The observed excited states of ¹²²Ce nucleus have been studied in the framework of projected shell model (PSM). The yrast band has been studied up to spin 26ħ. The first band crossing has been predicted above a rotational frequency of 0.4 MeV/ħ that corresponds to first backbending. The calculation reproduces the experimentally observed ground state band up to spin 14ħ. The electromagnetic quantities, transition quadrupole moments and g-factors are predicted and there is a need to measure these quantities experimentally.

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.

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.