High-Energy Nucleus-Nucleus Collisions. I. General Theory and Applications to Deuteron-Deuteron Scattering

A theoretical analysis of the collisions of high-energy nuclei with nuclei is carried out by means of a simple extension of the Glauber approximation. Effects of multiple collisions are taken into account. The general formalism is applied to deuteron-deuteron collisions. Expressions are derived for single-, double-, triple-, and quadruple-scattering amplitude operators for deuteron-deuteron collisions in terms of nucleon-nucleon scattering amplitude operators. A new type of double-scattering effect, qualitatively quite different from the Glauber "shadow" effect which was discovered for particle-deuteron collisions, is described. For the case of nucleon-nucleon interactions described by purely absorbing (black) spheres, it corresponds qualitatively to a "double-counting" correction in the deuteron-deuteron absorption cross section. This effect corresponds to collisions in which one nucleon in the incident deuteron interacts with only one nucleon in the target, and the other nucleon in the incident deuteron interacts with only the other nucleon in the target. The formalism is applied to a calculation of the deuteron-deuteron total cross section ${\sigma }_{\mathrm{dd}}$. It is shown that the contribution to ${\sigma }_{\mathrm{dd}}$ arising from the new type of double-scattering correction is approximately 50% of that arising from the usual (i.e., shadow-type) double-scattering correction. Numerical results are compared with measurements. A simple analysis of the deuteron-deuteron elastic scattering angular distribution is presented. It is shown that for a rather large range of scattering angles away from the forward direction, double scattering is the dominant process in elastic scattering, and that in this region the new type of double scattering is quantitatively much more important than the usual double-scattering process which also appears in nucleon-deuteron collisions.