In this work, a detailed theoretical investigation of the even–even ^188-196 Hg isotopes has been carried out employing the Triaxial Projected Shell Model (TPSM). The study focuses on the interplay between shape coexistence, triaxial deformation and the nature of γ -bands in these isotopes. Two sets of deformation parameters i.e., oblate and prolate, have been used to examine the shape coexistence in these nuclei. The analysis of energy spectra reveals that the yrast bands exhibit oblate character while the γ -bands are better described with prolate deformation.The evolution of low lying excited 0 ^+ bands has also been examined across the isotopic chain. R_4/2 ratios and energy staggering in γ -bands suggest that these isotopes exhibit γ softness. Moreover, the calculated rotational alignment, B(E2) and g-factors exhibit good consistency with the available experimental observations. Overall, this comprehensive study provides a deeper understanding of the structural properties and shape transition of the Hg isotopes in the vicinity of Z = 82 shell closure.

The even–even 94–100Mo isotopes have been studied using the Triaxial Projected Shell Model with zero triaxiality (ϵ ^'∼ 0) and with triaxiality incorporated (ϵ ^') to examine the evolution of triaxial deformation as we move from the shell closure at N = 50 towards the more deformed region approaching N ∼ 60. The calculated yrast and γ bands show excellent agreement with experimental data, with the inclusion of triaxiality providing substantial improvements particularly at higher spins. Band-diagram analysis, together with the corresponding wave-function composition, reveals the underlying quasiparticle structure and provides a microscopic explanation of key features such as band crossings and backbending. Backbending plots show a transition from rotational to vibrational behavior in heavier isotopes, indicating enhanced triaxiality. The evolution of B(E2) values, examined both as a function of spin and deformation, further supports the effect of triaxiality as one moves along the isotopic chain under study. An analysis of γ -band energy staggering demonstrates that the even–even 94–100Mo isotopes exhibit predominantly γ -soft behavior. These findings demonstrate a smooth transition from axial symmetry to triaxial shapes along the chosen Mo isotopic chain.

Chiral bands observed in 128-134La isotopes are investigated using the well-developed multiquasiparticle microscopic triaxial projected shell model (TPSM) approach. The TPSM results for energy levels and transition probabilities are in good agreement with available experimental data. In particular, it is demonstrated that the transition probabilities characteristic of doublet bands arising from chiral symmetry breaking are accurately reproduced. The calculated root-mean-square values of the angular momentum components for both the yrast and side bands suggest that these nearly degenerate doublet bands, with similar transition probabilities, possess a chiral nature.

A microscopic analysis of the nuclear structure of the odd-mass 117Te has been carried out using the theoretical framework of the Projected Shell Model (PSM). The tellurium isotopes lie in a transitional region near the closed proton shell at Z=50, where the coupling between individual particle motion and collective nuclear dynamics plays a crucial role. The present study focuses on the description of negative-parity yrast band structures, energy spectra, back-bending behavior, and reduced electric quadrupole transition probabilities B(E2). The calculated results, show close consistency when compared with the experimental observations, successfully reproducing the band-head spins, yrast energies, and the observed back-bending at spin 19/2−. The calculated B(E2) values exhibit an rising trend with spin, indicating enhanced collectivity and nuclear deformation. Present work demonstrates the efficacy of the PSM in modeling the structure of deformed odd-A isotopes.

A theoretical investigation of the nuclear structure of 196Pt has been carried out within the framework of Triaxial Projected Shell Model (TPSM) to explore its shape evolution, shape coexistence and γ-soft nature. The potential energy surface (PES) shows two distinct minima corresponding to prolate and oblate deformation indicating the presence ofshape coexistence. Calculated yrast states reproduce the available experimental data reasonably well. At lower spins, results are better reproduced by prolate deformation, whereas at higher spins, oblate deformation reproduces the experimental data. While γ band is reproduced by prolate deformation predominantly. The analysis of energy staggering parameters and R4/2 ratios confirm the γ soft triaxial nature of this nucleus. The observed rotational alignment near I = 10ℏ suggests the alignment of i13/2 neutron pairs. Furthermore, the calculated values of B(E2) strengths show good accuracy with the experimental data available for low spins only, supporting the reliability of adopted deformation parameters. Overall, this study offers microscopic insight into the triaxial deformation and shape coexistence in 196Pt, confirming its transitional nature in the Os–Pt–Hg region.

The triaxial projected shell model (TPSM) is employed for a comprehensive theoretical analysis of collective band structures in neutron-deficient, odd-mass caesium isotopes ranging from A = 117 to 125. The TPSM uses a triaxially deformed Nilsson potential combined with angular momentum projection to construct one-quasiparticle and three-quasiparticle configurations. Analysis of band diagrams, nuclear moments of inertia, and energy level systematics reveals good overall agreement between TPSM calculations and experimental data. Our calculations consistently utilize a large triaxial deformation of gamma similar to 30 degrees, a value validated against the gamma-bandhead energies, to accurately reproduce the observed alignment frequencies and signature splitting for these isotopes. Consequently, the findings validate the necessity of a large triaxial description for these complex transitional nuclei.

High-spin structures of odd-mass 111-119Sb isotopes are investigated using the Triaxial Projected Shell Model (TPSM), with deformation parameters extracted from constrained Covariant Density Functional Theory (CDFT) calculations. The band diagrams exhibit characteristic crossings between one-and three-quasiparticle (1-qp and 3-qp) configurations in the mid-spin region, which are explained through the evolution of 3-qp wavefunction amplitudes. These structural changes are reflected in alignment diagrams, signature splitting and transition probabilities. The study demonstrates the necessity of including multi-quasiparticle configurations in the model basis to accurately reproduce experimentally observed electromagnetic transition rates particularly in 113Sb. Angular momentum projections, evaluated across three intrinsic sectors, provide direct evidence for triaxiality in this isotope. Overall, this work offers new insights into the influence of triaxial deformation and quasiparticle dynamics on the rotational behavior of Sb nuclei near the Z = 50 shell closure.

A microscopic analysis of the nuclear structure of the odd-mass 117 Te has been carried out using the theoretical framework of the Projected Shell Model (PSM). The tellurium isotopes lie in a transitional region near the closed proton shell at Z=50, where the coupling between individual particle motion and collective nuclear dynamics plays a crucial role. The present study focuses on the description of negative-parity yrast band structures, energy spectra, back-bending behavior, and reduced electric quadrupole transition probabilities B(E2) . The calculated results, show close consistency when compared with the experimental observations, successfully reproducing the band-head spins, yrast energies, and the observed back-bending at spin 19/2 − . The calculated B(E2) values exhibit an rising trend with spin, indicating enhanced collectivity and nuclear deformation. Present work demonstrates the efficacy of the PSM in modeling the structure of deformed odd-A isotopes.

The structural evolution of the odd-mass nucleus 109Sb has been investigated using the Triaxial Projected Shell Model (TPSM). This nucleus, located close to the Z = 50 shell closure, serves as an ideal system for investigating the interplay between single-particle motion and collective rotation. Using angular-momentum projected quasiparticle configurations built on a triaxially deformed basis, we analyze the yrast and yrare band structures and compare the calculated energies with available experimental data. The TPSM results reproduce the observed band crossings and the overall evolution of the yrast and yrare bands reasonably well. A detailed examination of the dynamic moment of inertia, J2 and the reduced electric quadrupole transition probabilities reveals a gradual loss of collectivity with increasing spin for the yrast band, consistent with experimental observations. The present study provides a microscopic understanding of the structural evolution and decreasing collectivity in this nucleus.

A comprehensive analysis is done to study the structural evolution and triaxial deformation in the even-even 144-148Ce isotopes using Triaxial Projected Shell Model (TPSM) approach. A thorough investigation of the yrast and y-band explains the shape transition and presence of gamma collectivity in these neutron rich nuclei. Various observables and phenomena like R4/2 ratios, odd even staggering patterns in y-bands, shape invariants, reduced transition probabilities, g-factors etc. have been calculated and found to be reasonably consistent with the available experimental data. Also, these results reveal a progressive shape evolution from y-soft towards axially symmetric rotor at N=90. This study enhances our understanding of nuclear deformation mechanisms in this critical mass region by revealing the structural changes driven by multiquasiparticle configurations.

A theoretical investigation on shape coexistence in the isotopes 119I and 121I has been carried out using both the Projected Shell Model (PSM) and Triaxial Projected Shell Model (TPSM). We analyze the energy spectra, band structures, potential energy surfaces and signature splitting for these nuclei. Our study reveals that the yrast band for 119I is better described by TPSM with gamma similar to 28 degrees and the yrast band of 121I is described by PSM (Prolate) at low spins and by TPSM with gamma similar to 27 degrees at higher spins. In contrast, the yrast band exhibits predominantly an oblate character for both 119I and 121I isotopes. The intrinsic structures of these isotopes have been discussed by interpreting their band diagrams. Also, signature splitting in these isotopes obtained via PSM and TPSM has been compared with experimental observations to mark some significant conclusions.

In the present work, a theoretical attempt using triaxial projected shell model (TPSM) has been made to understand and confirm the structural evolution observed in even–even isotopes (A = 152–164) of Gd ( Z=64 ) nucleus. The TPSM study of yrast, γ , γγ -bands provides a reasonable description about the triaxial nature of these isotopes. The E-GOS plots along with R_42 -ratios predict shape transition phenomenon along isotopic chain under study. Further, backbending in moment of inertia, g factors, transition probabilities, energy staggering in γ -bands, etc., have also been calculated and found to be in good agreement with the available experimental data.

Theoretical investigation of negative parity bands in odd-mass ^123-131 La isotopes has been carried out by using Triaxial Projected Shell Model approach (TPSM). Potential Energy Surface (PES) calculations suggest γ -soft nature of these isotopes. This finding is further supported by an analysis of their quadrupole shape invariants, which indicates that the nuclei have a soft-triaxial shape. Suitable deformation parameters, which are in agreement with the previous studies, are used to generate the band energies of the yrast band, γ -band, and their signature partners. The bandhead energies of all the bands are in good agreement with the experimental values. Further, structural properties like band diagrams, backbending in moment of inertia, dynamic moment of inertia, signature splitting and reduced transition probabilities (B(E2) and B(M1)) have also been calculated.

The structural properties of even-even Sr isotopes near neutron shell closure (N = 50) have been systematically studied by using Triaxial Projected Shell Model (TPSM), revealing significant variations in deformation, collectivity, and quasiparticle dynamics. Band diagram plots reveal the quaiparticle structure of these isotopes. The variation in reduced transition probabilities [B(E2)] reflects the evolution of collectivity with changes in neutron number and angular momentum, demonstrating a gradual decline near the shell closure (N = 50) and a sharp increase at N = 60, indicative of a transition to a more deformed regime. Furthermore, staggering plots and Potential Energy Surface (PES) analysis reveal a systematic shift from γ -soft to γ -rigid nuclear behavior as the isotopes approach the shell closure, underscoring the interplay between deformation parameters and nuclear configurations.

The positive and negative parity rotational band structures of odd-odd Nb isotopes with atomic masses 90, 92 and 94 are investigated using the theoretical framework of the projected shell model. These odd-odd nuclei are found to be ideal for investigating the significant structural changes occurring in the region situated far from the valley of stability. This is the first time that such comprehensive theoretical data for both positive and negative parities together for the odd-odd 90-94Nb isotopes have been disclosed. The g-factor and electromagnetic transition probabilities are among the various nuclear structure quantities that are examined for the first time. Using a broad configuration space for both protons and neutrons, the computed data have been anticipated up to high spin values.

A comprehensive analysis of high spin band structures for odd mass ^117-127 I nuclei is performed using Triaxial Projected Shell Model (TPSM) approach. Using suitable values for the relevant parameters, the estimated energy spectrum of odd mass ^117-127 I agrees well with the experimental results The potential energy surfaces reveal that the isotopes are heading from γ -softness towards rigidity. The current analysis further revealed that the typical band crossing along the yrast as well as the yrare line is caused by the three-quasipaticle band crossing the one-quasiparticle band. Further, transitional probabilities [B(E2) and B(M1)] have been computed and found to be consistent with the available experimental data. Chirality in ^123 I has also been discussed.

A systematic study on the structural evolution induced by the change in neutron number as well as by the increase in angular momentum for even-even 160−178 Yb isotopes has been made using the triaxial projected shell model (TPSM). A detailed analysis of γ-vibrational bands built on ground state has been presented in addition to the yrast band for these nuclei in the present study. The structural changes arising with the increase in neutron number have been quite extensively explained with the help of some interesting nuclear phenomenon. The characteristics of energy ratio and staggering parameter indicate the shape evolution from γ-soft to rigid rotational nuclei as one moves from 160 to 178 Yb. Additionally, the calculated electric quadrupole reduced probabilities B(E2), both in-band and inter-band, and gyro-magnetic factors present a reasonably good agreement with the experimental results.

The current work exhibits the effective implementation of the triaxial projected shell model (TPSM) to explore the non–axial features displayed by 82−88 Ge and 66−74 Se isotopes located close to the shell closures at Z = 28 and N = 50.The interaction of excited band structures with the ground state seems to have a profound and considerable impact on the pattern of deformation of these nuclei. The systematic comparison and analysis of the deformation systematics of E ( 2_1^+ ) and R 4/2 ratio reflect the γ -soft nature of the neutron-deficient Se isotopes, whereas neutron-rich Ge isotopes demonstrate a shape transition from spherical to γ -soft nature. The application of TPSM in the present work not only yields the yrast band but also brings forth γ - and 2 γ -vibrational band spectra upto high spins for the first time. To properly comprehend the evolution of intrinsic nuclear structural features of the studied even-even Ge and Se isotopic chains, numerous other nuclear structure properties, such as back-bending in MOI, variation of g-factor with angular momentum, and reduced transition probabilities of γ - and g -band, have also been covered within the deformed triaxial basis. The TPSM results, generated by using the most appropriate values of parameters in the Hamiltonian for studied even-even Ge and Se isotopic chains, are in reasonable accordance with their experimental counterparts as well as other theoretical results.

The present work demonstrates the application of multi-quasiparticle triaxial projected shell model (TPSM) to investigate the band structures of 98−106Ru isotopes. These nuclei, falling in the mass region A ~ 100 of nuclear chart, exhibit a variety of interesting properties including the description of band structures with well developed γ- and 2γ-bands. By performing the exact three-dimensional angular-momentum projection technique used in TPSM, a reliable description of yrast and near yrast bands is presented in detail in the present work. The discussion on the importance of 2-quasiparticle neutron bands with K = 1 and K = 3 has proven to be quite substantial in describing various structural properties of these nuclei. It is reported that the comparison of calculations and experiments yields good agreement and a reasonable description of structure variations, transition rates and many other observed properties of isotopes under consideration has been quite systematically provided.

Odd-mass nuclei are the excellent candidates for studying the possible structure variations which are away from the valley of stability. Highly deformed odd-mass nuclei have been found in the A $$\sim $$ 110 mass region, provide opportunities to study the deformed rotational bands. The description of the odd-mass $$^{103-117}Ag$$ isotopes with the projected shell model is presented in this paper. Calculations are comprehensively performed for the quasi-particle excitations. Reasonable agreement between theory and experiment is obtained which supports the adequacy of the parameters and the configuration used for the calculation and some important characteristics of these nuclei are discussed which include the kinetic moment of inertia $$2J^{(1)}$$ , backbending effects, E-GOS plots, AMR, etc.