We use effective field theory to compute the influence of nuclear structure on precision calculations of atomic energy levels. As usual, the EFT’s effective couplings correspond to the various nuclear properties (such as the charge radius, nuclear polarizabilities, Friar and Zemach moments etc.) that dominate its low-energy electromagnetic influence on its surroundings. By extending to spinning nuclei the arguments developed for spinless ones in Burgess, et al. (2018), we use the EFT to show – to any fixed order in $Z\alpha$ (where $Z$ is the atomic number and $\alpha$ the fine-structure constant) and the ratio of nuclear to atomic size – that nuclear properties actually contribute to electronic energies through fewer parameters than the number of these effective nuclear couplings naively suggests. Our result is derived using a position-space method for matching effective parameters to nuclear properties in the EFT, that more efficiently exploits the simplicity of the small-nucleus limit in atomic systems. By showing that precision calculations of atomic spectra depend on fewer nuclear uncertainties than naively expected, this observation allows the construction of many nucleus-independent combinations of atomic energy differences whose measurement can be used to test fundamental physics (such as the predictions of QED) because their theoretical uncertainties are not limited by the accuracy of nuclear calculations. We provide several simple examples of such nucleus-free predictions for Hydrogen-like atoms.

我们使用有效场论来计算核结构对原子能级精度计算的影响。像往常一样，EFT的有效耦合对应于控制其对周围环境的低能电磁影响的各种核特性（例如电荷半径，核极化率，Friar和Zemach矩等）。通过扩展到旋转核，Burgess等人提出了无旋转核的论点。（2018），我们使用电子转帐显示–以任何固定顺序显示$ž\alpha$ （在哪里 $ž$ 是原子序数， $\alpha$精细结构常数）和核与原子尺寸的比率–核性质实际上通过比这些天真的有效核耦合数少的参数而对电子能量有贡献。我们的结果是使用位置空间方法得出的，该方法用于将有效参数与EFT中的核特性进行匹配，从而更有效地利用原子系统中小核子极限的简单性。通过显示原子光谱的精确计算所依赖的核不确定性比天真的预期要少，该观察结果允许构造许多原子核独立的原子能差组合，其测量结果可用于测试基本物理学（例如QED的预测），因为它们的理论不确定性不受核计算精度的限制。我们提供了几个类似氢原子的无核预测的简单例子。