无核误差的$H$谱的核预测
Nuclear Predictions for $H$ Spectroscopy without Nuclear Errors
摘要：
原子核结构效应常常会产生不可减少的理论误差，从而阻碍了用精确的原子测量来检验基础理论。我们将新近发展的有效场论工具应用于氢原子，并利用它们证明了（在目前测量的精度范围内）所有的核有限尺寸效应（如电荷半径、Friar矩、核极化率、反冲修正、Zemach矩{ \it etc.}）只有通过两个参数进入原子能，与任何核模型的不确定性无关。由于精确的测量可用于氢中两个以上的原子水平，因此这种观察允许使用精确的原子测量来消除与核矩阵元素相关的理论误差。我们将这种推理应用于实验精度小于10 kHz的7个原子测量，以提供对核尺寸效应的预测，其理论精度不受核建模不确定性的影响，因此远小于1 kHz。此外，这些预测的准确性可以随着原子测量的改进而提高，使得精确的基本测试成为可能，远低于核理论的“不可约”误差下限。
英文摘要：
Nuclear-structure effects often provide an irreducible theory error that prevents using precision atomic measurements to test fundamental theory. We apply newly developed effective field theory tools to Hydrogen atoms, and use them to show that (to the accuracy of present measurements) all nuclear finite-size effects (e.g. the charge radius, Friar moments, nuclear polarizabilities, recoil corrections, Zemach moments {\it etc.}) only enter into atomic energies through exactly two parameters, independent of any nuclear-modelling uncertainties. Since precise measurements are available for more than two atomic levels in Hydrogen, this observation allows the use of precision atomic measurements to eliminate the theory error associated with nuclear matrix elements. We apply this reasoning to the seven atomic measurements whose experimental accuracy is smaller than 10 kHz to provide predictions for nuclear-size effects whose theoretical accuracy is not subject to nuclear-modelling uncertainties and so are much smaller than 1 kHz. Furthermore, the accuracy of these predictions can improve as atomic measurements improve, allowing precision fundamental tests to become possible well below the 'irreducible' error floor of nuclear theory.
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