A low-energy magnetic dipole $\left(M1\right)$ spin-scissors resonance (SSR) located just below the ordinary orbital scissors resonance (OSR) was recently predicted in deformed nuclei within the Wigner function moments (WFM) approach. We analyze this prediction using fully self-consistent Skyrme quasiparticle random phase approximation (QRPA) method. Skyrme forces SkM*, SVbas, and SG2 are implemented to explore SSR and OSR in ${}^{160,162,164}\mathrm{Dy}$ and ${}^{232}\mathrm{Th}$. Accuracy of the method is justified by a good description of $M1$ spin-flip giant resonance. The calculations show that isotopes ${}^{160,162,164}\mathrm{Dy}$ indeed have at 1.5–2.4 MeV (below OSR) $I^{\pi }K=1^{+}1$ states with a large $M1$ spin strength ($K$ is the projection of the total nuclear moment to the symmetry $z$ axis). These states are almost fully exhausted by $pp[411\uparrow ,411\downarrow ]$ and $nn[521\uparrow ,521\downarrow ]$ spin-flip configurations corresponding to $pp[2d_{3/2},2d_{5/2}]$ and $nn[2f_{5/2},2f_{7/2}]$ structures in the spherical limit. So the predicted SSR is actually reduced to low-orbital ($l=2,3$) spin-flip states. Following our analysis and in contradiction with WFM spin-scissors picture, deformation is not the principle origin of the low-energy spin $M1$ states but only a factor affecting their features. The spin and orbital strengths are generally mixed and exhibit interference: weakly destructive in SSR range and strongly constructive in OSR range. In ${}^{232}\mathrm{Th}$, the $M1$ spin strength is very small. Two groups of $I^{\pi }=1^{+}$ states observed experimentally at 2.4–4 MeV in ${}^{160,162,164}\mathrm{Dy}$ and at 2–4 MeV in ${}^{232}\mathrm{Th}$ are mainly explained by fragmentation of the orbital strength. Distributions of nuclear currents in QRPA states partly correspond to the isovector orbital-scissors flow but not to the spin-scissors one.

中文翻译：

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变形核中低能自旋和轨道磁偶极子激发的微观分析

低能磁偶极子 $\left(米1\right)$最近在 Wigner 函数矩 (WFM) 方法中在变形核中预测了位于普通轨道剪刀共振 (OSR) 正下方的自旋剪刀共振 (SSR)。我们使用完全自洽的 Skyrme 准粒子随机相位近似 (QRPA) 方法分析此预测。Skyrme 强制实施 SkM*、SVbas 和 SG2 以探索 SSR 和 OSR${}^{160,162,164}\mathrm{染料}$ 和 ${}^{232}钍$. 该方法的准确性通过良好的描述来证明$米1$自旋翻转巨共振。计算表明，同位素${}^{160,162,164}\mathrm{染料}$ 确实有 1.5–2.4 MeV（低于 OSR） ${\mathrm{一世}}^{\pi }钾=1^{+}1$ 有大 $米1$ 自旋强度（$钾$ 是总核矩对对称性的投影 $z$轴）。这些状态几乎完全耗尽$磷磷[411\uparrow ,411\downarrow ]$ 和 $nn[521\uparrow ,521\downarrow ]$ 自旋翻转配置对应于 $磷磷[2d_{3/2},2d_{5/2}]$ 和 $nn[2F_{5/2},2F_{7/2}]$球极限内的结构。所以预测的SSR实际上降低到了低轨道（$升=2,3$) 自旋翻转状态。根据我们的分析，与 WFM 自旋剪刀图相矛盾，变形不是低能自旋的主要起源$米1$状态，但只是影响其特征的一个因素。自旋和轨道强度通常混合并表现出干扰：在 SSR 范围内具有弱破坏性，在 OSR 范围内具有强建设性。在${}^{232}钍$， 这 $米1$旋转强度非常小。两组${\mathrm{一世}}^{\pi }=1^{+}$ 在 2.4-4 MeV 实验观察到的状态 ${}^{160,162,164}\mathrm{染料}$ 并且在 2–4 MeV in ${}^{232}钍$主要由轨道强度的分裂来解释。QRPA 状态中核电流的分布部分对应于等向量轨道剪刀流，而不是自旋剪刀流。