Phases of clusterized nuclei

Complete text of publication follows. The atomic nucleus is a rich microscopic laboratory of physical phenomena. Among others it shows evidence for different kind of phase transitions. Some of them are governed by the temperature, like the transition from the liquid to gas phase of the finite nucleonic matter, or from the hadronic to the deconfined phases at higher energy. In some sense these phenomena are similar to the macroscopic phase transitions, apart from the (important role of the) finite-size effects. There are, however, other kind of phase transitions as well, which take place at (practically) zero temperature. They are called shape phase transitions. They are not the same, of course, like those which are studied in classical thermodynamics, yet there is so close similarity both on the qualitative, and on the quantitative level, that the language of the phase transitions has been accepted for their discussion. A large amount of work has been dedicated to the study of shape-phase transitions in relation with the quadrupole deformation of nuclei. The atomic nuclei have, however, another important type of collectivity as well, based on the dipole degrees of freedom, which is related to the clusterization. The study of the phases and phase transitions of this collectivity has just started [1-3]. In particular, the question of shape-phase transitions due to the relative motion of the clusters have been discussed in [1-3]. This motion is describe by an algebraic model of U(4) group-structure, called vibron model. Actually, the vibron model is applied in molecular physics, and in hadron spectroscopy, too; thus the treatment is similar to those. (The specific feature in nuclear cluster studies is the important role of the Pauli-principle.) This model has a one-dimensional phase diagram, and a phase transition is expected between the soft vibrator (shell-like clusterization), and the rigid rotor (molecule-like clusterization) phases. Recently we have extended our investigations [4] by the incorporation of the coupling between the degrees of freedom associated to the relative motion and the internal cluster structure (of a binary cluster system). It turns out that in addition to the U(3) and O(4) dynamical symmetries, a third one, the O(3) dynamical symmetry shows up, as well. Thus the phase diagram is of two-dimensional, and can be illustrated as a triangle, shown in Fig. 1. A similar phase diagram has been proposed recently for the shell model [5], in which the endpoints represent the SU(3), SU(2), dynamical symmetries, and the independent particle approximation. Since the SU(3) dynamical symmetry is common in the phase diagrams of the shell and cluster models, we propose, that their interrelation is like that on Fig. 2. This can be considered as a formulation of the connection of the two models in terms of their phase diagrams.