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The ground-state bands (GSBs) in the even-even hafnium isotopes$^{170-184}$Hf are investigated by using the cranked shell model (CSM) withpairing correlations treated by the particle-number conserving (PNC) method.The experimental kinematic moments of inertia are reproduced very well bytheoretical calculations. The second upbending of the GSB at high frequency$\hbar\omega\approx0.5$ MeV observed (predicted) in $^{172}$Hf($^{170,174-178}$Hf) attributes to the sudden alignments of the proton high-$j$orbitals $\pi1i_{13/2}$ $(1/2^{+}[660])$, $\pi1h_{9/2}$ $(1/2^{-}[541])$ andorbital $\pi1h_{11/2}$ $(7/2^{-}[523])$. The first upbendings of GSBs at lowfrequency $\hbar\omega=0.2-0.3$ MeV in $^{170-178}$Hf, which locate below thedeformed neutron shell $N=108$, attribute to the alignment of the neutronorbital $\nu1i_{13/2}$. For the heavier even-even isotopes $^{180-184}$Hf,compared to the lighter isotopes, the first band-crossing is delayed to thehigh frequency due to the existence of the deformed shells $N=108,116$. Theupbendings of GSBs in $^{180-184}$Hf are predicted to occur at$\hbar\omega\approx0.5$MeV, which come from the sharp raise of the simultaneousalignments of both proton $\pi1i_{13/2}$, $\pi1h_{9/2}$ and neutron$\nu2g_{9/2}$ orbitals. The pairing correlation plays a very important role inthe rotational properties of GSBs in even-even isotopes $^{180-184}$Hf. Itseffects on upbendings and band-crossing frequencies are investigated.

physical review. c

Effects of high-$j$ orbitals, pairing and deformed neutron shells on  upbendings of ground-state bands in neutron-rich even-even isotopes  $^{170-184}$Hf