Cluster Decomposition of the S Matrix and Density Expansion of Nuclear Phase Shifts

Abstract

A systematic way of improving the Glauber multiple-scattering theory is discussed from the standpoint of the cluster decomposition of the S matrix. Since the decomposition is worked out without appealing to any specific approximations, the result is formally exact. Prescriptions which specify the order of each cluster contribution are considered (Z-ordering) in order to minimize the error arising when one introduces truncations in the theoretical scheme. Due to this Z-ordering technique, the convergence of the scheme seems very rapid especially for non-overlapping potentials. The structure and some basic properties of the two-body clusters are discussed in some detail. From the cluster-factorized expression for the S matrix, nuclear-density expansion for optical phase shifts is derived.