made by using the factorization of the single-particle wave functions. The multiple-scattering or multistep processes are fully taken into account within the Glauber theory. We demonstrate that proton- $^{12}$C, $^{20}$Ne, and $^{28}$Si elastic and inelastic scattering ($J^\pi=0^+ \to 2^+$ and $0^+ \to 4^+$) processes are very well described in a wide range of the incident energies from $\sim$50 MeV to $\sim$ 1 GeV. We evaluate the validity of a simple one-step approximation andfind that the approximation works fairly well for the inelastic $0^+ \to 2^+$ processes but not for $0^+ \to 4^+$ where the multistep processes become more important. As an application, we quantify the difference between the total reaction and interaction cross sections of proton-$^{12}$C, $^{20}$Ne, and $^{28}$Si collisions.