Collective Excitations and Ground State Correlations

A generalized RPA formalism is presented which treats pp and ph correlations on an equal footing. The effect of these correlations on the single-particle Green function is discussed and it is demonstrated that a self-consistent treatment of the single-particle Green function is required to obtain stable solutions. A simple approximation scheme is presented which incorporates for this self-consistency requirement and conserves the number of particles. Results of numerical calculations are given for $^{16}$O using a G-matrix interaction derived from a realistic One-Boson-Exchange potential.