EFFECTIVE-INTERACTION FORMULATION OF BOUND AND CONTINUUM SHELL-MODEL CALCULATIONS

The Bloch-Horwitz effective interaction, or reaction matrix, V(E), plays a central role in most of the current realistic shell-model calculations of bound-state nuclear spectra. Its relation to continuum shell-model calculations is less widely appreciated, however, and the purpose of the present review is to formulate the usual bound-state calculation in a manner which is readily generalized to describe scattering as well, in order to show that the analytic continuation of V(E) to continuum energies is just the effective or closed-channel interaction which appears in the reaction formalisms of MacDonald and Feshbach. Since the utility of the effective-interaction concept in practical calculations appears to depend on the convergence of its Born series, this convergence is discussed in terms of Weinberg eigenvalues, and its relation to the state dependence of V(E) is indicated. © 1969.