Introduction

Heavy atomic nuclei belong to the class of many-body systems that are too complex for a direct description from first principles, and too small for a quantitative statistical approach. Quantum effects, strong interactions, and repulsive core are common features of several physical systems, like nuclei, metal clusters and grains, and atomic clouds, that are at present intensively studied.

The fact that nucleon-nucleon (NN) interaction is a long-range remnant of the QCD interactions between quarks and gluons coupled to colorless states, and hence is not known in a closed form, adds all the more to the complexity of nuclear systems. Although on-shell properties of the NN interactions in the vacuum are phenomenologically very well known and parametrized, see, e.g., Ref. [1], the off-shell properties are not. Nevertheless, light nuclei (up to A=10 nucleons) can be with a large success described by direct methods based on phenomenological NN potentials [2,3]. However, much work is being performed, and even more is needed, to achieve a more complete state of knowledge of the NN and NNN interactions.

A direct description of heavy nuclei, based on the NN interactions and leading to a complete wave function, is neither feasible nor, in fact, sensible. Only a limited number of specific states of heavy nuclei, mostly at low energies, can be studied in experiment. These states do not depend on the whole complexity of the NN interactions, and do not probe the whole A-body Hilbert space. Therefore, a great deal of effort and success in nuclear structure physics has been devoted to deriving effective interactions that would describe main features of nuclei within a restricted space. Due to applications of the effective field theory and renormalization group techniques, such derivations are recently gaining dramatically new momentum [4,5].

Shell-model calculations that use derived effective interactions are by now possible for systems with A$\sim$12 nucleons [6]. These methods look very promising, and can probably be applied to still heavier systems. It is extremely encouraging that similar shell-model calculations using phenomenological effective interactions fitted to data, are very successful in describing properties of all nuclei with up to about A$\sim$50 particles [7]. In special cases such methods can be even used in much heavier systems. This shows that basic low-energy properties of nuclei are indeed governed by relatively simple two-body effective interactions acting in manageable Hilbert spaces, and gives us hope that derived effective interactions may become a link between the NN forces and the present-day phenomenology in heavy nuclei.

Significant progress was achieved in recent years in a phenomenological mean-field description of a multitude of nuclear states and phenomena. Although detailed formulations vary, most mean-field approaches are presently based on the energy density formalism, either in a relativistic or non-relativistic flavor. On the other hand, much too little work has been done to derive the energy density functionals from the underlying NN forces and/or effective interactions. This direction of research is far behind the analogous efforts and successes achieved in molecular physics, and will probably see a substantial increase of activity in the coming years.

In general, mean-field methods correctly reproduce the main features of structure of heavy nuclei. Very often, however, this is not sufficient, and a higher degree of precision is requested from theoretical descriptions in order to understand fine-scale nuclear phenomena. In particular, the limits of nuclear binding depend on a detailed balance between the bulk, surface, and pairing effects, see, e.g., Ref. [8]. Although a large progress has recently been achieved [9], a microscopic description of nuclear binding energies within a 100keV precision is, for the moment, an unreachable goal. Similarly, detailed properties of rotational bands give us extremely precise information on the structure of microscopic states, and are fairly well understood on the phenomenological level, whereas a link to the corresponding terms in the energy functional is still unclear.

In the present talk, a number of recent specific achievements in the theoretical studies of heavy nuclei are briefly discussed. For example, deformations and halos in heavy neutron-drip nuclei, as well as widths of one-body resonances, were calculated with the coupling of bound and continuum states taken into account. A great progress in understanding proton-neutron correlations in N$\sim$Z nuclei was achieved. New kind of collective motion, the magnetic rotation, was predicted and found in experiment. Origins of the pseudospin symmetry are now being traced back to simple relativistic single-particle effects. Self-consistent calculations of superheavy nuclei gave us a new insight into the shell structure in the presence of a very strong Coulomb field. Since it would be impossible to give here a full bibliography of the discussed subjects, only the recent works are usually cited, and more references can be found there. There are also many other subject that cannot be presented here because of limited space; some of them are covered in other plenary talks [7,10,11] during this conference. The reader may also wish to consult the contents of nuclear-structure talks that have been given during the previous INPC'98 conference [12], where the three-years-ago status of the field was presented.