The problem of the proton charge radius, its correlation with the Rydberg constant, difficulties in determination of the Rydberg constant using hydrogen atom spectroscopy, and redetermination of fundamental constants in the new CODATA18 revision are discussed. Theoretical and experimental aspects of precision spectroscopy of the molecular hydrogen ion HD⁺ are considered. It is shown that new experiments allow the Doppler broadening of spectral lines to be eliminated and a relative error of ~10^–11 to be achieved in the transition frequency measurements. A comparison of these experiments and theoretical calculations leads to an unambiguous conclusion that the proton charge radius should be determined from the muonic hydrogen experiment and the Rydberg constant from the \(1S\)–\(2S\) transition in the ordinary hydrogen atom. Only in this case experiment and theory in HD⁺ are in reasonable consent.

中文翻译：

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HD ^+的光谱 ：质子电荷半径和里德堡常数

讨论了质子电荷半径，其与Rydberg常数的相关性，使用氢原子光谱法确定Rydberg常数的困难以及在新的CODATA18修订版中重新确定基本常数的问题。考虑了分子氢离子HD ⁺的精密光谱学的理论和实验方面。结果表明，新的实验可以消除谱线的多普勒加宽现象，相对误差约为10 ^–11在过渡频率测量中要实现。通过对这些实验和理论计算的比较得出一个明确的结论，质子电荷半径应根据离子氢实验确定，而雷德堡常数应根据普通氢原子中的\（1S \）-\（2S \）跃迁确定。只有在这种情况下，HD ⁺中的实验和理论才能得到合理同意。