Introduction

A lot of effort has been made to evaluate the basic properties of nuclei, like binding energies and radii of charge distributions, directly from a realistic model of the nucleon-nucleon (NN) interaction which describes the experimental NN scattering data. Already many years ago it was realized that such investigations require a very careful consideration of the short-range correlations, which are induced by the strong short-range and tensor components of a realistic NN interaction. Various techniques of many-body theory have been developed to account for these particular correlations. Here we would like to mention the Brueckner-Bethe hole line expansion [1], the variational approach, in particular the extension to the method of correlated basis functions [2,3], the so-called ``exponential S'' method [4] and the self-consistent Green function approach [5,6].

Such microscopic calculations, however, had rather limited success. As an example we refer to the Brueckner hole-line expansion applied to nuclear matter, for which very detailed studies have been made considering various models for a realistic NN interaction. It turned out that Brueckner-Hartree-Fock (BHF) calculations employing a nuclear interaction with a weak tensor force were able to reproduce the empirical value for the binding energy of nuclear matter but predicted a saturation density which was too large by almost a factor 2. Other interactions with stronger tensor forces lead to satisfying results for the saturation density but underestimate the binding energy by around 5 MeV per nucleon. This result, that microscopic many-body calculations employing realistic NN interactions fail to reproduce binding energy and saturation density, is commonly referred to as the problem of the ``Coester band'' in nuclear matter [7]. Similar results are obtained also for the ground-state properties of finite nuclei [4,8,9].

Various attempts have been made to cure this problem and some of them even succeeded to determine a saturation point of nuclear matter which is very close to the empirical point. One possibility is to introduce many-body forces [10]. Kuo and coworkers demonstrated that the inclusion of particle-particle hole-hole (pphh) ring diagrams tends to shift the saturation point off the Coester band towards the empirical value [11,12]. Another possible solution is the inclusion of relativistic effects within the Dirac-BHF approximation. Motivated by the success of the Walecka model [13] various groups tried to incorporate the modification of the Dirac spinor for the nucleon, due to the interaction with the other nucleons, in BHF calculations [14,15,16]. With the inclusion of the relativistic effects one even obtains results for the saturation properties of nuclear matter which are in agreement with the empirical data [17].

The success of the Dirac-BHF approach cannot be extended to the description of finite nuclei. The relativistic features tend to significantly improve the agreement between calculated values for the energies and radii and the corresponding experimental data [18,19]. The remaining discrepancies (around 0.7 MeV per nucleon in energy and around 0.2 fm for the radius of light nuclei like ¹⁶O and ⁴⁰Ca), however, are still too large to be accounted for.

This situation encourages the investigation of correlations beyond those included in the Dirac-BHF approximation. Such correlations should have a sizeable effect on the groundstate properties of finite nuclei but should not spoil the success of Dirac-BHF in nuclear matter. One can expect that differences of this kind show up in correlations, which are due to surface effects in finite nuclei. Such correlations are typically described in terms of particle-hole (ph) excitations. Therefore our studies should incorporate the correlation effects contained in the particle-hole random phase approximation (ph RPA). Furthermore we would also like to account for the effects of pphh ring diagrams. As discussed above, these correlations show very desirable effects in studies of nuclear matter. Therefore it is interesting to investigate these correlations for finite nuclei as well.

A ``super-RPA'' (SRPA) technique which allows the study of ph, pphh and the possible interference between these kinds of correlations was presented a few years ago [20]. It has been possible to solve the non-linear equations resulting from this SRPA approach for a small model space or by an artificial weakening of the residual interaction. No solution could be obtained for larger model-spaces using realistic interactions. In the present investigation we would like to demonstrate that this failure of the SRPA can be cured by a consistent definition of the single-particle propagator.

After this introduction we summarize in section 2 of this paper the basic ingredients of the SRPA and recall the equations to calculate expectation values for the correlation energy and the occupation probabilities. The self-consistent definition of the single-particle propagator is discussed in section 3. As an example for an application of the SRPA we present in section 4 results on ¹⁶O employing various realistic One-Boson-Exchange (OBE) interactions in different model-spaces. The main conclusions are summarized in the final section.