A systematic investigation of the nuclear observables related to the triaxial degree of freedom is presented using the multi-quasiparticle 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.

The microscopic origin of the $\gamma$ softness (fluctuations in the triaxiality parameter $\gamma$ of the nuclear shape) observed in atomic nuclei is studied in the framework of the triaxial projected shell model approach, which is based on a multiquasiparticle configuration space generated from a deformed mean field. It is demonstrated that the coupling to quasiparticle excitations drives the system from a $\gamma$-rigid to a $\gamma$-soft pattern. As an illustrative example for a $\gamma$-soft nucleus, a detailed study has been performed for the ${}^{104}\mathrm{Ru}$ nucleus. The experimental energies and a large sample of measured $E2$ matrix elements available for this nucleus are reproduced quite accurately. The shape invariant analysis of the calculated $E2$ matrix elements elucidates the $\gamma$-soft nature of ${}^{104}\mathrm{Ru}$.

In an effort to elucidate the rich band structures observed in odd-neutron systems, the triaxial projected shell model approach is extended to include three-quasineutron and five-quasiparticle configurations. This extension makes it possible to investigate the high-spin states up to and including the second band crossing. Detailed investigation has been performed for odd-mass Xe isotopes with the extended basis, and it is shown that the character of the band crossing along the yrast line changes with shell filling of the $1h_{11/2}$ orbital. Further, it is observed that the three-quasiparticle state that crosses the ground-state configuration, leading to the normal band crossing phenomenon along the yrast line, first crosses the $\gamma$ band based on the ground-state configuration at an earlier spin value. This crossing feature explains the occurrence of the signature inversion observed in the $\gamma$ bands for some of the studied isotopes.

High spin states with angular momentum up to 21ħ in ${}_{}{}^{84}{}_{}{}^{}\mathrm{Y}$ have been established for the first time through the discrete-line γ-ray spectroscopy using the ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ ${(}^{28}$Si,2pn${)}^{84}$Y reaction at 98 MeV. The experimental level scheme exhibits rotational characteristics with a large signature splitting and also signature inversion at I=11ħ. Theoretical calculations using the particle-rotor model with axial symmetry provide a good description of the observed phenomena.

An enhanced electric octupole (E3) strength of 45(5) W.u. has been measured for the 3 − → 0 + transition in Gd 150 , providing direct evidence for large octupole collectivity in this nucleus. The value was determined following two sensitive experiments, to measure the mean lifetime of the J π = 3 − level and the weak E 3 decay branch direct to the ground state. The systematics of the E 3 strength across the Gd isotopic chain reveals that enhanced octupole collectivity is obtained for Gd 150 . The increasing low-lying octupole strength in the Gd isotopes is analyzed with five state-of-the-art theoretical models. It is found to be best reproduced by quasiparticle random phase approximation calculations, providing a good understanding of octupole collectivity in the rare-earth region.