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 mα7 ln(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.
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
Key words
hydrogen molecular ions/hyperfine structure/quantum electrodynamic(QED)corrections/spin-orbit and spin-spin interactions
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