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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 the deformed mean-field picture with multi-quasiparticle configuration space. 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 $^{104}$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 $^{104}$Ru.

In an effort to elucidate the rich band structures observed in odd-neutron systems, 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 character of the band crossing along the yrast line changes with shell filling of the 1h11/2 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.

In the present work, the basis space in the triaxial projected shell-model approach is expanded to include three and five quasiparticle configurations for odd-proton systems. This extension allows us to investigate the high-spin band structures observed in odd-proton systems up to and including the second band-crossing region and, as a first major application of this development, the high-spin properties are investigated for odd-mass $^{125\ensuremath{-}137}\mathrm{Pr}$ and $^{127\ensuremath{-}139}\mathrm{Pm}$ isotopes. It is shown that band crossings in the studied isotopes have mixed structures with the first crossing dominated by one-proton coupled to two-neutron configuration for the lighter isotopes which then changes to three-proton configuration with increasing neutron number. Furthermore, $\ensuremath{\gamma}$ bands based on quasiparticle states are also delineated in the present work, and it is predicted that these band structures built on three-quasiparticle configurations become favored in energy for heavier systems in the high-spin region.

Lifetime measurements have been carried out for the levels of the negative parity yrast sequence in $^{103}\mathrm{Pd}$ nucleus using the Doppler shift attenuation method. The levels were populated via $^{94}\mathrm{Zr}(^{13}\mathrm{C}, 4n\ensuremath{\gamma})^{103}\mathrm{Pd}$ fusion-evaporation reaction at a beam energy of 55 MeV. De-exciting $\ensuremath{\gamma}$ rays were detected by utilizing the Indian National Gamma Array. The extracted transition probabilities and other auxiliary observations indicate that the sequence may be resulting from the antimagnetic rotational (AMR) motion of valence nucleons. The key characteristic feature of the AMR motion is the steady decrease of the $B(E2)$ transition probability with spin, which is seen in the present measured transitions for $^{103}\mathrm{Pd}$. The experimental results are compared with the theoretical predictions of tilted axis cranked approach based on the covariant density functional theory. It is noted that the properties of the AMR band structure for $^{103}\mathrm{Pd}$ predicted in this model analysis are in good agreement with the present experimental findings. Further, semi-classical particle-rotor model has been employed to substantiate the AMR interpretation of the observed band structure in $^{103}\mathrm{Pd}$ and it is shown that results are similar to the band structures observed in the neighboring isotopes, which have also been considered as candidates for AMR motion.

High-spin excited states of $^{135}\mathrm{Pm}$ have been investigated using the $^{107}\mathrm{Ag}(^{32}\mathrm{S}$, $2p2n$) reaction at 145-MeV beam energy. Three negative-parity bands have been investigated up to $\ensuremath{\sim}9.0\ensuremath{-}$, $7.6\ensuremath{-}$, and $6.9\ensuremath{-}\mathrm{MeV}$ excitation energies with spin parities $(55/{2}^{\ensuremath{-}})$, $(49/{2}^{\ensuremath{-}})$, and $(47/{2}^{\ensuremath{-}})\phantom{\rule{4pt}{0ex}}\ensuremath{\hbar}$, respectively. The experimental results have been interpreted using the triaxial projected shell model. It is shown that the observation of the parallel band structures can be explained in terms of crossing of two $s$ bands with the yrast band, which is a rare phenomenon for an odd-$A$ nucleus. Further, the lifetimes of levels in yrast band have been extracted using Doppler shift attenuation method. The evaluated $B(E2)$ values of yrast states show the loss of collectivity at higher spin, attributed to the alignment process.

The low-lying non-yrast states in $^{114}\mathrm{Te}$ have been investigated using the Indian National Gamma Array through the fusion-evaporation reaction $^{112}\mathrm{Sn}(^{4}\mathrm{He},2n)$ at a beam energy of 37 MeV. Eight new $\ensuremath{\gamma}$ transitions have been placed in the level scheme to establish the quasi-$\ensuremath{\gamma}$ band in this nucleus. Spin and parity of several excited states have been assigned from the present spectroscopy measurements. The comparison of experimental results on the observed bands with the interacting boson model (IBM) and triaxial projected shell model (TPSM) confirms the existence of the quasi-$\ensuremath{\gamma}$ band structure in the $^{114}\mathrm{Te}$ nucleus.

Lifetimes of excited states of the ground-state rotational band in the $^{136}\mathrm{Sm}$ nucleus have been measured up to ${I}^{\ensuremath{\pi}}={20}^{+}$ using the Doppler-shift attenuation method. The states were populated in the reaction $^{107}\mathrm{Ag}$($^{32}\mathrm{S}$, $1p2n$) at 145-MeV beam energy and the $\ensuremath{\gamma}$ rays emitted from the excited states were detected using the Indian National Gamma Array at the Tata Institute of Fundamental Research, Mumbai. The extracted transitional quadrupole moments indicate a reduction of collectivity with increasing spin after the band crossing. The results have been compared with the predictions of the cranked shell model as well as the triaxial projected shell-model calculations and indicate that the nucleus evolves from prolate $\ensuremath{\gamma}$-soft to a stable triaxially deformed shape after the first and the second crossing involving $\ensuremath{\pi}{h}_{11/2}^{2}$ and $\ensuremath{\pi}{h}_{11/2}^{2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}^{2}$ configurations, respectively.

Excited band structures recently observed in $^{156}\mathrm{Dy}$ are investigated using the microscopic triaxial projected shell model (TPSM) approach and the quasiparticle random phase approximation (QRPA) based on the rotating mean field. It is demonstrated that new observed excited bands, tracking the ground-state band, are the $\ensuremath{\gamma}$ bands based on the excited two-quasineutron configurations as conjectured in the experimental work.

Excited states in the $^{101}\mathrm{Pd}$ nucleus were investigated through the $^{75}\mathrm{As}(^{31}\mathrm{P},2p3n)$ fusion-evaporation reaction at ${E}_{\mathrm{lab}}=125$ MeV by using the Indian National Gamma Array spectrometer equipped with 21 clover Ge detectors. The level scheme is considerably extended for medium spin values. New positive-parity band structures in $^{101}\mathrm{Pd}$ have been studied within the framework of the projected shell model and are found to undergo transition from single quasiparticle to high-$K$ three quasiparticle configuration after band crossing, i.e., from principal-axis rotation to tilted-axis rotation. The negative-parity band structures are discussed in the framework of the hybrid version of tilted-axis cranking shell model calculations. The observed alignment gain in the lowest excited $\ensuremath{\nu}{h}_{11/2}$ negative-parity band results from successive ${(\ensuremath{\nu}{g}_{7/2})}^{2}$ and ${(\ensuremath{\pi}{g}_{9/2})}^{2}$ pair alignments. The higher excited negative-parity bands are reproduced for the $\ensuremath{\nu}[{h}_{11/2}{({g}_{7/2}/{d}_{5/2})}^{2}]$ and ${(\ensuremath{\pi}{g}_{9/2})}^{\ensuremath{-}2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ configurations.

The structure of $^{70}$Ge has been studied through in-beam gamma ray spectroscopy. A new band structure is identified that leads to forking of the ground-state band into two excited bands. Band structures have been investigated using the microscopic triaxial projected shell model approach. The observed forking is demonstrated to result from almost simultaneous band crossing of the two neutron aligned and the \gamma-band built on this two-quasiparticle configuration with the ground-state band.

High spin states in $^{105}\mathrm{Cd}$ were studied using $^{92}\mathrm{Mo}(^{16}\mathrm{O},2pn)^{105}\mathrm{Cd}$ reaction at an incident beam energy of 75 MeV. The level scheme of $^{105}\mathrm{Cd}$ has been observed up to ${J}^{\ensuremath{\pi}}=(47/{2}^{\ensuremath{-}})$ and excitation energy $\ensuremath{\sim}10.8\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ with the addition of 30 new $\ensuremath{\gamma}$ transitions to the previous work. Spin and parity for most of the reported levels are assigned from the directional correlation orientation (DCO) ratios and linear polarization measurements. The microscopic origin of the investigated band structures is discussed in the context of triaxial projected shell model (TPSM). The energies of observed positive- and negative-parity bands agree with the predictions of the TPSM by considering triaxial deformation for the observed excited band structures. The shape evolution with increasing angular momentum is explained in the framework of cranked shell model (CSM) and the total Routhian surface (TRS) calculations.

The mass region with a proton number just below the magic number $Z=82$ is known to exhibit a rich variety of shape phenomena. Inspired by the recent extensive experimental measurements of the transition probabilities for the yrast bands in some Pt isotopes in this mass region, we have performed a detailed investigation of ${}^{180\ensuremath{-}190}$Pt using the triaxial projected shell model approach (TPSM). It is demonstrated that by performing the exact three-dimensional angular-momentum projection on multi-quasiparticle configurations, constructed from the traxially deformed mean field, the TPSM provides a consistent description of the yrast band structures, the $\ensuremath{\gamma}$-vibrational band, and the second ${0}^{+}$ band in these nuclei. Further, the observed rapid variations in the quadrupole transition probability along the yrast line of these isotopes are well reproduced in the present study.

Evidence of strong coupling of quasiparticle excitations with gamma-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 multi-quasiparticle 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 gamma-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., 7 pages, 6 figures

High-spin levels of the neutron-rich $^{114}\mathrm{Ru}$ have been investigated by measuring the prompt $\ensuremath{\gamma}$ rays in the spontaneous fission of $^{252}\mathrm{Cf}$. The ground-state band and one-phonon $\ensuremath{\gamma}$-vibrational band have been extended up to 14${}^{+}$ and 9${}^{+}$, respectively. Two levels are proposed as the members of a two-phonon $\ensuremath{\gamma}$-vibrational band. A back bending (band crossing) has been observed in the ground-state band at $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}$ 0.40 MeV. Using the triaxial deformation parameters, the cranked shell model calculations indicate that this back bending in $^{114}\mathrm{Ru}$ should originate from the alignment of a pair of ${h}_{11/2}$ neutrons. Triaxial projected shell model calculations for the $\ensuremath{\gamma}$-vibrational band structures of $^{114}\mathrm{Ru}$ are in good agreement with the experimental data. However, when using the oblate deformation parameters, both of the above-calculated results are not in agreement with the experimental data.