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.

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.

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