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氢分子离子超精细结构理论综述

钟振祥

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氢分子离子超精细结构理论综述

钟振祥
cstr: 32037.14.aps.73.20241101

Review of the hyperfine structure theory of hydrogen molecular ions

Zhong Zhen-Xiang
cstr: 32037.14.aps.73.20241101
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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、里德伯常数、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20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21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$\text{H}_2^+$和$\text{HD}^+$体系中, 其中包括$m\alpha^7\ln(\alpha)$阶量子电动力学(QED)修正. 对于$\text{H}_2^+$, 超精细结构理论计算经过数十年的发展, 可以与20世纪的相应实验测量符合. 对于$\text{HD}^+$, 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$m\alpha^7$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$m\alpha^7$阶非对数项理论以进一步减小理论误差.
    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 $\text{H}_2^+$ and $\text{HD}^+$ in recent years, including the establishment of the $m\alpha^7\ln(\alpha)$ order correction. For the hyperfine structure of $\text{H}_2^+$, 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 $m\alpha^7$ 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 $m\alpha^7$ order correction.
      通信作者: 钟振祥, zxzhong@hainanu.edu.cn
    • 基金项目: 国家自然科学基金重大项目 (批准号: 12393821) 和国家重点研发计划 (批准号: 2021YFA1402103) 资助的课题.
      Corresponding author: Zhong Zhen-Xiang, zxzhong@hainanu.edu.cn
    • Funds: Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 12393821) and the National Key Research and Development Program of China (Grant No. 2021YFA1402103).
    [1]

    刘成卜 2020 量子化学 (北京: 科学出版社) 第98页

    Liu C P 2020 Quantum Chemistry (Beijing: Science Press) p98

    [2]

    曾谨言 2007 量子力学 (第1版) (北京: 科学出版社) 第473页

    Zeng J Y 2007 Quantum Mechanics (Vol. 1) (Beijing: Science Press) p473

    [3]

    Wing W H, Ruff G A, Lamb W E, Spezeski J J 1976 Phys. Rev. Lett. 36 1488Google Scholar

    [4]

    Schiller S, Korobov V 2005 Phys. Rev. A 71 032505Google Scholar

    [5]

    Liu J, Salumbides E J, Hollenstein U, Koelemeij J C J, Eikema K S E, Ubachs W, Merkt F 2009 J. Chem. Phys. 130 174306Google Scholar

    [6]

    Sprecher D, Liu J, Jungen C, Ubachs W, Merkt F 2010 J. Chem. Phys. 133 111102Google Scholar

    [7]

    Cheng C F, Hussels J, Niu M, Bethlem H, Eikema K, Salumbides E, Ubachs W, Beyer M, Hölsch N, Agner J, Merkt F, Tao L G, Hu S M, Jungen C 2018 Phys. Rev. Lett. 121 013001Google Scholar

    [8]

    Tao L G, Liu A W, Pachucki K, Komasa J, Sun Y, Wang J, Hu S M 2018 Phys. Rev. Lett. 120 153001Google Scholar

    [9]

    Liu Q H, Tan Y, Cheng C F, Hu S M 2023 Phys. Chem. Chem. Phys. 25 27914Google Scholar

    [10]

    Wang L M, Yan Z C 2018 Phys. Rev. A 97 060501Google Scholar

    [11]

    Puchalski M, Komasa J, Pachucki K 2020 Phys. Rev. Lett. 125 253001Google Scholar

    [12]

    Blythe P, Roth B, Fröhlich U, Wenz H, Schiller S 2005 Phys. Rev. Lett. 95 183002Google Scholar

    [13]

    Koelemeij J C J, Noom D W E, de Jong D, Haddad M A, Ubachs W 2012 Appl. Phys. B: Lasers Opt. 107 1075Google Scholar

    [14]

    Karr J P, Bielsa F, Valenzuela T, Douillet A, Hilico L, Korobov V I 2007 Can. J. Phys. 85 497

    [15]

    Zhang Y, Zhang Q Y, Bai W L, Ao Z Y, Peng W C, He S G, Tong X 2023 Phys. Rev. A 107 043101Google Scholar

    [16]

    Koelemeij J C J, Roth B, Wicht A, Ernsting I, Schiller S 2007 Phys. Rev. Lett. 98 173002Google Scholar

    [17]

    Alighanbari S, Kortunov I V, Giri G S, Schiller S 2023 Nat. Phys. 19 1263Google Scholar

    [18]

    Biesheuvel J, Karr J P, Hilico L, Eikema K S E, Ubachs W, Koelemeij J C J 2016 Nat. Commun. 7 10385Google Scholar

    [19]

    Korobov V I, Hilico L, Karr J P 2014 Phys. Rev. Lett. 112 103003Google Scholar

    [20]

    Korobov V I, Hilico L, Karr J P 2014 Phys. Rev. A 89 032511Google Scholar

    [21]

    Mohr P J, Taylor B N, Newell D B 2012 Rev. Mod. Phys. 84 1527Google Scholar

    [22]

    Tiesinga E, Mohr P J, Newell D B, Taylor B N 2021 Rev. Mod. Phys. 93 025010Google Scholar

    [23]

    Alighanbari S, Giri G S, Constantin F L, Korobov V I, Schiller S 2020 Nature 581 152Google Scholar

    [24]

    Patra S, Germann M, Karr J P, Haidar M, Hilico L, Korobov V I, Cozijn F M J, Eikema K S E, Ubachs W, Koelemeij J C J 2020 Science 369 1238Google Scholar

    [25]

    Köhler F, Sturm S, Kracke A, Werth G, Quint W, Blaum K 2015 J. Phys. B: At., Mol. Opt. Phys. 48 144032Google Scholar

    [26]

    Rau S, Heiße F, Köhler-Langes F, Sasidharan S, Haas R, Renisch D, Düllmann C E, Quint W, Sturm S, Blaum K 2020 Nature 585 43Google Scholar

    [27]

    Korobov V I 2000 Phys. Rev. A 61 064503Google Scholar

    [28]

    Yan Z C, Zhang J Y, Li Y 2003 Phys. Rev. A 67 062504Google Scholar

    [29]

    Li H, Wu J, Zhou B L, Zhu J M, Yan Z C 2007 Phys. Rev. A 75 012504Google Scholar

    [30]

    Zhong Z X, Yan Z C, Shi T Y 2009 Phys. Rev. A 79 064502Google Scholar

    [31]

    Zhong Z X, Zhang P P, Yan Z C, Shi T Y 2012 Phys. Rev. A 86 064502Google Scholar

    [32]

    Zhang P P, Zhong Z X, Yan Z C, Shi T Y 2016 Phys. Rev. A 93 032507Google Scholar

    [33]

    Aznabayev D T, Bekbaev A K, Korobov V I 2019 Phys. Rev. A 99 012501Google Scholar

    [34]

    Korobov V I 2004 Phys. Rev. A 70 012505Google Scholar

    [35]

    Korobov V I 2006 Phys. Rev. A 73 024502Google Scholar

    [36]

    Korobov V I 2012 Phys. Rev. A 85 042514Google Scholar

    [37]

    Korobov V I, Zhong Z X 2012 Phys. Rev. A 86 044501Google Scholar

    [38]

    Zhong Z X, Yan Z C, Shi T Y 2013 Phys. Rev. A 88 052520Google Scholar

    [39]

    Korobov V I, Tsogbayar T 2007 J. Phys. B: At., Mol. Opt. Phys. 40 2661Google Scholar

    [40]

    Korobov V I, Hilico L, Karr J P 2017 Phys. Rev. Lett. 118 233001Google Scholar

    [41]

    Korobov V I, Karr J P 2021 Phys. Rev. A 104 032806Google Scholar

    [42]

    Koelemeij J C J 2022 Mol. Phys. 120 e2058637Google Scholar

    [43]

    Dalgarno A, Patterson T N, B S W 1960 Proc. R. Soc. A 259 100

    [44]

    Babb J F, Dalgarno A 1991 Phys. Rev. Lett. 66 880Google Scholar

    [45]

    Babb J F, Dalgarno A 1992 Phys. Rev. A 46 R5317Google Scholar

    [46]

    Babb J F 1995 Phys. Rev. Lett. 75 4377Google Scholar

    [47]

    Bakalov D, Korobov V I, Schiller S 2006 Phys. Rev. Lett. 97 243001Google Scholar

    [48]

    Korobov V I, Karr J P, Haidar M, Zhong Z X 2020 Phys. Rev. A 102 022804Google Scholar

    [49]

    Karr J P, Haidar M, Hilico L, Zhong Z X, Korobov V I 2020 Phys. Rev. A 102 052827Google Scholar

    [50]

    Haidar M, Korobov V I, Hilico L, Karr J P 2022 Phys. Rev. A 106 042815Google Scholar

    [51]

    Korobov V I, Hilico L, Karr J P 2006 Phys. Rev. A 74 040502Google Scholar

    [52]

    Jefferts K B 1969 Phys. Rev. Lett. 23 1476Google Scholar

    [53]

    Fu Z W, Hessels E A, Lundeen S R 1992 Phys. Rev. A 46 R5313Google Scholar

    [54]

    Osterwalder A, Wüest A, Merkt F, Jungen C 2004 J. Chem. Phys. 121 11810Google Scholar

    [55]

    Luke S K 1969 Astrophys. J. 156 761Google Scholar

    [56]

    McEachran R, Veenstra C, Cohen M 1978 Chem. Phys. Lett. 59 275Google Scholar

    [57]

    Korobov V I, Hilico L, Karr J P 2009 Phys. Rev. A 79 012501Google Scholar

    [58]

    Korobov V I, Koelemeij J C J, Hilico L, Karr J P 2016 Phys. Rev. Lett. 116 053003Google Scholar

    [59]

    Haidar M, Korobov V I, Hilico L, Karr J P 2022 Phys. Rev. A 106 022816Google Scholar

    [60]

    Babb J F 1998 Current Topics in Physics (Vol. 2) (Singapore: World Scientific) pp531–540

    [61]

    Zhang P P, Zhong Z X, Yan Z C 2013 Phys. Rev. A 88 032519Google Scholar

    [62]

    Korobov V I 2006 Phys. Rev. A 74 052506Google Scholar

    [63]

    Alighanbari S, Hansen M G, Korobov V I, Schiller S 2018 Nat. Phys. 14 555Google Scholar

    [64]

    Kortunov I V, Alighanbari S, Hansen M G, Giri G S, Korobov V I, Schiller S 2021 Nat. Phys. 17 569Google Scholar

    [65]

    Schenkel M R, Alighanbari S, Schiller S 2024 Nat. Phys. 20 383Google Scholar

    [66]

    Mohr P J, Newell D B, Taylor B N 2016 Rev. Mod. Phys. 88 035009Google Scholar

    [67]

    Germann M, Patra S, Karr J P, Hilico L, Korobov V I, Salumbides E J, Eikema K S E, Ubachs W, Koelemeij J C J 2021 Phys. Rev. Res. 3 L022028Google Scholar

    [68]

    Heiße F, Köhler-Langes F, Rau S, Hou J, Junck S, Kracke A, Mooser A, Quint W, Ulmer S, Werth G, Blaum K, Sturm S 2017 Phys. Rev. Lett. 119 033001Google Scholar

    [69]

    Stone A P 1961 Proc. Phys. Soc., London 77 786Google Scholar

    [70]

    Stone A P 1963 Proc. Phys. Soc., London 81 868Google Scholar

    [71]

    Volkov S 2018 Phys. Rev. D 98 076018Google Scholar

    [72]

    Zhong Z X, Zhou W P, Mei X S 2018 Phys. Rev. A 98 032502Google Scholar

    [73]

    Haidar M, Zhong Z X, Korobov V I, Karr J P 2020 Phys. Rev. A 101 022501Google Scholar

    [74]

    Bethe H A, Salpeter E E 1957 Quantum Mechanics of One- and Two-Electron Atoms (New York, NY: Springer Berlin Heidelberg) pp109–111

    [75]

    Kinoshita T 1990 Quantum Electrodynamics (Singapore: World Scientific) pp580–586

    [76]

    Kinoshita T, Nio M 1996 Phys. Rev. D 53 4909Google Scholar

    [77]

    Eides M I, Grotch H, Shelyuto V A 2007 Theory of Light Hydrogenic Bound States (Berlin: Springer Berlin Heidelberg) pp217–231

    [78]

    Mondéjar J, Piclum J H, Czarnecki A 2010 Phys. Rev. A 81 062511Google Scholar

    [79]

    Carlson C E, Nazaryan V, Griffioen K 2008 Phys. Rev. A 78 022517Google Scholar

    [80]

    Zemach A C 1956 Phys. Rev. 104 1771Google Scholar

    [81]

    Karshenboim S G 1997 Phys. Lett. A 225 97Google Scholar

    [82]

    Faustov R, Martynenko A 2002 Eur. Phys. J. C 24 281Google Scholar

    [83]

    Friar J L, Payne G L 2005 Phys. Rev. C 72 014002Google Scholar

    [84]

    Friar J, Sick I 2004 Phys. Lett. B 579 285Google Scholar

    [85]

    Bodwin G T, Yennie D R 1988 Phys. Rev. D 37 498

    [86]

    Karshenboim S G 2005 Phys. Rep. 422 1Google Scholar

    [87]

    Yan Z C, Drake G W F 1994 Can. J. Phys. 72 822Google Scholar

    [88]

    Yan Z C, Drake G 1996 Chem. Phys. Lett. 259 96Google Scholar

    [89]

    Korobov V I 2002 J. Phys. B: At., Mol. Opt. Phys. 35 1959Google Scholar

    [90]

    Harris F E, Frolov A M, Smith V H 2004 J. Chem. Phys. 121 6323Google Scholar

    [91]

    Dalgarno A, Lewis J T 1955 Proc. R. Soc. A 233 70

    [92]

    Lewis M L, Serafino P H 1978 Phys. Rev. A 18 867Google Scholar

    [93]

    Karr J P, Bielsa F, Douillet A, Gutierrez J P, Korobov V I, Hilico L 2008 Phys. Rev. A 77 063410Google Scholar

    [94]

    Menasian S C, Dehmelt H G 1973 Bull. Am. Phys. Soc. 18 408

    [95]

    Varshalovich D A, Moskalev A N, Khersonskii V K 1988 Quantum Theory of Angular Momentum (Singapore: World Scientific) pp79,484

    [96]

    Lindgren I, Morrison J 1982 Atomic Many-Body Theory (Berlin: Springer Berlin Heidelberg) pp91,93

  • 图 1  氢分子离子$ \text{H}_2^+ $振转态$ (v, L=1, 3) $的超精细劈裂示意图

    Fig. 1.  Hyperfine structure of hydrogen molecular ion $ \text{H}_2^+ $ rovibrational states $ (v, L=1, 3) $.

    图 2  氢分子离子HD+振转态$ (v, L\geqslant2) $的超精细劈裂示意图

    Fig. 2.  Hyperfine structure of hydrogen molecular ion HD+ rovibrational states $ (v, L\geqslant2) $.

    表 1  通过氢分子离子精密光谱测定质子-电子质量比

    Table 1.  Determination of the proton-electron mass ratio through precision spectroscopy of hydrogen molecular ions.

    年份 作者(研究机构) 跃迁$ (v, L)\rightarrow (v', L') $ 所测频率/MHz 理论频率/MHz 质量比
    HD+
    2007 Koelemeij
    et al. (HHU)[16]
    $ (0, 2)\rightarrow (4, 3) $ 214978560.6(0.5) 214978560.88(7)[62]
    2016 Biesheuvel
    et al. (VU)[18]
    $ (0, 2)\rightarrow (8, 3) $ 383407177.38(41) 383407177.150(15)[20] 1836.1526695(53)
    2018 Alighanbari
    et al. (HHU)[63]
    $ (0, 0)_{J=2}\rightarrow (0, 1)_{J'=3} $ 1314935.8280(4)(3)a 1314935.8273(10)b 1836.1526739(24)
    2020 Alighanbari
    et al. (HHU)[23]
    $ (0, 0)\rightarrow (0, 1) $ 1314925.752910(17) 1314925.752896(18)(61)b,c 1836.152673449(24)
    (25)(13)d
    2020 Patra
    et al. (VU)[24]
    $ (4, 2)\rightarrow (9, 3) $ 415264925.5005(12) 415264925.4962(74)b 1836.152673406(38)
    2021 Kortunov
    et al. (HHU)[64]
    $ (0, 0)\rightarrow (1, 1) $ 58605052.16424(16)(85)e 58605052.1639(5)(13)b,c 1836.152673384(11)
    (31)(55)(12)f
    2023 Alighanbari
    et al. (HHU)[17]
    $ (0, 0)\rightarrow (5, 1) $ 259762971.0512(6)
    (0.00004)e
    259762971.05091[41] 1836.152673463
    (10)(35)(1)(6)f
    $ \text{H}_2^+ $
    2024 Schenkel
    et al. (HHU)[65]
    $ (1, 0)\rightarrow (3, 2) $ 124487032.7(1.5) 124487032.45(6) [40] 1836.152665(53)
    CODATA推荐值
    2014 CODATA group[66] CODATA 2014 1836.15267389(17)
    2018 CODATA group[22] CODATA 2018 1836.15267343(11)
    2022 CODATA groupg CODATA 2022 1836.152673426(32)
    注: a 第一个误差为统计误差, 第二个为系统误差; b 来自Korobov, 是该实验文章的共同作者; c 第一个误差来自理论, 第二个来自CODATAk 2018基本物理常数; d 第一个误差来自实验, 第二个来自理论, 第三个来自CODATAk 2018基本物理常数; e 第一个误差来自实验, 第二个来自超精细结构理论; f 第一个误差来自实验, 第二个来自QED理论, 第三个来自超精细结构理论, 第四个来自CODATA 2018基本物理常数; g 来自NIST的基本物理常数表https://physics.nist.gov/cuu/Constants/index.html.
    下载: 导出CSV

    表 2  基于HD+中不同的振转跃迁测量定出的质量比组合$ \mathcal{R}$之比较[17]

    Table 2.  Comparison of the combined mass ratio $\mathcal{R}$ determined from the measurements of different rovibrational transitions in HD+ [17].

    年份 振转跃迁 $ \mathcal{R} $ 相对误差 引文
    2020 $ (0, 0)\rightarrow (0, 1) $ 1223.899228658(23) $ 1.9\times10^{-11} $ HHU[23]
    2020 $ (0, 3)\rightarrow (9, 3) $ 1223.899228735(28) $ 2.3\times10^{-11} $ VU[67]
    2021 $ (0, 0)\rightarrow (0, 1) $ 1223.899228711(22) $ 1.8\times10^{-11} $ HHU[64]
    2023 $ (0, 0)\rightarrow (5, 1) $ 1223.899228720(25) $ 2.0\times10^{-11} $ HHU[17]
    1223.899228642(37) $ 3.0\times10^{-11} $ 潘宁阱[25,26,68]
    1223.899228723(56) $ 4.8\times10^{-11} $ CODATA 2018[22]
    下载: 导出CSV

    表 3  $ \text{H}_2^+ $等效哈密顿量(9)中的超精细劈裂系数, 单位为kHz. 每个振转态的第一行是理论值, 随后是实验值. d1d2需要乘以因子$ 3(2 L-1)(2 L+3) $才能与文献[51]中的值匹配

    Table 3.  The hyperfine splitting coefficients in the effective Hamiltonian of $ \text{H}_2^+ $, as appeared in Eq. (9), in units of kHz. The first line of each rovibrational state is for the theoretical values, followed by the experimental ones. d1 and d2 need to be multiplied by $ 3(2 L-1)(2 L+3) $ to match the values in Ref. [51].

    L v bF ce cI d1 d2
    1 0 922 930.1(9)a 42 417.32(15)b –41.673d 8566.174(17)b –19.837d
    922 940(20)[53] 42 348(29)[53] –3(15)[53] 8550.6(1.7)[53]
    923.16(21)[54]
    1 4 836 728.7(8)a 32 655.32(11)b –35.826c 6537.386(13)b –16.414c
    836 729.2(8)[52] 32 636[52] –34(1.5)e 6535.6[52]
    1 5 819 226.7(8)a 30 437.80(11)b –34.148c 6080.400(12)b –15.531c
    819 227.3(8)[52] 30 421[52] –33(1.5)e 6078.7[52]
    1 6 803 174.5(7)a 28 280.95(10)b –32.385c 5637.627(11)b –14.633c
    803 175.1(8)[52] 28 266[52] –31(1.5)e 5636.0[52]
    1 7 788 507.5(7)a
    788 507.9(8)[52] 26 156[52] –29(1.5)e 5204.9[52]
    1 8 775 171.2(7)a
    775 172.0(8)[52] 24 080[52] –27(1.5)e 4782.2[52]
    注: a 包含高阶修正的贡献, 来自文献[49]; b 包含高阶修正的贡献, 来自文献[59]; c 仅计算领头项$ m\alpha^4 $阶的Breit-Pauli哈密顿量的贡献, 误差为相应值乘以$ \alpha^2\approx5.3\times10^{-5} $, 来自文献[51]; d 仅计算领头项$ m\alpha^4 $阶的Breit-Pauli哈密顿量的贡献, 误差为相应值乘以$ \alpha^2\approx5.3\times10^{-5} $, 来自文献[30]; e 由Babb于1995年重新拟合实验数据获得, 来自文献[46].
    下载: 导出CSV

    表 4  $ \text{H}_2^+ $在特定的转动量子数L下, 可能具有的不同总自旋量子数F和总角动量量子数J的值. n是相应的超精细劈裂态的数目, 见文献[93]表I

    Table 4.  Possible values of different total spin quantum number F and total angular momentum quantum number J that $ \text{H}_2^+ $ may have under specific rotational quantum number L. n is the number of corresponding hyperfine splitting states, see Table I in Ref. [93].

    L se I F J n
    0 1/2 0 1/2 1/2 1
    1 1/2 1 1/2 1/2, 3/2 5
    3/2 1/2, 3/2, 5/2
    1/2 0 1/2 $ L-1/2, L+1/2 $ 2
    1/2 1 1/2 $ L-1/2, L+1/2 $ 6
    3/2 $ L-3/2, L-1/2, L+1/2, L+3/2 $
    下载: 导出CSV

    表 5  $ \text{H}_2^+ $在振转态$ (v=4—8, L=1) $下, 超精细劈裂态$ (F, J) $之间的跃迁频率理论和实验结果比较, 单位为MHz. 第一行是Korobov等[58]计算的理论值; 第二行中的实验值来源于文献[52]. 对于$ v=4—6 $的跃迁$ (1/2, 3/2)—(1/2, 1/2) $, 理论值已于2022年得到更新[59], 相应的实验值取自引文[94]

    Table 5.  Comparison of theoretical and experimental transition frequencies between hyperfine states of $ \text{H}_2^+ $ in rovibrational state $ (v=4—8, L=1) $, in MHz. The first row shows the theoretical values calculated by Korobov et al.[58]; the experimental values in the second row are from the Ref. [52]. For transitions $ (F, J)=(1/2, 3/2)—(1/2, 1/2) $ for $ v=4—6 $, the theoretical values were updated in 2022[59], and the corresponding experimental values are cited from Ref. [94].

    v $ \left(\dfrac{3}{2}, \dfrac{3}{2}\right)—\left(\dfrac{3}{2}, \dfrac{5}{2}\right) $ $ \left(\dfrac{3}{2}, \dfrac{3}{2}\right)—\left(\dfrac{3}{2}, \dfrac{1}{2}\right) $ $ \left(\dfrac{1}{2}, \dfrac{3}{2}\right)—\left(\dfrac{1}{2}, \dfrac{1}{2}\right) $ $ \left(\dfrac{3}{2}, \dfrac{5}{2}\right)—\left(\dfrac{1}{2}, \dfrac{3}{2}\right) $ $ \left(\dfrac{3}{2}, \dfrac{3}{2}\right)—\left(\dfrac{1}{2}, \dfrac{3}{2}\right) $
    4 5.7202 74.0249 15.371316(56)a 1270.5504 1276.2706
    5.721 74.027 15.371407(2)b 1270.550 1276.271
    5 5.2576 68.9314 14.381453(52)a 1243.2508 1248.5084
    5.258 68.933 14.381513(2)b 1243.251 1248.509
    6 4.8168 63.9879 13.413397(48)a 1218.1538 1222.9706
    4.817 63.989 13.413460(2)b 1218.154 1222.971
    7 4.3948 59.1626 12.4607 1195.1558 1199.5506
    4.395 59.164 12.461 1195.156 1199.551
    8 3.9892 54.4238 11.5172 1174.1683 1178.1576
    3.989 54.425 11.517 1174.169 1178.159
    注: a 来自引文[59]的理论值; b 来自引文[94]的实验值.
    下载: 导出CSV

    表 6  实验涉及的HD+振转态超精细劈裂系数, 单位kHz. 振转态(0, 1)的系数E1, E6E7实验值 (第二个条目) 由Haidar等[50]从实验数据[23]中提取

    Table 6.  Hyperfine coefficients for rovibrational states of HD+, in kHz. Experimental values (the second entry) of coefficients E1, E6 and E7 for rovibrational state (0, 1) were extracted by Haidar et al. in Ref. [50] from experimental data[23].

    (v, L) (0, 0) (0, 1) (1, 1) (6, 1) (0, 3) (9, 3)
    E1[50] 31985.41(12) 30280.74(11) 22643.89(8) 31628.10(11) 18270.85(6)
    31984.9(1)
    E2[47] –31.345(8) –30.463(8) –25.356(7) –30.832(8) –21.304(6)
    E3[47] –4.809(1) –4.664(1) –3.850(1)a –4.733(1) –3.225(1)
    E4[49] 925394.2(9) 924567.7(9) 903366.5(8) 816716.1(8) 920480.0(9) 775706.1(7)
    E5[49] 142287.56(8) 142160.67(8) 138910.27(8) 125655.51(7) 141533.07(8) 119431.93(7)
    E6[50] 8611.299(18) 8136.859(17) 6027.925(13) 948.5421(20) 538.9991(12)
    8611.17(5)
    E7[50] 1321.7960(28) 1248.9624(27) 925.2072(20) 145.5969(3) 82.7250(2)
    1321.72(4)
    E8[47] –3.057(1) –2.945(1) –2.369(1)a –0.335 –0.219
    E9[50] 5.660(1) 5.653(1) 5.204(1)a 0.612 0.501
    注: a 未见于文献中, 由本文作者计算.
    下载: 导出CSV

    表 7  HD+振转态(v, L)可能具有的总自旋角动量F和总角动量J的值

    Table 7.  Possible total spin angular momentum F and total angular momentum J values for HD+ rotational state (v, L).

    L F S J
    L 0 1 $ L-1, L, L+1 $
    1 0 L
    1 $ L-1, L, L+1 $
    2 $ L-2, L-1, L, L+1, L+2 $
    下载: 导出CSV

    表 8  HD+超精细劈裂跃迁频率fij的理论值和实验值比较, 单位kHz. $ f_{ij}=f_j-f_i $, 这里fi是振转跃迁$ (v, L)\rightarrow (v', L') $光谱的第i个超精细劈裂峰, 参考实验文献[23, 24, 64]. $ \varDelta_{ij}=f_{ij}^\text{exp}-f_{ij}^\text{theor} $是实验与理论之间的偏差, $ \sigma_{\mathrm{c}}=\{[u(f_{ij}^\text{exp})]^2+ $$ [u(f_{ij}^\text{theor})]^2\}^{1/2} $是实验与理论值之间的标准误差, 这里$ u(f) $表示f的相对误差

    Table 8.  Comparison between experimental and theoretical results for some hyperfine intervals, in kHz. $ f_{ij}=f_j-f_i $, where fi is the i-th hyperfine component of rovibrational transition $ (v, L)\rightarrow (v', L') $, see Refs. [23, 24, 64]. $ \varDelta_{ij}=f_{ij}^\text{exp}- $$ f_{ij}^\text{theor} $ is the deviation between experimental and theoretical frequencies, and $ \sigma_{\mathrm{c}}=\{[u(f_{ij}^\text{exp})]^2+[u(f_{ij}^\text{theor})]^2\}^{1/2} $ is the standard deviation, with $ u(f) $ being the relative uncertainty in f.

    i $ FSJ\rightarrow F'S'J' $ j $ FSJ\rightarrow F'S'J' $ $ f_{ij}^\text{exp} $ $ f_{ij}^\text{theor} $[50] $ \varDelta_{ij} $ $ \varDelta_{ij}/\sigma_c $
    $ (v=0, L=0)\longrightarrow(v'=0, L'=1) $ $ f_{ij}^\text{exp} $来自引文[23]
    12 122→121 14 100→101 2434.211(75) 2434.465(23) –0.254 –3.2
    12 122→121 16 011→012 31074.752(43) 31074.102(56) –0.350 –4.9
    12 122→121 19 122→123 43283.419(54) 43284.10(12) –0.677 –5.0
    12 122→121 20 122→122 44944.338(72) 44945.289(64) –0.951 –9.8
    12 122→121 21 111→112 44996.486(61) 44997.14(11) –0.652 –5.3
    14 100→101 16 011→012 6939.541(66) 6939.636(42) –0.095 –1.2
    14 100→101 19 122→123 1949.208(47) 1948.63(11) –0.423 –3.2
    14 100→101 20 122→122 20810.127(88) 20810.823(63) –0.696 –6.5
    14 100→101 21 111→112 20862.275(79) 20862.673(91) –0.398 –3.3
    16 011→012 19 122→123 12209.667(41) 12209.994(72) –0.327 –4.0
    16 011→012 20 122→122 13870.586(62) 13871.187(42) –0.601 –7.9
    16 011→012 21 111→112 13922.734(49) 13923.037(51) –0.303 –4.3
    19 122→123 20 122→122 1660.919(70) 1661.19(10) –0.274 –2.2
    19 122→123 21 111→112 1713.067(59) 1713.042(25) 0.025 0.4
    20 122→122 21 111→112 52.148(6) 51.850(75) 0.298 2.8
    $ (v=0, L=0)\longrightarrow(v'=1, L'=1) $ $ f_{ij}^\text{exp} $来自引文[64]
    12 122→121 16 122→123 41294.06(32) 41293.66(12) 0.40 1.2
    $ (v=0, L30)\longrightarrow(v'=9, L'=3) $ $ f_{ij}^\text{exp} $来自引文[24]
    $ F=0 $ 014→014 $ F=1 $ 125→125 178254.4(9) 178245.89(28) 8.5 9.0
    下载: 导出CSV
  • [1]

    刘成卜 2020 量子化学 (北京: 科学出版社) 第98页

    Liu C P 2020 Quantum Chemistry (Beijing: Science Press) p98

    [2]

    曾谨言 2007 量子力学 (第1版) (北京: 科学出版社) 第473页

    Zeng J Y 2007 Quantum Mechanics (Vol. 1) (Beijing: Science Press) p473

    [3]

    Wing W H, Ruff G A, Lamb W E, Spezeski J J 1976 Phys. Rev. Lett. 36 1488Google Scholar

    [4]

    Schiller S, Korobov V 2005 Phys. Rev. A 71 032505Google Scholar

    [5]

    Liu J, Salumbides E J, Hollenstein U, Koelemeij J C J, Eikema K S E, Ubachs W, Merkt F 2009 J. Chem. Phys. 130 174306Google Scholar

    [6]

    Sprecher D, Liu J, Jungen C, Ubachs W, Merkt F 2010 J. Chem. Phys. 133 111102Google Scholar

    [7]

    Cheng C F, Hussels J, Niu M, Bethlem H, Eikema K, Salumbides E, Ubachs W, Beyer M, Hölsch N, Agner J, Merkt F, Tao L G, Hu S M, Jungen C 2018 Phys. Rev. Lett. 121 013001Google Scholar

    [8]

    Tao L G, Liu A W, Pachucki K, Komasa J, Sun Y, Wang J, Hu S M 2018 Phys. Rev. Lett. 120 153001Google Scholar

    [9]

    Liu Q H, Tan Y, Cheng C F, Hu S M 2023 Phys. Chem. Chem. Phys. 25 27914Google Scholar

    [10]

    Wang L M, Yan Z C 2018 Phys. Rev. A 97 060501Google Scholar

    [11]

    Puchalski M, Komasa J, Pachucki K 2020 Phys. Rev. Lett. 125 253001Google Scholar

    [12]

    Blythe P, Roth B, Fröhlich U, Wenz H, Schiller S 2005 Phys. Rev. Lett. 95 183002Google Scholar

    [13]

    Koelemeij J C J, Noom D W E, de Jong D, Haddad M A, Ubachs W 2012 Appl. Phys. B: Lasers Opt. 107 1075Google Scholar

    [14]

    Karr J P, Bielsa F, Valenzuela T, Douillet A, Hilico L, Korobov V I 2007 Can. J. Phys. 85 497

    [15]

    Zhang Y, Zhang Q Y, Bai W L, Ao Z Y, Peng W C, He S G, Tong X 2023 Phys. Rev. A 107 043101Google Scholar

    [16]

    Koelemeij J C J, Roth B, Wicht A, Ernsting I, Schiller S 2007 Phys. Rev. Lett. 98 173002Google Scholar

    [17]

    Alighanbari S, Kortunov I V, Giri G S, Schiller S 2023 Nat. Phys. 19 1263Google Scholar

    [18]

    Biesheuvel J, Karr J P, Hilico L, Eikema K S E, Ubachs W, Koelemeij J C J 2016 Nat. Commun. 7 10385Google Scholar

    [19]

    Korobov V I, Hilico L, Karr J P 2014 Phys. Rev. Lett. 112 103003Google Scholar

    [20]

    Korobov V I, Hilico L, Karr J P 2014 Phys. Rev. A 89 032511Google Scholar

    [21]

    Mohr P J, Taylor B N, Newell D B 2012 Rev. Mod. Phys. 84 1527Google Scholar

    [22]

    Tiesinga E, Mohr P J, Newell D B, Taylor B N 2021 Rev. Mod. Phys. 93 025010Google Scholar

    [23]

    Alighanbari S, Giri G S, Constantin F L, Korobov V I, Schiller S 2020 Nature 581 152Google Scholar

    [24]

    Patra S, Germann M, Karr J P, Haidar M, Hilico L, Korobov V I, Cozijn F M J, Eikema K S E, Ubachs W, Koelemeij J C J 2020 Science 369 1238Google Scholar

    [25]

    Köhler F, Sturm S, Kracke A, Werth G, Quint W, Blaum K 2015 J. Phys. B: At., Mol. Opt. Phys. 48 144032Google Scholar

    [26]

    Rau S, Heiße F, Köhler-Langes F, Sasidharan S, Haas R, Renisch D, Düllmann C E, Quint W, Sturm S, Blaum K 2020 Nature 585 43Google Scholar

    [27]

    Korobov V I 2000 Phys. Rev. A 61 064503Google Scholar

    [28]

    Yan Z C, Zhang J Y, Li Y 2003 Phys. Rev. A 67 062504Google Scholar

    [29]

    Li H, Wu J, Zhou B L, Zhu J M, Yan Z C 2007 Phys. Rev. A 75 012504Google Scholar

    [30]

    Zhong Z X, Yan Z C, Shi T Y 2009 Phys. Rev. A 79 064502Google Scholar

    [31]

    Zhong Z X, Zhang P P, Yan Z C, Shi T Y 2012 Phys. Rev. A 86 064502Google Scholar

    [32]

    Zhang P P, Zhong Z X, Yan Z C, Shi T Y 2016 Phys. Rev. A 93 032507Google Scholar

    [33]

    Aznabayev D T, Bekbaev A K, Korobov V I 2019 Phys. Rev. A 99 012501Google Scholar

    [34]

    Korobov V I 2004 Phys. Rev. A 70 012505Google Scholar

    [35]

    Korobov V I 2006 Phys. Rev. A 73 024502Google Scholar

    [36]

    Korobov V I 2012 Phys. Rev. A 85 042514Google Scholar

    [37]

    Korobov V I, Zhong Z X 2012 Phys. Rev. A 86 044501Google Scholar

    [38]

    Zhong Z X, Yan Z C, Shi T Y 2013 Phys. Rev. A 88 052520Google Scholar

    [39]

    Korobov V I, Tsogbayar T 2007 J. Phys. B: At., Mol. Opt. Phys. 40 2661Google Scholar

    [40]

    Korobov V I, Hilico L, Karr J P 2017 Phys. Rev. Lett. 118 233001Google Scholar

    [41]

    Korobov V I, Karr J P 2021 Phys. Rev. A 104 032806Google Scholar

    [42]

    Koelemeij J C J 2022 Mol. Phys. 120 e2058637Google Scholar

    [43]

    Dalgarno A, Patterson T N, B S W 1960 Proc. R. Soc. A 259 100

    [44]

    Babb J F, Dalgarno A 1991 Phys. Rev. Lett. 66 880Google Scholar

    [45]

    Babb J F, Dalgarno A 1992 Phys. Rev. A 46 R5317Google Scholar

    [46]

    Babb J F 1995 Phys. Rev. Lett. 75 4377Google Scholar

    [47]

    Bakalov D, Korobov V I, Schiller S 2006 Phys. Rev. Lett. 97 243001Google Scholar

    [48]

    Korobov V I, Karr J P, Haidar M, Zhong Z X 2020 Phys. Rev. A 102 022804Google Scholar

    [49]

    Karr J P, Haidar M, Hilico L, Zhong Z X, Korobov V I 2020 Phys. Rev. A 102 052827Google Scholar

    [50]

    Haidar M, Korobov V I, Hilico L, Karr J P 2022 Phys. Rev. A 106 042815Google Scholar

    [51]

    Korobov V I, Hilico L, Karr J P 2006 Phys. Rev. A 74 040502Google Scholar

    [52]

    Jefferts K B 1969 Phys. Rev. Lett. 23 1476Google Scholar

    [53]

    Fu Z W, Hessels E A, Lundeen S R 1992 Phys. Rev. A 46 R5313Google Scholar

    [54]

    Osterwalder A, Wüest A, Merkt F, Jungen C 2004 J. Chem. Phys. 121 11810Google Scholar

    [55]

    Luke S K 1969 Astrophys. J. 156 761Google Scholar

    [56]

    McEachran R, Veenstra C, Cohen M 1978 Chem. Phys. Lett. 59 275Google Scholar

    [57]

    Korobov V I, Hilico L, Karr J P 2009 Phys. Rev. A 79 012501Google Scholar

    [58]

    Korobov V I, Koelemeij J C J, Hilico L, Karr J P 2016 Phys. Rev. Lett. 116 053003Google Scholar

    [59]

    Haidar M, Korobov V I, Hilico L, Karr J P 2022 Phys. Rev. A 106 022816Google Scholar

    [60]

    Babb J F 1998 Current Topics in Physics (Vol. 2) (Singapore: World Scientific) pp531–540

    [61]

    Zhang P P, Zhong Z X, Yan Z C 2013 Phys. Rev. A 88 032519Google Scholar

    [62]

    Korobov V I 2006 Phys. Rev. A 74 052506Google Scholar

    [63]

    Alighanbari S, Hansen M G, Korobov V I, Schiller S 2018 Nat. Phys. 14 555Google Scholar

    [64]

    Kortunov I V, Alighanbari S, Hansen M G, Giri G S, Korobov V I, Schiller S 2021 Nat. Phys. 17 569Google Scholar

    [65]

    Schenkel M R, Alighanbari S, Schiller S 2024 Nat. Phys. 20 383Google Scholar

    [66]

    Mohr P J, Newell D B, Taylor B N 2016 Rev. Mod. Phys. 88 035009Google Scholar

    [67]

    Germann M, Patra S, Karr J P, Hilico L, Korobov V I, Salumbides E J, Eikema K S E, Ubachs W, Koelemeij J C J 2021 Phys. Rev. Res. 3 L022028Google Scholar

    [68]

    Heiße F, Köhler-Langes F, Rau S, Hou J, Junck S, Kracke A, Mooser A, Quint W, Ulmer S, Werth G, Blaum K, Sturm S 2017 Phys. Rev. Lett. 119 033001Google Scholar

    [69]

    Stone A P 1961 Proc. Phys. Soc., London 77 786Google Scholar

    [70]

    Stone A P 1963 Proc. Phys. Soc., London 81 868Google Scholar

    [71]

    Volkov S 2018 Phys. Rev. D 98 076018Google Scholar

    [72]

    Zhong Z X, Zhou W P, Mei X S 2018 Phys. Rev. A 98 032502Google Scholar

    [73]

    Haidar M, Zhong Z X, Korobov V I, Karr J P 2020 Phys. Rev. A 101 022501Google Scholar

    [74]

    Bethe H A, Salpeter E E 1957 Quantum Mechanics of One- and Two-Electron Atoms (New York, NY: Springer Berlin Heidelberg) pp109–111

    [75]

    Kinoshita T 1990 Quantum Electrodynamics (Singapore: World Scientific) pp580–586

    [76]

    Kinoshita T, Nio M 1996 Phys. Rev. D 53 4909Google Scholar

    [77]

    Eides M I, Grotch H, Shelyuto V A 2007 Theory of Light Hydrogenic Bound States (Berlin: Springer Berlin Heidelberg) pp217–231

    [78]

    Mondéjar J, Piclum J H, Czarnecki A 2010 Phys. Rev. A 81 062511Google Scholar

    [79]

    Carlson C E, Nazaryan V, Griffioen K 2008 Phys. Rev. A 78 022517Google Scholar

    [80]

    Zemach A C 1956 Phys. Rev. 104 1771Google Scholar

    [81]

    Karshenboim S G 1997 Phys. Lett. A 225 97Google Scholar

    [82]

    Faustov R, Martynenko A 2002 Eur. Phys. J. C 24 281Google Scholar

    [83]

    Friar J L, Payne G L 2005 Phys. Rev. C 72 014002Google Scholar

    [84]

    Friar J, Sick I 2004 Phys. Lett. B 579 285Google Scholar

    [85]

    Bodwin G T, Yennie D R 1988 Phys. Rev. D 37 498

    [86]

    Karshenboim S G 2005 Phys. Rep. 422 1Google Scholar

    [87]

    Yan Z C, Drake G W F 1994 Can. J. Phys. 72 822Google Scholar

    [88]

    Yan Z C, Drake G 1996 Chem. Phys. Lett. 259 96Google Scholar

    [89]

    Korobov V I 2002 J. Phys. B: At., Mol. Opt. Phys. 35 1959Google Scholar

    [90]

    Harris F E, Frolov A M, Smith V H 2004 J. Chem. Phys. 121 6323Google Scholar

    [91]

    Dalgarno A, Lewis J T 1955 Proc. R. Soc. A 233 70

    [92]

    Lewis M L, Serafino P H 1978 Phys. Rev. A 18 867Google Scholar

    [93]

    Karr J P, Bielsa F, Douillet A, Gutierrez J P, Korobov V I, Hilico L 2008 Phys. Rev. A 77 063410Google Scholar

    [94]

    Menasian S C, Dehmelt H G 1973 Bull. Am. Phys. Soc. 18 408

    [95]

    Varshalovich D A, Moskalev A N, Khersonskii V K 1988 Quantum Theory of Angular Momentum (Singapore: World Scientific) pp79,484

    [96]

    Lindgren I, Morrison J 1982 Atomic Many-Body Theory (Berlin: Springer Berlin Heidelberg) pp91,93

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出版历程
  • 收稿日期:  2024-08-06
  • 修回日期:  2024-08-27
  • 上网日期:  2024-09-26
  • 刊出日期:  2024-10-20

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