The interacting boson model.

Signatures of criticality in the evolution of the nuclear ground-state shapes across the NxZ plane are discussed. Attention is paid to specific data indicating sudden structural changes in various isotopic and isotonic chains of medium-mass and heavy even-even nuclei, as well as to diverse theoretical aspects of the models used to describe these changes. The interacting boson model and the geometric collective model, in particular, are discussed in detail, the former providing global predictions for the evolution of collective observables in nuclei between closed shells and the latter yielding a parameter-efficient description of nuclei at the critical points of shape transitions. Some issues related to the mechanism of first- and second-order quantum phase transitions in general many-body systems are also outlined.

Quantum phase transitions in the shapes of atomic nuclei

Recently, the idea of quantum phase transitions has been applied to equilibrium shape changes in finite atomic nuclei. An introduction to and discussion of this concept, both from the macroscopic perspective and from a microscopic approach, in terms of shell structure and residual interactions is presented. Following this, the quantitative predictions of the critical point symmetries (CPS) X(5) and E(5) are discussed in some detail and compared to the data in a number of nuclei and mass regions. Any successful new model paradigm soon generates modifications to improve the predictions and, likewise, often spawns related models inspired by the original ansatz. This is eminently true of the CPS and we make an effort to briefly discuss this rapidly advancing area in terms of a number of recent modifications to the CPS as well as related models that are couched in a geometrical perspective.

Quantum phase transitions and structural evolution in nuclei

Atomic nuclei exhibit phase transitions as a function of the number of their constituent protons and neutrons. These phase transitions are not of the usual thermodynamic type, but rather they are quantum phase transitions in the equilibrium shape and structure of the ground and low-lying states. This realization has sparked a new area of research, focusing on the concept of 'critical-point symmetries', which describe the structure of nuclei at phase-transitional points. Both macroscopic (geometric or algebraic) and microscopic (shell-model) aspects of these phase transitions and of changes in structure with proton and neutron number in nuclei are discussed, along with an interpretation in terms of simple Landau theory. Finally, some alternative scenarios and schematic models for different classes of nuclei based on other simple potentials are briefly summarized.

Shape phase transitions and critical-point phenomena in atomic nuclei

The first case of a Bose-Fermi critical point symmetry, E(5/4), representing the coupling of a $j=3/2$ fermion to an E(5) core, was recently proposed. Since $^{134}\mathrm{Ba}$ has been found to be an empirical manifestation of E(5), we carried out a \ensuremath{\beta}-decay experiment to study levels in $^{135}\mathrm{Ba}$, where the last neutron can occupy the $2{d}_{3/2}$ orbit, as the first test of E(5/4). The comparison shows significant areas of agreement as well as significant discrepancies. Comparison of interacting boson-fermion approximation and shell model calculations with the data are also presented.

First test of the E(5/4) Bose-Fermi symmetry: The structure of Ba-135

There has been intense recent interest in equilibrium shape / phase transitions in nuclei and the concept of critical point symmetries to describe them. The first critical point symmetry for an odd‐mass nucleus has been recently proposed, namely, the E(5/4) Bose‐Fermi critical point symmetry, it corresponds to coupling between an odd particle in a j = 3/2 orbit and the E(5) critical point symmetry, at the transition between the O(6) gamma‐soft and the U(5) vibrator symmetries. Since 134Ba is a candidate for the E(5) critical point symmetry, we carried out a β‐decay experiment on 135Ba whose last neutron can occupy a 2d3/2 orbit as a first test of E(5/4). The experimental results were compared to E(5/4) and also with the Interacting Boson‐Fermion Approximation Model (IBFA) and Shell Model calculations. We see fair agreement with E(5/4) for B(E2) values but not for all energies. The IBFA shows better agreement with data than E(5/4) and the Shell model shows the best agreement.

A First Test of the E(5/4) Bose‐Fermi Symmetry : 135Ba

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First test of the E(5/4) Bose-Fermi symmetry: The structure of Ba-135

A First Test of the E(5/4) Bose‐Fermi Symmetry : 135Ba