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

Abstract

The ground-state bands (GSBs) in the even-even hafnium isotopes ${}^{170-184}$Hf are investigated by using the cranked shell model (CSM) with pairing correlations treated by the particle-number conserving (PNC) method. The experimental kinematic moments of inertia are reproduced very well by theoretical calculations. The second upbending of the GSB at high frequency $\hslash \omega \approx 0.5$ MeV observed (predicted) in ${}^{172}$Hf (${}^{170,174-178}$Hf) attributes to the sudden alignments of the proton high-$j$ orbitals $\pi 1i_{13/2}$ $(1/2^{+}[660])$, $\pi 1h_{9/2}$ $(1/2^{-}[541])$ and orbital $\pi 1h_{11/2}$ $(7/2^{-}[523])$. The first upbendings of GSBs at low frequency $\hslash \omega =0.2-0.3$ MeV in ${}^{170-178}$Hf, which locate below the deformed neutron shell $N=108$, attribute to the alignment of the neutron orbital $\nu 1i_{13/2}$. For the heavier even-even isotopes ${}^{180-184}$Hf, compared to the lighter isotopes, the first band-crossing is delayed to the high frequency due to the existence of the deformed shells $N=108,116$. The upbendings of GSBs in ${}^{180-184}$Hf are predicted to occur at $\hslash \omega \approx 0.5$MeV, which come from the sharp raise of the simultaneous alignments of both proton $\pi 1i_{13/2}$, $\pi 1h_{9/2}$ and neutron $\nu 2g_{9/2}$ orbitals. The pairing correlation plays a very important role in the rotational properties of GSBs in even-even isotopes ${}^{180-184}$Hf. Its effects on upbendings and band-crossing frequencies are investigated.

Comments: 14pages,12figures