Isotope shift of atomic spectra is considered as a probe of new interaction between electrons and neutrons in atoms. We employ the method of seeking a breakdown of King's linearity in the isotope shifts of two atomic transitions. In the present work, we evaluate the magnitudes of the nonlinearity using relativistic wave functions and the result is compared with that of nonrelativistic wave functions in our previous work. It turns out that the nonrelativistic calculation underestimates the nonlinearity owing to the new interaction in the mass range of the mediator greater than 1 MeV. Further, we find that the nonlinearity within the standard model of particle physics is significantly magnified by the relativistic effect in the $\text{p}_{1/2}$ state. To get rid of this obstacle in the new physics search, we suggest to avoid $\text{p}_{1/2}$, and use $\text{p}_{3/2}$ instead for example.

中文翻译：

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寻找具有同位素位移的新原子内力的相对论效应

原子光谱的同位素位移被认为是原子中电子和中子之间新相互作用的探针。我们采用了在两个原子跃迁的同位素位移中寻找 King 线性分解的方法。在目前的工作中，我们使用相对论波函数评估非线性的幅度，并将结果与​​我们之前工作中的非相对论波函数的结果进行比较。事实证明，由于介体质量范围内大于 1 MeV 的新相互作用，非相对论计算低估了非线性。此外，我们发现粒子物理标准模型中的非线性被 $\text{p}_{1/2}$ 状态中的相对论效应显着放大。为了在新物理搜索中摆脱这个障碍，我们建议避免$\text{p}_{1/2}$，