The static and dynamic polarizabilities of the ground state and low-lying excited states of ${\mathrm{Ba}}^{+}$ ions are calculated by using a relativistic semiempirical method: the relativistic configuration interaction plus core polarization (RCICP) method. The tune-out wavelengths of the ground state and magic wavelengths of the $6s_{1/2}\to 6p_{1/2,3/2},5d_{3/2,5/2}$ transitions are determined. One visible tune-out wavelength, 480.658(18) nm, is found. High-precision measurements on this tune-out wavelength could be used to determine the ratio of the oscillator strengths of the $6s_{1/2}\to 6p_{1/2,3/2}$ transitions. In addition, we suggest that the measurements on the magic wavelengths corresponding to the $6s_{1/2}\to 5d_{3/2,5/2}$ transitions could be used to determine the oscillator strengths of the $5d_{5/2}\to 4f_{7/2}$ and $5d_{3/2}\to 4f_{5/2}$ transitions, while the measurements of the magic wavelengths near 416 nm for the $6s_{1/2}\to 6p_{3/2}$ transition could be used to determine the ratio of the oscillator strengths of the $6p_{3/2}\to 6d_{3/2,5/2}$ transitions.

中文翻译：

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Ba +离子的微调和魔幻波长

基态和低激发态的静态和动态极化率。 ${巴}^{+}$离子是使用相对论的半经验方法计算的：相对论的构型相互作用加核心极化（RCICP）方法。基态的调出波长和原子的魔幻波长。$6s_{\mathrm{1个}/\mathrm{2个}}\to 6p_{\mathrm{1个}/\mathrm{2个}，3/\mathrm{2个}}，5d_{3/\mathrm{2个}，5/\mathrm{2个}}$确定过渡。找到了一个可见的调出波长480.658（18）nm。可以在此调出波长上进行高精度测量，以确定振荡器的振子强度与振子强度的比值。$6s_{\mathrm{1个}/\mathrm{2个}}\to 6p_{\mathrm{1个}/\mathrm{2个}，3/\mathrm{2个}}$过渡。另外，我们建议在魔术波长上的测量值对应于$6s_{\mathrm{1个}/\mathrm{2个}}\to 5d_{3/\mathrm{2个}，5/\mathrm{2个}}$ 过渡可以用来确定振荡器的振荡器强度。 $5d_{5/\mathrm{2个}}\to 4F_{7/\mathrm{2个}}$ 和 $5d_{3/\mathrm{2个}}\to 4F_{5/\mathrm{2个}}$ 跃迁，而对于416 nm附近的魔术波长的测量 $6s_{\mathrm{1个}/\mathrm{2个}}\to 6p_{3/\mathrm{2个}}$ 过渡可以用来确定振荡器的强度比。 $6p_{3/\mathrm{2个}}\to 6d_{3/\mathrm{2个}，5/\mathrm{2个}}$ 过渡。