The high spin states in N=80 ¹³⁹Pr have been investigated by in-beam γ-spectroscopic techniques following the reaction ¹³⁰Te (¹⁴N, 5n) reaction at E=75 MeV, using a gamma detector array, consisting of seven 23% compton-suppressed high purity germanium detectors and a multiplicity ball of fourteen bismuth germanate elements. Based on γ-γ coincidence data, the level scheme of ¹³⁹Pr has been considerably extended up to 7.2 MeV excitation. Tentative spin-parity assignments are done for the newly proposed levels on the basis of the DCO ratios corresponding to strong gates and the available information from the earlier light ion experiments.

The variety of shapes and structures, observed in light rare earth $A \sim 130$ nuclei, have been discussed in view of different angular momentum coupling schemes and their interplay that comes into effect at high spin. The $N = 79$ and 80 isotopes in La–Ce region, produced via fusion evaporation reaction, have been studied using the Indian National Gamma Array (INGA) consisting of 18 clover HPGe detectors. Two nearly degenerate $\Delta I = 1$ bands have been observed at high spin of ¹³⁷Ce and a triaxial deformation of $\gamma = \pm 30^{\circ}$ has been assigned to the bands, from the total Routhian surface (TRS) calculations. The high-spin candidates of the yrast band of ¹³⁸Ce show signature splitting both in energy and $B(M1)/B(E2)$ values. The bandcrossing due to the alignment of a pair of $h_{11}/2$ proton particles has been conjectured at $\hbar ω \sim 0.3$ MeV, from the single-particle Routhians obtained from TRS calculations. Lifetime measurements by Doppler shift attenuation method (DSAM) has been carried out and from the estimated reduced transition probability $B(M 1)$, the $\Delta I = 1$ band in ¹³⁸Ce has been characterized as a magnetic rotation (MR) band. The rise in the values of $B(M1)$, for the higher spin candidates of the band, has been conjectured as the reopening of a different shear at the top of the Band B1. The characteristic of the MR bands in $A \sim 130$ region has been discussed in the light of a phenomenological calculation and compared to the MR bands in other mass regions.