Chiral rotation observed in128 Cs is studied using the newly developed microscopic triaxial projected shell model (TPSM) approach. The observed energy levels and the electromagnetic transition probabilities of the nearly degenerate chiral dipole bands in this isotope are well reproduced by the present model. This demonstrates the broad applicability of the TPSM approach, based on a schematic interaction and angular-momentum projection technique, to explain a variety of low-and high-spin phenomena in triaxial rotating nuclei.The classification of band structures from symmetry considerations has played a central role in our understanding of nuclear structure physics. Most of the rotational nuclei are axially symmetric with conserved angular-momentum projection along the symmetry axis. This symmetry has allowed to classify a multitude of rotational bands using Nilsson scheme and has been instrumental to unravel the intrinsic structures of deformed nuclei [1,2]. Although, most of the deformed nuclei obey axial symmetry at low-excitation energies and spin, there are also known regions of the periodic table, referred to as transitional nuclei, that violate axial symmetry and are described using the triaxial deformed mean-field. Further, some nuclei that are axial in the ground-state become triaxial at higher excitation energies and angular momenta. There are several empirical observations indicating that axial symmetry is broken in transitional regions. For instance, the moment of inertia of the transitional nuclei rises sharply with angular-momentum for

We expand the triaxial projected shell model basis to include triaxially deformed multi-quasiparticle states. This allows us to study the yrast and γ -vibrational bands up to high spins for both γ -soft and well-deformed nuclei. As a first application, a systematic study of the high-spin states in Er isotopes is performed. The calculated yrast and γ bands are compared with the known experimental data, and it is shown that the agreement between theory and experiment is quite satisfactory. The calculation leads to predictions for bands based on one-and two-γ phonons where current data are still sparse. It is observed that γ bands for neutron-deficient isotopes of 156 Er and 158 Er are close to the yrast band, and further these bands are predicted to be nearly degenerate for high-spin states.

The newly developed multi-quasiparticle triaxial projected shell-model approach is employed to study the high-spin band structures in neutron-deficient even-even Ce-and Nd-isotopes. It is observed that γ-bands are built on each intrinsic configuration of the triaxial mean-field deformation. Due to the fact that a triaxial configuration is a superposition of several K-states, the projection from these states results in several low-lying bands originating from the same intrinsic configuration. This generalizes the well-known concept of the surface γ-oscillation in deformed nuclei based on the ground-state to γ-bands built on multi-quasiparticle configurations. This new feature provides an alternative explanation on the observation of two I = 10 aligning states in 134 Ce and both exhibiting a neutron character.

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Recent experimental data have demonstrated that 76 Ge may be a rare example of a nucleus exhibiting rigid γ-deformation in the low-spin regime. In the present work, the experimental analysis is supported by microscopic calculations using the multi-quasiparticle triaxial projected shell model (TPSM) approach. It is shown that to best describe the data of both yrast and γ-vibrational bands in 76 Ge, a rigid-triaxial deformation parameter γ ≈ 30 • is required. TPSM calculations are discussed in conjunction with the experimental observations and also with the published results from the spherical shell model. The occurrence of a γγ-band in 76 Ge is predicted with the bandhead at an excitation energy of ∼ 2.5 MeV. We have also performed TPSM study for the neighboring Ge-and Se-isotopes and the distinct γ-soft feature in these nuclei is shown to result from configuration mixing of the ground-state with multi-quasiparticle states.

Excited states of 133 La have been investigated to search for the wobbling excitation mode in the low-spin regime. Wobbling bands with nω = 0 and 1 are identified along with the interconnecting ∆I = 1, E2 transitions, which are regarded as one of the characteristic features of the wobbling motion. An increase in wobbling frequency with spin implies longitudinal wobbling for 133 La, in contrast with the case of transverse wobbling observed in 135 Pr. This is the first observation of a longitudinal wobbling band in nuclei. The experimental observations are accounted for by calculations using the quasiparticle-triaxial-rotor (QTR) model, which attribute the appearance of longitudinal wobbling to the early alignment of a π = + proton pair.

Evidence of strong coupling of quasiparticle excitations with γ-vibration is shown to occur in transitional nuclei. High-spin band structures in 166,168,170,172 Er are studied by employing the recently developed multiquasiparticle triaxial projected shell model approach. It is demonstrated that a low-lying K = 3 band observed in these nuclei, the nature of which has remained unresolved, originates from the angular-momentum projection of triaxially deformed two-quasiparticle (qp) configurations. Further, it is predicted that the structure of this band depends critically on the shell filling: in 166 Er the lowest K = 3 2-qp band is formed from proton configuration, in 168 Er the K = 3 neutron and proton 2-qp bands are almost degenerate, and for 170 Er and 172 Er the neutron K = 3 2-qp band becomes favored and can cross the γ-vibrational band at high rotational frequencies. We consider that these are few examples in even-even nuclei, where the three basic modes of rotational, vibrational, and quasi-particle excitations co-exist close to the yrast line.

A systematic investigation of the nuclear observables related to the triaxial degree of freedom is presented using the multiquasiparticle triaxial projected shell model (TPSM) approach.These properties correspond to the observation of γ-bands, chiral doublet bands and the wobbling mode. In the TPSM approach, γ-bands are built on each quasiparticle configuration and it is demonstrated that some observations in high-spin spectroscopy that have remained unresolved for quite some time could be explained by considering γ-bands based on two-quasiparticle configurations. It is shown in some Ce-, Nd-and Ge-isotopes that the two observed aligned or s-bands originate from the same intrinsic configuration with one of them as the γ-band based on a two-quasiparticle configuration. In the present work, we have also performed a detailed study of γ-bands observed up to the highest spin in Dysposium, Hafnium, Mercury and Uranium isotopes. Furthermore, several measurements related to chiral symmetry breaking and wobbling motion have been reported recently. These phenomena, which are possible only for triaxial nuclei, have been investigated using the TPSM approach. It is shown that doublet bands observed in lighter odd-odd Cs-isotopes can be considered as candidates for chiral symmetry breaking. Transverse wobbling motion recently observed in 135 Pr has also been investigated and it is shown that TPSM approach provides a reasonable description of the measured properties.