For study of dipole excitations, a new method of variation after $K$-projection in the framework of antisymmetrized molecular dynamics (AMD) with the deformation $\beta$ constraint was proposed. The method was applied to $^{10}$Be and $^{16}$O to describe low-energy dipole excitations and found to be a useful and economical approach for dipole excitations. In the application to $^{10}$Be, two dipole states in low-energy region were described. For $^{16}$O, the $1_1^-$ and $1_2^-$ states with remarkable dipole strengths were obtained. The $1_1^-$ state is characterized by significant toroidal dipole (TD) and compressional dipole strengths, whereas the $1_2^-$ has significant TD strength and shows a developed $\alpha + {}^{16}$O cluster structure. Dipole properties in $^{16}$O were discussed by analysis of current densities of the dipole transitions.

中文翻译：

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10Be 和 16O 中低能偶极激发的反对称分子动力学中 K 投影后的变化

为了研究偶极子激发，提出了一种在反对称分子动力学（AMD）框架下具有变形$\beta$约束的$K$-投影后的变化方法。该方法应用于 $^{10}$Be 和 $^{16}$O 来描述低能量偶极子激发，并被发现是一种有用且经济的偶极子激发方法。在$^{10}$Be 的应用中，描述了低能区的两个偶极子态。对于 $^{16}$O，获得了具有显着偶极强度的 $1_1^-$ 和 $1_2^-$ 状态。$1_1^-$ 状态的特征在于显着的环形偶极子 (TD) 和压缩偶极子强度，而 $1_2^-$ 具有显着的 TD 强度并显示出发达的 $\alpha + {}^{16}$O 簇结构. 通过分析偶极跃迁的电流密度讨论了 $^{16}$O 中的偶极特性。