Nuclear Collisions and Factorization

Total cross sections for nucleon-$\alpha$ and $\alpha \alpha$ collisions are calculated for $86<s<\mathrm{}2776\mathrm{}$ ${\mathrm{GeV}}^2$ in the Glauber approximation. The results are compared with those obtained by assuming factorization for the Pomeron. Calculations for $s>\mathrm{}2776\mathrm{}$ ${\mathrm{GeV}}^2$, with simple assumptions regarding nucleon-nucleon elastic collisions, are also given. For $100<s<\mathrm{}2776\mathrm{}$ ${\mathrm{GeV}}^2$, where $\mathrm{NN}$ data exist, the Glauber-approximation results differ from the factorization predictions by ∼ 4-10%. At higher energies the factorization predictions are approached slowly.