The Hartree–Bogoliubov (HB) framework of calculations has been applied for calculating various nuclear structure quantities for ^154−166Dy mass chains. In this framework, the intrinsic quadrupole moments, the low-lying yrast states ($E_{2}^{+}$ and $E_{4}^{+}$) and occupation numbers for various shell model orbits have been obtained. The calculated results indicate that the observed onset of deformation in going from ¹⁵⁴Dy to ¹⁶⁶Dy arises due to enhanced occupation of $(h_{11/2})_{\pi}$ orbit, increased polarization of $(d_{5/2})_{\pi}$ orbit and increase in the occupation of down-slopping $`k'$ components of $(i_{13/2})_{v} and $(h_{9/2})_{υ}$ orbits.

The yrast bands of even-even selenium isotopes with $A = 68-78$ are studied in the framework of projected shell model, by employing quadrupole plus monopole and quadrupole pairing force in the Hamiltonian. The oblate and prolate structures of the bands have been investigated. The yrast energies, backbending plots and reduced $E2$ transition probabilities and 𝑔-factors are calculated and compared with the experimental data. The calculated results are in reasonably good agreement with the experiments.

Variation-after-projection (VAP) calculations in conjunction with Hartree–Bogoliubov (HB) ansatz have been carried out for $A = 98–106$ strontium isotopes. In this framework, the yrast spectra with $J^{\Pi} \geq 10^{+}$ , $B(E2)$ transition probabilities, quadrupole deformation parameter and occupation numbers for various shell model orbits have been obtained. The results of the calculation for yrast spectra give an indication that it is important to include the hexadecapole–hexadecapole component of the two-body interaction for obtaining various nuclear structure quantities in Sr isotopes. Besides this, it is also found that the simultaneous polarization of $p_{3}/2$ and $f_{5}/2$ proton subshells is a significant factor in making a sizeable contribution to the deformation in neutron-rich Sr isotopes.

The negative parity yrast bands of neutron-deficient ^125-131Ce nuclei are studied by using the projected shell model approach. Energy levels, transition energies and $B(M1)/B(E2)$ ratios are calculated and compared with the available experimental data. The calculations reproduce the band-head spins of negative parity yrast bands and indicate the multi-quasiparticle structure for these bands.

The positive-parity bands in ^224−234Th are studied using the projected shell model (PSM) approach. The energy levels, deformation systematics, $B(E2)$ transition probabilities and nuclear 𝑔-factors are calculated and compared with the experimental data. The calculation reproduces the observed positive-parity yrast bands and $B(E2)$ transition probabilities. Measurement of $B(E2)$ transition probabilities for higher spins and 𝑔-factors would be a stringent test for our predictions. The results of theoretical calculations indicate that the deformation systematics in ^224−234Th isotopes depend on the occupation of low 𝑘 components of high j orbits in the valence space and the deformation producing tendency of the neutron–proton interaction operating between spin orbit partner (SOP) orbits, the $[(2g_{9/2}_{\pi}) - (2g_{7/2})_{\nu}]$ and $[(1i_{13/2})_{\pi} - (1i_{11/2})_{\nu}]$ SOP orbits in the present context. In addition, the deformation systematics also depend on the polarization of $(1h_{11/2})_{\pi}$ orbit. The low-lying states of yrast spectra are found to arise from 0-quasiparticle (qp) intrinsic states whereas the high-spin states turn out to possess composite structure.

The projected shell model (PSM) calculations have been performed for the neutron-rich even–even ^102−110Mo and odd–even ^103−109Mo isotopes. The present calculation reproduces the available experimental data on the yrast bands. In case of even–even nuclei, the structure of yrast bands is analysed and electromagnetic quantities are compared with the available experimental data. The 𝑔-factors have been predicted for high spin states. For the odd-neutron nuclei, the structures of yrast positive- and negative-parity bands are analysed and found to be in reasonable agreement with the experiments for ${}^{103−107}$Mo. The disagreement of the calculated and observed plots for energy staggering quantity clearly establishes the occurrence of sizable triaxiality in ${}^{103,105}$Mo and also predicts a decrease in the quantum of triaxiality with increasing neutron number and angular momentum for odd mass neutron-rich Mo isotopes.