Reaction matrix theory for finite nuclei

Abstract

A reaction matrix for calculations on finite nuclei is defined. It is shown that the single-particle energies in the propagator of the reaction matrix should be calculated self-consistently from the reaction matrix. With this definition, which in fact has been used in several previous publications, important terms in the Goldstone expansion are effectively summed, when one calculates the total energy to first order in the reaction matrix. This result is important if one e.g. calculates with harmonic oscillator wave functions. The remaining terms in the energy expansion are three-body terms and the single-particle excitation terms. The latter will cancel or be small only if a self-consistent single-particle potential is used. Some other higher-order terms are also discussed. The definition of the self-consistent or shell-model potential is briefly discussed.