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 bandcross 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.

中文翻译：

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高中位数，成对和变形的中子壳对富含中子的偶数同位素170-−184Hf中基态带上隆的影响

偶数ha同位素中的基态带（GSB） ${}^{170-184}$通过使用具有颗粒数守恒（PNC）方法处理的配对相关性的曲柄壳模型（CSM）研究Hf。通过理论计算可以很好地再现实验的运动惯性矩。GSB在高频下第二次上升$\hslash \omega \approx 0.5$ MeV观测（预测）于 ${}^{172}$高频${}^{170，174-178}$Hf）归因于质子高位的突然对齐-$Ĵ$ 轨道 $\pi \mathrm{1个}{\mathrm{一世}}_{13/2}$ $（\mathrm{1个}/2^{+}[660]）$， $\pi \mathrm{1个}{H}_{9/2}$ $（\mathrm{1个}/2^{-}[541]）$ 和轨道 $\pi \mathrm{1个}{H}_{11/2}$ $（7/2^{-}[523]）$。低频GSB的首次上升$\hslash \omega =0.2-0.3$ MeV输入 ${}^{170-178}$Hf，位于变形的中子壳下方 $ñ=108$，归因于中子轨道的对准 $\nu \mathrm{1个}{\mathrm{一世}}_{13/2}$。对于较重的偶数同位素${}^{180-184}$Hf，与较轻的同位素相比，由于存在变形的壳层，因此第一个带隙被延迟至高频 $ñ=108，116$。GSB的崛起${}^{180-184}$预计Hf发生在 $\hslash \omega \approx 0.5$MeV，来自两个质子同时排列的急剧上升 $\pi \mathrm{1个}{\mathrm{一世}}_{13/2}$， $\pi \mathrm{1个}{H}_{9/2}$ 和中子 $\nu 2G_{9/2}$轨道。配对相关性在偶数同位素中GSB的旋转特性中起着非常重要的作用${}^{180-184}$f 研究了其对上升和跨频带频率的影响。