Introduction

The range of unstable nuclei accessible with radioactive nuclear beam (RNB) facilities opens up enormous opportunities for the study of nuclear structure, nuclear astrophysics, and fundamental interaction physics [1,2,3]. Intriguing possibilities occur both at the drip lines and in the long iso-chains of nuclei between the valley of stability and the extremes of nuclear existence. Exotica in the latter region are almost sure to appear since the mean field in weakly bound neutron-rich nuclei is modified relative to nuclei near stability, since new types of correlations are likely to occur, and since reduced binding should modify residual interactions among the outermost nucleons. Between the regions of known and near-drip-line nuclei lies an extensive zone where studies will reveal much about the microscopy of the nucleus.

In this paper, we intend to discuss - rather briefly - several theoretical challenges related to the mean-field description of exotic nuclei. We focus on several recent developments and trends while the reader is referred to the review [4] for more discussion on earlier studies and aspects not covered here.