The tune‐out and magic wavelengths (TMWs) for the hydrogenlike and screened‐hydrogenlike atoms (Z = 1‐8) are calculated using a variational method. The first three tune‐out wavelengths for each of the nS (n = 1, 2, 3) states and the first three magic wavelengths for each of the 1S‐nS (n = 2, 3) transitions of the hydrogenlike atoms in terms of nuclear charge Z, and the first TMWs for the above mentioned states or transitions of the screened‐hydrogenlike atoms in terms of the screening parameter μ and Z are presented. All the results for the TMWs are reported for the first time in the literature except the magic wavelengths for the hydrogen atom. The magic wavelengths for hydrogen atom are in agreement with the available data. The precise estimation of the TMWs would be helpful for the design of the ion‐trapping experiment of the hydrogenic systems. Our study is expected to be useful for the measurements of the hydrogenic 1S‐2S and 1S‐3S transitions spectroscopy for the improved accuracy.

中文翻译：

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类氢原子和筛选出的类氢原子的调谐波长和魔术波长

类氢原子和筛分类氢原子（Z = 1-8）的调出和魔幻波长（TMW）使用变分方法计算。类氢原子的每个n S（n = 1，2，3）状态的前三个调出波长和每个1 S -n S（n = 2，3）跃迁的前三个魔术波长核电荷Z的形式，以及上述状态或以筛选参数μ形式筛选的类氢原子的跃迁的第一个TMWs 和Z被提出。除氢原子的魔幻波长外，所有有关TMWs的结果均首次在文献中报道。氢原子的魔幻波长与可用数据一致。TMWs的精确估算将有助于设计氢气系统的离子阱实验。预期我们的研究将对氢1 S ‐ 2 S和1 S ‐ 3 S跃迁光谱的测量有用，以提高准确性。