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

Nuclear Data Sheets for A=132

Magnetic rotation and antimagnetic rotation are exotic rotational phenomena observed in weakly deformed or near-spherical nuclei, which are respectively interpreted in terms of the shears mechanism and two shearslike mechanism. Since their observations, magnetic rotation and antimagnetic rotation phenomena have been mainly investigated in the framework of tilted axis cranking based on the pairing plus quadrupole model. For the last decades, the covariant density functional theory and its extension have been proved to be successful in describing series of nuclear ground-states and excited states properties, including the binding energies, radii, single-particle spectra, resonance states, halo phenomena, magnetic moments, magnetic rotation, low-lying excitations, shape phase transitions, collective rotation and vibrations, etc. This review will mainly focus on the tilted axis cranking covariant density functional theory and its application for the magnetic rotation and antimagnetic rotation phenomena.

Progress on tilted axis cranking covariant density functional theory for nuclear magnetic and antimagnetic rotation

Nuclear Data Sheets for A = 103

High spin levels in $^{108}\mathrm{Cd}$ have been populated through $^{100}\mathrm{Mo}(^{13}\mathrm{C},5n\ensuremath{\gamma})^{108}\mathrm{Cd}$ reaction using a 65 MeV $^{13}\mathrm{C}$ beam. The lifetime of the ${14}^{+},{16}^{+},{18}^{+}$, and ${20}^{+}$ levels of the positive parity yrast band of $^{108}\mathrm{Cd}$ have been measured using the Doppler shift attenuation method. The evaluated B(E2) values from the measured lifetimes have been compared with the B(E2) values calculated using the semiclassical model, which assume shears mechanism, and the values obtained from total Routhian surface (TRS) calculations. Both calculations show good agreement with the measured values. In addition, the large ${\mathcal{J}}^{(2)}/B(E2)$ ratio may indicate that a large contribution to the angular momentum of this band is generated by shears mechanism. Thus, the present work indicates that the states of the positive parity yrast band from ${16}^{+}$ onwards in $^{108}\mathrm{Cd}$, originate due to antimagnetic rotation.

Observation of antimagnetic rotation in **108Cd

The hybrid version of tilted axis cranking has been used to study the existence of magnetic rotation in the $\ensuremath{\Delta}I=1$ bands of odd-$A$ ${}^{79,81,83,85}\mathrm{Rb}$ isotopes. The bands are found to be built on prolate three quasiparticle $\ensuremath{\pi}{(g}_{9/2})\ensuremath{\bigotimes}\ensuremath{\nu}[{g}_{9/2}{(\mathrm{fp})}^{1}]$ configuration. The results exhibit a rapid onset and decline of magnetic rotation as we go from $N=42$ to 48. The ${}^{83}\mathrm{Rb}$ appears to be a better case of magnetic rotation among these four Rb isotopes.

Magnetic dipole rotational bands in odd-A Rb isotopes

Shape transition and tilted axis rotation in 136 Ce

A detailed numerical analysis of the semi-classical dynamics of single-j particle rotor model in the nonlinear regime is carried out. The ensuing numerical results exhibit similarities with many features of the superdeformed bands. In particular a ΔI=2 staggering is obtained and is attributed to the tunneling in the double-well potential of j3.

Semiclassical quantisation of particle-rotor model and δi=2 staggering of superdeformed bands

The deformed mean field of nuclei exhibits various geometrical and dynamical symmetries which manifest themselves as various types of rotational and decay patterns. Most of the symmetry operations considered so far have been defined for a situation wherein the angular momentum coincides with one of the principal axes and the principal axis cranking may be invoked. New possibilities arise with the observation of rotational features in weakly deformed nuclei and now interpreted as magnetic rotational bands. More than 120 MR bands have now been identified by filtering the existing data. We present a brief overview of these bands. The total angular momentum vector in such bands is tilted away from the principal axes. Such a situation gives rise to several new possibilities including breaking of chiral symmetry as discussed recently by Frauendorf. We present the outcome of such symmetries and their possible experimental verification. Some possible examples of chiral bands are presented.

Magnetic rotation and chiral symmetry breaking

The Patterson densities in terms of model electron densities and model nuclear densities have been performed on α-phase of Fe2O3. A theoretical work is carried out using VESTA software on the crystallographic visualization of Patterson densities of α-Fe2O3. The analyzed result mainly attributes to the packing fraction of α-Fe2O3 and is promising for the use of α-phase of Fe2O3 as ultraviolet (UV) blocking agent in paints.

Crystallographic representation of Patterson densities of polymorphs α-Fe2O3

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