Complementary descriptions of shape/phase transitions in atomic nuclei

TL;DR

This paper explores the relationship between the Interacting Boson Approximation and geometrical models in describing shape and phase transitions in atomic nuclei, demonstrating their complementarity through three key examples.

Contribution

It demonstrates the correspondence between IBA and Bohr Hamiltonian solutions, linking critical point symmetries with IBA transition regions and energy staggering patterns.

Findings

Special solutions of the Bohr Hamiltonian align with IBA critical regions.

Experimental gamma-band energy staggering patterns are reproduced by both models.

A preliminary method to derive IBA SU(3) schemes from Bohr solutions is presented.

Abstract

Shape/phase transitions in atomic nuclei have first been discovered in the framework of the Interacting Boson Approximation (IBA) model. Critical point symmetries appropriate for nuclei at the transition points have been introduced as special solutions of the Bohr Hamiltonian, stirring the introduction of additional new solutions describing wide ranges of nuclei. The complementarity of the IBA and geometrical approaches will be demonstrated by three examples. First, it will be shown that specific special solutions of the Bohr Hamiltonian correspond to the borders of the critical region of the IBA. Second, it will be demonstrated that the distinct patterns exhibited in different transitional regions by the experimental energy staggering in gamma-bands can be reproduced both by the IBA and by special solutions of the Bohr Hamiltonian. Third, a first attempt to obtain a IBA SU(3) level scheme from a special solution of the Bohr Hamiltonian will be presented.