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

Phase transitions in angle variables are studied. An example of angular phase transition, an axially to triaxially deformed "shape" transition in nuclei, is discussed. Spectroscopic signatures for the occurrence of these transitions are suggested. Preliminary experimental evidence is presented.

Phase transitions in angle variables

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

We carry out an interacting boson model study of the Ru isotopes using a U(5)-SO(6) transitional Hamiltonian with fixed parameters, where the variation is due only to the change in boson number N. Transitional behavior in ${}^{104}\mathrm{Ru}$ is compared with recent predictions of an E(5) critical symmetry, including a modified version with an alternative $\ensuremath{\beta}$ dependence for the ${T}^{(\mathrm{E}2)}$ operator.

Search for E(5) symmetry in nuclei: The Ru isotopes

Istituto Nazionale di Fisica Nucleare de Italia y Ministerio de Ciencia Y Tecnologia de Espana ACI2009-1047, AIC10-D-000590

/pdf/phase-diagram-for-a-cubic-q-interacting-boson-model-2q3ntxahn8.pdf

Phase diagram for a cubic- Q interacting boson model Hamiltonian: Signs of triaxiality

An analysis of both positive- and negative-parity states of the odd-neutron Ba and the odd-proton La transitional isotopes (N<82) within the framework of the proton-neutron interacting boson-fermion model (IBFA-2) is presented. Energy spectra, electromagnetic properties, isotope shifts and one-nucleon transfer spectroscopic strengths for odd-mass Ba and La isotopes are compared with experiment. Generally good agreement is obtained with a restricted number of adjusted parameters. Some predictions on the properties mentioned above are presented for nuclei for which no experimental data are available.

https://iopscience.iop.org/article/10.1088/0305-4616/13/10/015/pdf

Nuclear structure studies of the odd-mass Ba and La isotopes with the IBFA-2 model

We present systematic calculations on nuclei in the region around A = 190 within the framework of the proton-neutron interacting boson-fermion model Energy levels and electromagnetic properties of both positive and negative parity states in odd proton (/sub 77/Ir,/sub 79/Au) and odd neutron (/sub 78/Pt) nuclei are compared with experimental data A general good agreement is obtained with a few adjustable parameters

Test of the proton-neutron interacting boson-fermion model in the region around A=190

Double-$\ensuremath{\gamma}$ vibrations in deformed nuclei are studied in the context of the interacting boson model with special reference to their anharmonic character. It is shown that large anharmonicities can be obtained with interactions that are (at least) of three-body nature between the bosons. As an example the $\ensuremath{\gamma}$ vibrations of the nucleus ${}_{ 68}^{166}{\mathrm{Er}}_{98}$ are studied in detail.

/pdf/anharmonic-double-g-vibrations-in-nuclei-and-their-596en0bolp.pdf

Anharmonic double- γ vibrations in nuclei and their description in the interacting boson model

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