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

TL;DR

This paper investigates the behavior of 0+ states in the Interacting Boson Approximation model at large boson numbers, revealing regular energy patterns and phase transition indicators across different symmetries.

Contribution

It demonstrates linear growth of 0+ state energies with their order and identifies simple empirical measures to distinguish phase transition types in the IBA model.

Findings

0+ state energies grow linearly with their ordinal number n.

Energy ratios serve as effective order parameters for phase transitions.

Near the first-order transition, 0+ energies follow a quadratic growth pattern n(n+3).

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_2^+)=E(6_1^+), E(0_3^+)=E(10_1^+), E(0_4^+)=E(14_1^+), 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.