The application of Glauber theory has been playing an increasingly important role with the study of unstable or exotic nuclei. Its adaptation to medium- and high-energy nucleus-nucleus collisions is severely limited because one has to evaluate the matrix elements of multiple-scattering operators. The extraction of physical observables has been done using “approximate” Glauber theory, whose validity is hard to evaluate. We perform a full calculation of the matrix elements using Monte Carlo integration and analyze the elastic differential cross sections and the total reaction cross sections for $p+{}^{12}\mathrm{C}, {}^{4,6}\mathrm{He}+{}^{12}\mathrm{C}$, and ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ collisions. We use the variational Monte Carlo wave functions for ${}^{4,6}\mathrm{He}$ and ${}^{12}\mathrm{C}$ obtained by using realistic two- and three-nucleon potentials. We demonstrate the performance of the Glauber-theory calculations by comparing with available experimental data. We further discuss the accuracy of the conventional approximate methods in light of the cumulant expansion for Glauber's phase-shift function.

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• Nuclear reactions
• Nuclear many-body theory