Partial and Quasi Dynamical Symmetries in Nuclei

One of the interesting aspects in the study of atomic nuclei is the strikingly regular behaviour many display in spite of being complex quantum-mechanical systems, prompting the universal question of how regularity emerges out of complexity. It is often conjectured that symmetries play a pivotal role in our understanding of this emerging simplicity. But most symmetries are likely to be broken, partial or both. Under such more realistic conditions, does the concept of symmetry still provide a basis for our understanding of regularity? I suggest that this requires the enlarged concepts of partial and quasi dynamical symmetry.Comment: 5 pages, 5 figures, accepted for publication in Nuclear Physics New

Seniority in quantum many-body systems

The use of the seniority quantum number in many-body systems is reviewed. A brief summary is given of its introduction by Racah in the context of atomic spectroscopy. Several extensions of Racah's original idea are discussed: seniority for identical nucleons in a single-$j$ shell, its extension to the case of many, non-degenerate $j$ shells and to systems with neutrons and protons. To illustrate its usefulness to this day, a recent application of seniority is presented in Bose--Einstein condensates of atoms with spin.Comment: 16 pages, 1 figure, accepted for publication in the Proceedings of The American Institute of Physic

Neutron-proton pairs in nuclei

A review is given of attempts to describe nuclear properties in terms of neutron--proton pairs that are subsequently replaced by bosons. Some of the standard approaches with low-spin pairs are recalled but the emphasis is on a recently proposed framework with pairs of neutrons and protons with aligned angular momentum. The analysis is carried out for general $j$ and applied to $N=Z$ nuclei in the $1f_{7/2}$ and $1g_{9/2}$ shells.Comment: 16 figures, 4 tables, accepted for publication in Int. J. of Modern Physics

Seniority in quantum many-body systems. I. Identical particles in a single shell

A discussion of the seniority quantum number in many-body systems is presented. The analysis is carried out for bosons and fermions simultaneously but is restricted to identical particles occupying a single shell. The emphasis of the paper is on the possibility of {\em partial} conservation of seniority which turns out to be a peculiar property of spin-9/2 fermions but prevalent in systems of interacting bosons of any spin. Partial conservation of seniority is at the basis of the existence of seniority isomers, frequently observed in semi-magic nuclei, and also gives rise to peculiar selection rules in one-nucleon transfer reactions.Comment: 41 pages, 7 figures, 1 tables, submitted to Annals of Physic

Exactly solvable models of nuclei

In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated systems as well as collective modes of motion in the atomic nucleus.Comment: 34 pages, 8 figures accepted for publication in Scholarpedi

Generalized Partial Dynamical Symmetry in Nuclei

We introduce the notion of a generalized partial dynamical symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6) symmetry in the framework of the interacting boson model. The resulting spectrum and electromagnetic transitions are compared with empirical data in $^{162}$Dy.Comment: 12 pages, 3 figures, 1 table, Phys. Rev. Lett., in pres

Triaxiality in the interacting boson model

The signature splitting of the $\gamma$-vibrational band of several Ru, Pd, Xe, Ba, Os and Pt isotopes is analyzed in the framework of the interacting boson model (IBM). The nuclei studied are close to the $\gamma$-unstable SO(6) limit of the IBM and have well-known $\gamma$ bands. It is shown that in most nuclei the signature splitting is better reproduced by the inclusion of a three-body interaction between the $d$ bosons. In none of the nuclei evidence for a stable, triaxial ground-state shape is found.Comment: Accepted for publication in Nuclear Physics

Consistent description of nuclear charge radii and electric monopole transitions

A systematic study of energy spectra throughout the rare-earth region (even-even nuclei from $_{58}$Ce to $_{74}$W) is carried out in the framework of the interacting boson model (IBM), leading to an accurate description of the spherical-to-deformed shape transition in the different isotopic chains. The resulting IBM Hamiltonians are then used for the calculation of nuclear charge radii (including isotope and isomer shifts) and electric monopole transitions with consistent operators for the two observables. The main conclusion of this study is that an IBM description of charge radii and electric monopole transitions is possible for most of the nuclei considered but that it breaks down in the tungsten isotopes. It is suggested that this failure is related to hexadecapole deformation.Comment: 13 pages, 5 tables, 3 figures, accepted for publication in Physical Review

The scientific legacy of J. P. Elliott

14 pagesJames Philip Elliott, one of the towering figures of nuclear physics of the second half of the twentieth century, died on the 21st of October 2008. Obituaries appeared in the British press but relatively little attention was paid by the international scientific community to Elliott's contributions. Given their importance, in particular for theoretical nuclear physics, it seems appropriate to reflect here, two years after his death, on the scientific legacy left by Phil Elliott