NUCLEAR STRUCTURE THEORY: QUESTIONS AND CHALLENGES

Theoretical nuclear structure deals with the nuclear many-body problem in the very finite limit of particle number. In the non-relativistic limit, the goal is to solve the many-body Schrödinger equation with the nuclear Hamiltonian $\hat{H}$:

$$\hat{H}\Psi = E\Psi.$$ (1)

Unlike other areas of the many-body problem (atomic physics, condensed matter physics), nuclear physics is still struggling to understand the origin of the force which produces nuclear binding. Although it is clear that the nucleon-nucleon (NN) interaction has its roots in quark-gluon dynamics, the microscopic derivation is not yet in place. To add insult to injury, due to strong in-medium effects, additional complications arise when one tries to derive the effective inter-nucleon interaction in the heavy nucleus. This brings us to the first major scientific question pertaining to Eq. (1): What is the effective nuclear Hamiltonian? In this context, some specific issues related to the RNB experimentation are: What is the (N-Z) and mass dependence of the effective NN interaction? What is the interaction dependence on spin degrees of freedom? What is the interplay between strong, electromagnetic, and weak components of the NN force? What is the nuclear matter equation of state?

The second major challenge pertaining to Eq. (1) - What is the nature of the nucleonic matter? - concerns the properties of the many-body wave function $\Psi$. Here, the specific fundamental questions are: What is the microscopic mechanism of nuclear binding? Which combinations of protons and neutrons make up a nucleus? What is the single-nucleonic motion in a very neutron-rich environment? What are the collective phases of nucleonic matter? What is the nature of collective modes of the nucleus (a finite fermion system having a pronounced surface)? What are relevant collective degrees of freedom? How to understand microscopically the large-amplitude nuclear collective motion (fusion, fission, coexistence phenomena)?

Coming back to RNB physics, there are many theoretical challenges related to nuclei far from stability. Clearly, it is not ``business as usual"! In many respects, weakly bound exotic nuclei are indeed much more difficult to treat theoretically than well-bound systems [2]. The major theoretical difficulty and challenge is the treatment of the particle continuum. The residual-interaction coupling to the continuum can influence nuclear binding, effective interaction, and core polarization. It can give rise to a new class of collective phenomena (soft modes). Continuum can also dramatically influence shell structure, many-body correlations (such as pairing) and can impact the appearance of cluster structures. Consequently, many cherished approaches of nuclear theory such as the conventional shell model and the pairing theory must be modified in order to properly take into account unbound states. But there is also a splendid opportunity: the presence of low-lying scattering states invites strong interplay and cross-fertilization between nuclear structure and reaction theory. Many methods developed by reaction theory can now be applied to structure aspects of loosely bound systems. And, of course, nuclear structure effects can clearly manifest themselves in reactions involving exotic nuclei. Some examples, nicely illuminating this point, are presented in the following sections.