We derive, within the framework of the Glauber approximation, an exact expression for the optical phase shift function $\overline{\chi }\mathrm{}\left(b\right)\mathrm{}$ which takes into account the center-of-mass correlation function. We calculate total and differential cross sections using the first-order term for $\overline{\chi }\mathrm{}\left(b\right)\mathrm{}$ and compare them with the usual (first-order) optical limit results and, for the lighter nuclei, with the exact Glauber results. The nucleus-nucleus elastic scattering amplitude does not exhibit the large-$q$ divergence which characterizes the usual optical limit. Our results improve the calculated total and differential cross sections dramatically for light nuclei, and significantly for medium and heavy nuclei.

NUCLEAR REACTIONS Glauber approximation, high-energy scattering theory, center-of-mass effects ${}_{}{}^2{}_{}{}^{}\mathrm{H}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ projectiles and targets, $E=2.1\mathrm{}$ GeV/nucleon; calculated $\sigma$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ (${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$), ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$), $E=2.1\mathrm{}$ GeV/nucleon; calculated $\sigma \left(\theta \right)$.

• Received 28 June 1976

DOI:https://doi.org/10.1103/PhysRevC.16.658