Background] Low-energy dipole states have been hot topics in stable and unstable nuclei. Recently, Nestrenko {} proposed two low-energy dipole modes of the individual toroidal state and the compressional state in ${}^{24}$Mg. They associated the toroidal state with cluster structure, but there is no explicit analysis of the cluster structure. [Purpose] Our purpose is to investigate low-lying $1^{-}$ states in ${}^{24}$Mg and clarify their natures such as the dipole transition strengths, nuclear vorticity, and cluster features. [Method] Wave functions of $1^{-}$ states of ${}^{24}$Mg are described with the antisymmetrized molecular dynamics framework combined with the generator coordinate method. Excitation energies and dipole transition strengths are calculated. Cluster wave functions are explicitly taken into account to reveal the role of cluster correlations in $1^{-}$ states. Intrinsic matter density and transition current density are analyzed. [Results] Two low-lying dipole states, the $1_{K=1}^{-}$ and $1_{K=0}^{-}$, are obtained. The $1_{K=1}^{-}$ state has the strongest isoscalar toroidal dipole strength and shows two vortexes structure in the intrinsic transition current density. The $1_{K=0}^{-}$ state features the isoscalar compressional dipole strength and exhibits the ${}^{16}$O+${}^{8}Be$ cluster correlation. [Conclusions] The toroidal and compressional dipole modes separately appear as the $K=1$ and $K=0$ states in the deformed ${}^{24}$Mg system. The $1_{K=1}^{-}$ state is the toroidal dipole state with the strong nuclear vorticity but no prominent cluster structure, and the $1_{K=0}^{-}$ state is the compressional dipole state having enhanced cluster structure but has the weaker vorticity.

中文翻译：

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24 Mg处于低位1-态的团簇相关性和核涡度

背景技术低能偶极子态一直是稳定和不稳定核中的热门话题。最近，涅斯捷连科（Nestenko）{}提出了两种低能偶极子态，分别是环面态和压缩态${}^{24}$镁 他们将环形状态与簇结构相关联，但是没有对簇结构的明确分析。[目的]我们的目的是调查低洼地带${\mathrm{1个}}^{-}$ 州 ${}^{24}$镁并阐明其性质，例如偶极跃迁强度，核涡度和团簇特征。[方法]波函数${\mathrm{1个}}^{-}$ 的状态 ${}^{24}$用抗对称分子动力学框架与生成器坐标法相结合来描述镁。计算出激发能和偶极跃迁强度。明确考虑了聚类波动函数，以揭示聚类相关性在${\mathrm{1个}}^{-}$状态。分析了本征密度和跃迁电流密度。[结果]两个低地偶极子态${\mathrm{1个}}_{ķ=\mathrm{1个}}^{-}$ 和 ${\mathrm{1个}}_{ķ=0}^{-}$获得。的${\mathrm{1个}}_{ķ=\mathrm{1个}}^{-}$态具有最强的等量环面偶极强度，并在本征跃迁电流密度中显示出两个涡旋结构。的${\mathrm{1个}}_{ķ=0}^{-}$ 态具有等标压缩偶极强度并表现出 ${}^{16}$O +${}^8乙Ë$聚类相关。[结论]环形和压缩偶极子模式分别显示为$ķ=\mathrm{1个}$ 和 $ķ=0$ 变形中的状态 ${}^{24}$镁系统。的${\mathrm{1个}}_{ķ=\mathrm{1个}}^{-}$ 态是具有强核涡度但没有明显的团簇结构的环形偶极态。 ${\mathrm{1个}}_{ķ=0}^{-}$ 态是具有增强的团簇结构但涡旋性较弱的压缩偶极子态。