In recent years there has been a growing interest in many-body approaches to QHD beyond the mean-field limit. As the corresponding calculations can be quite involved, only a limited number of studies of nuclear properties for finite systems have been performed to date in terms of the Hartree-Fock (HF) approximation [9-12]. Even fewer efforts address the question of correlation effects for the case of finite nuclei [13-17]. The situation is more auspicious for the nuclear matter problem. Correlation effects have been studied extensively in the framework of the relativistic generalization of the Brueckner-Bethe approach. The resulting Dirac-Brueckner method [18,19] may now be considered as the state-of-the-art for nuclear matter calculations. Due to the complicated nonlocal structure of the Dirac-Brueckner equations fully selfconsistent calculations for finite systems do not (yet) seem possible .
This situation is somewhat similar to the difficulties one has to face in the ab initio description of complex Coulomb systems. In this field, however, density functional (DF) methods have attracted considerable interest in recent years (see e.g.). The high efficiency of DF-calculations mainly originates from the local character of the density-dependent exchange-correlation potential, the key ingredient of the basic, single-particle-type equations of DF-theory. The success of DF-methods in quantum chemical and condensed matter applications motivates their extension to relativistic nuclear physics. The foundations of a DF-approach to QHD have been given in  by generalizing the fundamental DF existence theorem to QHD and deriving the Kohn-Sham equations, which, in spite of their single particle character, in principle contain all exchange and correlation effects. More recently, the local density approximation (LDA) for the exchange potential has been introduced and applied to a number of nuclei [22,23]. A comparison with the corresponding HF-results [9-12] has demonstrated that the LDA is an accurate approximation to the computationally much more demanding nonlocal HF-exchange potential. Moreover, a study of the stability of superheavy nuclei  seems to indicate that the inclusion of the LDA-exchange within a linear QHD model has a qualitatively (though not quantitatively) similar effect as the inclusion of nonlinear meson self-interaction terms on the mean-field level.
Last modified: Sep 15, 1997