0[sup +] states in the large boson number limit of the Interacting Boson Approximation model

Abstract

Abstract.Studies of the Interacting Boson Approximation (IBA) model for large boson numbers have been triggered by the discovery of shape/phase transitions between different limiting symmetries of the model. These transitions become sharper in the large boson number limit, revealing previously unnoticed regularities, which also survive to a large extent for finite boson numbers, corresponding to valence nucleon pairs in collective nuclei. It is shown that energies of 0 + n states grow linearly with their ordinal number n in all three limiting symmetries of IBA [U(5), SU(3), and O(6)]. Furthermore, it is proved that the narrow transition region separating the symmetry triangle of the IBA into a spherical and a deformed region is described quite well by the degeneracies E(0, while the energy ratio E(6 + 1 )/E(0 + 2 ) turns out to be a simple, empirical, easy-to-measure effective order parameter, distinguishing between first-and second-order transitions. The energies of 0 + n states near the point of the first order shape/phase transition between U(5) and SU(3) are shown to grow as n(n+3), in agreement with the rule dictated by the relevant critical point symmetries resulting in the framework of special solutions of the Bohr Hamiltonian. The underlying partial dynamical symmetries and quasi-dynamical symmetries are also discussed. The Interacting Boson Approximation (IBA) model [1], describing collective phenomena in atomic nuclei in terms of s and d bosons (of angular momentum 0 and 2, respectively), is known to possess an overall U(6) symmetry, containing three different dynamical symmetries, U(5), SU(3), and O(6), corresponding to near-spherical (vibrational), axially symmetric prolate deformed (rotational), and soft with respect to axial asymmetry (γ-unstable) nuclei respectively. These limiting symmetries are shown at the vertices of the symmetry triangle [2] of the model, shown in Fig. 1. KeywordsAn energy functional can be obtained [4] in the classical limit of the model, through the use of the coherent state formalism [5,6]. Studying this energy functional in the framework of catastrophe theory one can see [7] that a first order phase transition (in the Ehrenfest classification) is predicted to occur between the limiting symmetries U(5) and SU(3), while a second order phase transition is expected between U(5) and O(6). We refer to these transitions as shape/phase transitions. A narrow shape coexistence region is then predicted [4] in the symmetry triangle of the IBA, separating the spherical and deformed phases. The shape coexistence region shrinks into the point of second order phase transition as the U(5)-O(6) line is approached, as shown in Fig. 1.