In this paper, we present the tune-out and magic wavelengths of the Mg${}^{+}$, Ca${}^{+}$, Sr${}^{+}$ and Ba${}^{+}$ alkaline earth-metal ions by determining dynamic E1 polarizabilities. Furthermore, we have evaluated the electric quadrupole (E2) matrix elements of a large number of forbidden transitions using an all-order relativistic many-body method and compare them with the previously reported values for a few selective transitions. Compilation of both the E1 and E2 transition matrix elements, will now provide a more complete knowledge about the transition properties of the considered singly charged alkaline earth-metal ions. Similarly, the listed precise values of tune-out and magic wavelengths due to the dominant E1 polarizabilities can be helpful to conduct experiments using the above ions with reduced systematics. Therefore, all these data will be immensely useful for various applications for carrying out the high-precision experiments and laboratory simulations in atomic physics, and interpreting transition lines in the astrophysical observations. This work is a continuation of our earlier reported data on the electric dipole (E1) matrix elements and lifetimes of the metastable states of the alkaline earth ions in Kaur et al. (2021).

在本文中，我们介绍了 Mg 的调出和神奇波长${}^{+}$, 钙${}^{+}$, 锶${}^{+}$ 和巴${}^{+}$通过确定动态 E1 极化率来确定碱土金属离子。此外，我们使用全阶相对论多体方法评估了大量禁止跃迁的电四极 (E2) 矩阵元素，并将它们与先前报道的一些选择性跃迁的值进行了比较。E1 和 E2 过渡矩阵元素的汇编现在将提供关于所考虑的单电荷碱土金属离子的过渡特性的更完整的知识。同样，由于主要的 E1 极化率，列出的调谐和神奇波长的精确值有助于使用上述离子进行实验，并降低系统性。所以，所有这些数据对于在原子物理中进行高精度实验和实验室模拟以及解释天体物理观测中的过渡线的各种应用都非常有用。这项工作是我们之前报道的关于电偶极子 (E1) 矩阵元素和 Kaur 等人中碱土金属离子亚稳态寿命的数据的延续。(2021)。