Introduction: From Bound States to the Continuum

The paramount complexity of nuclear many-body problem and its great importance for an understanding of various systems ranging from the subnucleon to astronomical scales makes it to the intellectual challenge of first importance. Complexity of this problem is the reason why the theory of atomic nucleus does not exist and one deals with various models, describing selected features of the nuclear many-body problem. As a result, our understanding of the nuclear properties and structure remains incomplete and in certain aspects incoherent. Let us take an example of the low-energy excitations in light atomic nuclei, where the states are described using either the nuclear shell model or the cluster model. Organization of nucleons according to these two models is quite different. Shell model is based on a concept of single-particle mean field and associated to it the shell structure. On the other hand, cluster model builds the wave functions from the correlated substructures, such as the α-particles. Can such two different pictures of nuclear structure coexist, and can they be reconciled?