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).

中文翻译：

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偶数甚至偶数的{弯曲现象$$ {} ^ {\ boldsymbol {162 {-} 172}} $$ Hf同位素

摘要

这项研究探讨了偶数– （{} ^ {162 {-} 172} \） Hf同位素中的弯曲现象。高达\（J ^ {\ pi} = 36 ^ {+} \）状态的实验基态旋转能被用于计算惯性矩相对于旋转角频率平方的变化。结果表明，重同位素的惯性矩计算值较高。\（{} ^ {170} \） Hf和\（{} ^ {172} \） Hf在角频率的平方上逐渐增大。但是，\（{} ^ {162} \） Hf，\（{} ^ {164} \） Hf，\（{} ^ {166} \） Hf和\（{} ^ {168} \） f同位素表现出急剧的弯曲，并带有\（S \）形曲线。而\（j ^ {（1）} \）的惯性运动学力矩保持在这些核的回弯形状，惯性动力学力矩\（j ^ {（2）} \）示出了在改变显著响应\（ J ^ {（1）} \）和\（\ omega _ {\ mathrm {rot}} \），为每个同位素赋予唯一的签名。这些向后弯曲的形状\（J ^ {（1）} \）增大，并且\（J ^ {（2）} \）的波动可能是由于所考虑的Hf核中的快速准粒子排列所致。还研究了第一和第二条带之间的交叉频率的接近度，我们认为第二条带交叉是由于一对质子的对准（质子对对准）引起的。