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通过氢分子离子振转光谱的高精度实验测量和理论计算，可以精确确定基本物理常数，如质子-电子质量比、氘核-电子质量比、里德堡常数、以及质子和氘核的电荷半径。氢分子离子光谱包含丰富的超精细结构，为了从光谱中提取物理信息，我们不仅需要研究振转光谱跃迁理论，还需要研究超精细结构理论。本文回顾了氢分子离子精密光谱的实验和理论研究历程，着重介绍了氢分子离子超精细结构的研究历史和现状。在上世纪的下半叶就有了关于氢分子离子超精细劈裂的领头项Breit-Pauli哈密顿量的理论。随着本世纪初非相对论量子电动力学（NRQED）的发展，氢分子离子超精细结构的高阶修正理论也得到了系统的发展，并于最近应用到H2+和HD+体系中，其中包括mα7ln (α)阶QED修正。对于H2+，超精细结构理论计算经过数十年的发展，可以与上世纪的相应实验测量符合。对于HD+，最近发现超精细劈裂实验测量和理论计算存在一定的偏差，且无法用mα7阶非对数项的理论误差来解释。理解这种偏差一方面需要更多的实验来相互检验，另一方面对理论也需要进行独立验证并发展mα7阶非对数项理论以进一步减小理论误差。
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关键词:
- 氢分子离子 /
- 超精细结构 /
- 量子电动力学（QED）修正 /
- 自旋-轨道 /
- 自旋-自旋相互作用
The study of high-precision spectroscopy for hydrogen molecular ions enables the determination of fundamental constants, such as the proton-to-electron mass ratio, the deuteron-to-electron mass ratio, the Rydberg constant, and the charge radii of proton and deuteron. This can be accomplished through a combination of high precision experimental measurements and theoretical calculations. The spectroscopy of hydrogen molecular ions reveals abundant hyperfine splittings, necessitating not only an understanding of rovibrational transition frequencies but also a thorough grasp of hyperfine structure theory to extract meaningful physical information from the spectra. This article reviews the history of experiments and theories related to the spectroscopy of hydrogen molecular ions, with a particular focus on the theory of hyperfine structure. As far back as the second half of the last century, the hyperfine structure of hydrogen molecular ions was described by a comprehensive theory based on its leading-order term, known as the Breit-Pauli Hamiltonian. Thanks to the advancements in non-relativistic quantum electrodynamics (NRQED) at the beginning of this century, a systematic development of next-to-leading-order theory for hyperfine structure has been achieved and applied to H2+ and HD+ in recent years, including the establishment of the mα7ln(α) order correction. For the hyperfine structure of H2+, theoretical calculations show good agreement with experimental measurements after decades of work. However, for HD+, discrepancies have been observed between measurements and theoretical predictions that cannot be accounted for by the theoretical uncertainty in the non-logarithmic term of the mα7 order correction. To address this issue, additional experimental measurements are needed for mutual validation, as well as independent tests of the theory, particularly regarding the non-logarithmic term of the mα7 order correction.-
Keywords:
- hydrogen molecular ions /
- hyperfine structure /
- quantum electrodynamic (QED) corrections /
- spin-orbit and spin-spin interactions /
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