Backbending Phenomena in Even–Even $${}^{\boldsymbol{162{-}172}}$$Hf Isotopes

Abstract

This study probes the backbending phenomena in even–even $${}^{162{-}172}$$ Hf isotopes. Experimental ground-state rotational energies up to $$J^{\pi}=36^{+}$$ states were used to calculate the variation of the moment of inertia against the square of rotational angular frequency. The result shows that the calculated values of the moment of inertia for heavy mass isotopes; $${}^{170}$$ Hf and $${}^{172}$$ Hf, increase progressively over an increasing square of angular frequency. However, the $${}^{162}$$ Hf, $${}^{164}$$ Hf, $${}^{166}$$ Hf, and $${}^{168}$$ Hf isotopes exhibit a sharp bending with an $$S$$ -shaped curve. While $$J^{(1)}$$ the kinematical moment of inertia maintains the backbending shapes in these nuclei, the dynamical moment of inertia $$J^{(2)}$$ shows significant responses to the changes in $$J^{(1)}$$ and $$\omega_{\mathrm{rot}}$$ , giving each of these isotopes a unique signature. These backbending shapes, $$J^{(1)}$$ increasing, and the fluctuations in $$J^{(2)}$$ may be due to a rapid quasiparticle alignment in the considered Hf nuclei. The closeness of the crossing frequency between the first and second bands is also investigated, we propose that the second band crossing is due to the alignment of a pair of protons (proton-pair alignment).