Nucleus-nucleus cross sections and the validity of the factorization hypothesis at intermediate and high energies

Abstract

We use an impact parameter representation of the scattering amplitude to predict nucleus-nucleus and nucleon-nucleus total, reaction, and elastic cross sections at intermediate and high energies. We investigate the question of factorization for these quantities and find that factorization holds to 20% if the radii of the projectile and target nuclei do not differ by more than 50%. This fact and the gross violation of factorization when the nuclei are very different in size are interpreted in the context of a simple geometric model. The dependence of composite particle cross sections and factorization ratios on the size of the elementary nucleon-nucleon cross section ${\ensuremath{\sigma}}_{\mathrm{NN}}^{T}$ is investigated. It is shown that strict functional factorization for total and reaction cross sections in the impact parameter scheme only applies in the limit of a "weak" ${\ensuremath{\sigma}}_{\mathrm{NN}}^{T}$, for which a single scattering approximation is valid. This situation is not realized in practice, and nucleus-nucleus cross sections are instead found to be close to a geometric limit for all but the lightest nuclei. The energy dependence of nucleus-nucleus cross sections is found to be negligible above 100 MeV/particle.