Coexistence in even-mass nuclei

The concept of spontaneous symmetry breaking is applied to the rotating mean field of nuclei. The description is based on the tilted-axis cranking model, which takes into account that the rotational axis can take any orientation with respect to the deformed density distribution. The appearance of rotational bands in nuclei is analyzed, focusing on weakly deformed nuclei at high angular momentum. The quantization of the angular momentum of the valence nucleons leads to new phenomena. Magnetic rotation represents the quantized rotation of the anisotropic current distribution in a near spherical nucleus. The restricted amount of angular momentum of the valence particles causes band termination. The discrete symmetries of the mean-field Hamiltonian provide a classification scheme of rotational bands. New symmetries result from the combination of the spatial symmetries of the density distribution with the vector of the angular momentum. The author discusses in detail which symmetries appear for a reflection-symmetric density distribution and how they show up in the properties of the rotational bands. In particular, the consequences of rotation about a nonprincipal axis and of breaking the chiral symmetry are analyzed. Also discussed are which symmetries and band structures appear for non-reflection-symmetric mean fields. The consequences of breaking the symmetry with respect to gauge and isospin rotations are sketched. Some analogies outside nuclear physics are mentioned. The application of symmetry-restoring methods to states with large angular momentum is reviewed.

Spontaneous symmetry breaking in rotating nuclei

We discuss several pairing-related phenomena in nuclear systems, ranging from superfluidity in neutron stars to the gradual breaking of pairs in finite nuclei. We focus on the links between many-body pairing as it evolves from the underlying nucleon-nucleon interaction and the eventual experimental and theoretical manifestations of superfluidity in infinite nuclear matter and of pairing in finite nuclei. We analyse the nature of pair correlations in nuclei and their potential impact on nuclear structure experiments. We also describe recent experimental evidence that points to a relation between pairing and phase transitions (or transformations) in finite nuclear systems. Finally, we discuss recent investigations of ground-state properties of random two-body interactions where pairing plays little role although the interactions yield interesting nuclear properties such as 0+ ground states in even-even nuclei.

https://arxiv.org/pdf/nucl-th/0210033.pdf

Pairing in Nuclear Systems: From Neutron Stars to Finite Nuclei

A small proportion of atomic nuclei can form highly excited metastable states, or isomers. Of particular interest is a class of isomers found in deformed axially symmetric nuclei; these isomers are among the longest-lived and have the potential to reach the highest energies. By probing their properties, insights into nuclear structure have been gained. The possibility of stimulated isomer decay may ultimately lead to new forms of energy storage and γ-ray lasers.

Energy traps in atomic nuclei

Structure of superdeformed bands in the A ≈ 150 mass region

Empirical evidence for the existence of pair fluctuations in rapidly rotating nuclei in connection with the pair gap is reviewed. The quantities considered are single-particle energies (routhians) and alignments. While the cranked shell model in the presence of static pair correlations provides an accurate description of data at rotational frequencies below the critical frequency corresponding to the collapse of the static pair gap, conspicuous discrepancies are found in the region of and above the pairing phase transition. In particular, a group of excitations is observed displaying lower excitation energies and smaller alignments than those predicted by the cranked shell model. Such excitations can be characterized as behaving as if the correlations induced by the presence of a pairing condensate were not totally obliterated after the "phase transition." A theoretical model, based on the renormalization of the single-particle motion mixed by the coupling to pairing vibrations, is quite successful in explaining the overall trend of the data at rotational frequencies larger than the critical frequency. Smaller alignments and excitation energies are correlated with configurations displaying particle coupling schemes which profit most from fluctuations of the pair gap about its zero equilibrium value. While this model reproduces many of the experimental features, it still overpredicts the alignments by 2-3 units of $\ensuremath{\hbar}$ in the crossing region. Thus other degrees of freedom (both static and dynamic), e.g., deformations, also must play a role at large rotational frequencies.

R. A. Broglia

Papers

Pairing fluctuations in rapidly rotating nuclei