Microscopic theory of multiple scattering for open-shell nuclei

Abstract

We consider the scattering of a distinguishable projectile from a nucleus assuming that the underlying interaction Hamiltonian is a sum of two-body potentials. We show that the effective interaction of the projectile with the nucleus in a truncated nuclear model space can be calculated as a linked-cluster expansion. The rules for evaluating this expansion are given in terms of the nucleon-nucleon and projectile-nucleon potentials and the exact eigenstates of the (effective) shell-model interaction. The shell-model interaction is required to be an energy-independent, Hermitian potential; its expression in terms of the underlying two-body potential is given by folded diagrams. The terms in the expansion of the effective projectile-nucleus interaction must also contain folded diagrams but, unlike the shell-model potential, these are energy-dependent in order to describe the singularities associated with the crossing of the scattering thresholds as the projectile energy is varied. Once the effective interaction is known, elastic and inelastic scatterings may be evaluated numerically by solving a finite-dimensional coupled-channel equation.