Contribution of particle-particle, hole-hole and particle-hole ring diagrams to the binding energies of finite nuclei

Two classes of diagrams, namely particle-particle, hole-hole (pp, hh) and particle-hole (ph) ring diagrams are summed for the nuclei 16O and 40Ca, and their contributions to the ground-state energy shift ΔE of these nuclei is calculated. We find that hh and mixed diagrams (involving both pp and hh interactions) are not less important than the usual pp ladder diagrams which are summed in the standard Brueckner approach. We also study the convergence of these two classes of diagrams as the dimension of the model space involved is increased, and as a function of the residual interaction used. In evaluating these diagrams a transition-amplitude method is used. This is compared to the quasi-boson correlation expression for the ground-state energy due to particle-hole excitations and to an analogous correlation expression resulting from particle-particle and hole-hole excitations. Additionally we derive expresssions for, and evaluate a subclass of these diagrams namely 'TDA' ring diagrams, where unlike the usual pp, hh and ph diagrams, backward-folding graphs are excluded. We find that the backward-folding graphs are negligible for pp, hh ring diagrams and small for ph graphs. In the smallest model space considered for 40Ca we also obtained the TDA ring diagram contributions via matrix inversion techniques which additionally allow us to study the relative importance of ph exchange graphs neglected in the ring-diagram formalism, and of cross TDA diagrams (i.e. TDA ring diagrams where both pp, hh, and ph interactions are allowed). Finally we study the uncertainties spurious effects introduce in ring-diagram calculations. (orig.)