Multichannel approach to the Glauber model for heavy-ion collisions

A formalism is developed in order to describe, within the Glauber model, the scattering processes between heavy ions in situations involving several coupled channels. The approach is based on a suitable truncation of the number of nuclear states which can be excited at each microscopic nucleon-nucleon collision. The set of coupled equations for the S-matrix elements of the conventional reaction theory is replaced by simple matrix relations, only involving the nucleon-nucleon scattering amplitude and the nuclear densities and transition densities. This method avoids the difficulties arising from the combinatorial aspects of the multiple scattering theories, the slow convergence of the series, and the problems of center-of-mass correlations. We discuss some specific examples of multichannel collisions where the multiple-scattering series can be summed to give analytic expressions for the scattering amplitude. We finally explicate the formalism for the perturbative treatment of mutual excitation and charge-exchange processes