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精密原子光谱实验和理论在测量基本物理常数和检验量子电动力学理论中起着关键作用, 同时为研究原子核内部结构和发展高精度核结构理论提供重要观测平台. 许多原子光谱实验中, 核结构效应如电荷分布、磁矩分布和核极化度已被精确测定, 大大提高了核结构检测的精度. 本文系统论述了关于轻质量电子原子与缪子原子兰姆位移和超精细结构中的双光子交换效应的理论框架与研究发展. 着重介绍了先进的核力模型和核结构第一性原理计算方法在上述问题中的应用. 轻质量原子中双光子交换效应的理论研究对于从原子光谱测量中确定核电荷半径和Zemach半径具有重要作用. 这些研究结果不仅能加深对原子核内部结构以及核子-核子相互作用的理解, 还为未来实验提供重要的理论指导, 推进对质子半径难题以及其他轻核半径测量问题的理解.
The development of precision atomic spectroscopy experiments and theoretical advancements plays a crucial role in measuring fundamental physical constants and testing quantum electrodynamics (QED) theories. It also provides a significant platform for studying the internal structure of atomic nuclei and developing high-precision nuclear structure theories. Nuclear structure effects such as charge distribution, magnetic moment distribution, and nuclear polarizability have been accurately determined in many atomic spectroscopy experiments, significantly enhancing the precision of nuclear structure detection. This paper systematically reviews the theoretical research and developments on the corrections of two-photon exchange (TPE) effects on the Lamb shift and hyperfine structure (HFS) in light ordinary and muonic atoms. Advanced nuclear force models and ab initio methods are employed to analyze the TPE nuclear structure corrections to the Lamb shift in a series of light muonic atoms. The paper compares the calculation of TPE effects from various nuclear models and evaluates the model dependencies and theoretical uncertainties of TPE effect predictions. Furthermore, the paper discusses the significant impact of TPE theory on explaining the discrepancies between experimental measurements and QED theoretical predictions in atomic hyperfine structures, resolving the accuracy difficulties in traditional theories. Detailed analyses of TPE effects on HFS in electronic and muonic deuterium using pionless effective field theory show good agreement with experimental measurements, validating the accuracy of theoretical predictions. The theoretical studies of TPE effects in light atoms are instrumental for determining nuclear charge radii and Zemach radii from spectroscopy measurements. These results not only enhance the understanding of nuclear structure and nuclear interactions but also offer crucial theoretical guidance for future experiments, thereby advancing the understanding of the proton radius puzzle and related studies. -
Keywords:
- two-photon exchange /
- nuclear ab initio method /
- Lamb shift /
- hyperfine splitting
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图 1 轻子-原子核系统中的双光子交换费曼图, 从左至右依次对应箱图、交叉图与海鸥图. 波浪线、细直线、粗直线与椭圆分别对应光子、轻子、核基态与核激发态
Fig. 1. Two-photon exchange diagrams in lepton-nucleus systems. The diagrams from left to right are respectively the box, cross and seagull diagrams. Wiggled, thin-straight, thick-straight lines and ellipse represent respectively the photon, lepton, nuclear ground state and nuclear excited states.
表 1 不同μ原子中$ \delta_{\rm TPE} $的计算结果和理论误差(单位meV). 结果被分解为弹性部分和核极化部分, 以及单核子部分. 数据来源于文献[51]
Table 1. Theoretical prediction and uncertainty of $ \delta_{\rm TPE} $ in various muonic atoms (in unit of meV). The results are decomposed into elastic, polarizability, and single-nucleon parts. Data collected from Ref. [51].
$ \delta^{N}_{\rm el} $ $ \delta^{N}_{\rm pol} $ $ \delta^{A}_{\rm el} $ $ \delta^{A}_{\rm pol} $ $ \delta_{\rm TPE} $ $ \text{µ}^2{\rm H} $ –0.030(02) –0.020(10) –0.423(04) –1.245(13) –1.718(17) $ \text{µ}^3{\rm H} $ –0.033(02) –0.031(17) –0.227(06) –0.480(11) –0.771(22) $ \text{µ}^3 {\rm He}^{+} $ –0.52(03) –0.25(13) –10.49(23) –4.23(18) –15.49(33) $ \text{µ}^4 {\rm He}^{+} $ –0.54(03) –0.34(20) –6.14(31) –2.35(13) –9.37(44) 
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表 2 单质子、单中子、核弹性和核极化TPE效应对2H与µ2H中HFS的修正. 数据来源于文献[29]
Table 2. The single-proton, single-neutron, nuclear elastic, and nuclear-polarizability TPE contributions to HFS in 2H and µ2H. Data from Ref. [29].
2H (1S)/kHz µ2H (1S)/meV µ2H (2S)/meV $ E_{\rm el} $ –42.1(2.1) –0.984(46) –0.123(6) $ E_{\rm pol} $ 109.8(4.5) 2.86(12) 0.358(14) $ E_{\rm nucl}=E_{\rm el}+E_{\rm pol} $ 67.7(4.2) 1.878(88) 0.235(11) $ E_{\rm 1 p} $[71] –35.54(8) –1.018(2) –0.1272(2) $ E_{\rm 1 n} $[72] 9.6(1.0) 0.079(32) 0.010(4) $ \varDelta_{3\gamma} $ ±0.49 ±0.052 ±0.0065 $ E_{\rm TPE} $ 41.7(4.4) 0.94(11) 0.117(13) Ref. [64,65] 43 Ref. [26,69] mod 64.5 Ref. [70] 0.304(68) 0.0383(86) $ \nu_{\rm exp}-\nu_\text{QED} $[25,68] 45.2 0.0966(73) 注: “mod”对原文献修正核子反冲与极化效应; TPE效应在µ2H的1S和2S态中相差8倍.
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[1] Mohr P J, Taylor B N, Newell D B 2012 Rev. Mod. Phys. 84 1527
Google Scholar
[2] Pohl R, Antognini A, Nez F, et al. 2010 Nature 466 213
Google Scholar
[3] Antognini A, Nez F, Schuhmann K, et al. 2013 Science 339 417
Google Scholar
[4] Mohr P J, Newell D B, Taylor B N 2016 Rev. Mod. Phys. 88 035009
Google Scholar
[5] Xiong W, Gasparian A, Gao H, et al. 2019 Nature 575 147
Google Scholar
[6] Bernauer J C, Achenbach P, Ayerbe Gayoso C, et al. 2010 Phys. Rev. Lett. 105 242001
Google Scholar
[7] Gilman R, Downie E J, Ron G, et al. 2017 arXiv:1709.09753 [physics.ins-det]
[8] Pohl R, Nez F, Fernandes L M P, et al. 2016 Science 353 669
Google Scholar
[9] Krauth J J, Schuhmann K, Ahmed M A, et al. 2021 Nature 589 527
Google Scholar
[10] Schuhmann K, Fernandes L M P, Nez F, et al. 2023 arXiv:2305. 1 1679 [physics. atom-ph]
[11] Borie E 2012 Annals of Physics 327 733
Google Scholar
[12] Hellwig H, Vessot R F C, Levine M W, Zitzewitz P W, Allan D W, Glaze D J 1970 IEEE Trans. Inst. Meas. 19 200
Google Scholar
[13] Wineland D J, Ramsey N F 1972 Phys. Rev. A 5 821
Google Scholar
[14] Rosner S D, Pipkin F M 1970 Phys. Rev. A 1 571
Google Scholar
[15] Kowalski J, Neumann R, Noehte S, Scheffzek K, Suhr H, Putlitz G z 1983 Hyp. Int. 15 159
Google Scholar
[16] Guan H, Chen S, Qi X Q, et al. 2020 Phys. Rev. A 102 030801
Google Scholar
[17] Sun W, Zhang P P, Zhou P, et al. 2023 Phys. Rev. Lett. 131 103002
Google Scholar
[18] Sato M, Ishida K, Iwasaki M, et al. 2014 20th International Conference on Particles and Nuclei (Hamburg, Germany), August 24, 2014 pp460–463
[19] Pizzolotto C, Adamczak A, Bakalov D, et al. 2020 Eur. Phys. J. A 56 185
Google Scholar
[20] Amaro P, Adamczak A, Ahmed M A, et al. 2022 SciPost Phys. 13 020
Google Scholar
[21] Ohayon B, Abeln A, Bara S, et al. 2024 MDPI Phys. 6 206
Google Scholar
[22] Strasser P, Fukumura S, Ino T, et al. 2023 J. Phys.: Conf. Ser. 2462 012023
Google Scholar
[23] Schwartz C 1955 Phys. Rev. 97 380
Google Scholar
[24] Woodgate G K 1983 Elementary Atomic Structure. (2nd Ed.) (London, England: Oxford University Press) pp168–174
[25] Eides M I, Grotch H, Shelyuto V A 2001 Phys. Rep. 342 63
Google Scholar
[26] Friar J L, Payne G L 2005 Phys. Rev. C 72 014002
Google Scholar
[27] Rosenfelder R 1983 Nucl. Phys. A 393 301
Google Scholar
[28] Leidemann W, Rosenfelder R 1995 Phys. Rev. C 51 427
Google Scholar
[29] Ji C, Zhang X, Platter L 2024 Phys. Rev. Lett. 133 042502
Google Scholar
[30] Friar J, Rosen M 1974 Annals of Physics 87 289
Google Scholar
[31] Zemach A C 1956 Phys. Rev. 104 1771
Google Scholar
[32] Friar J, Sick I 2004 Phys. Lett. B 579 285
Google Scholar
[33] Carlson C E, Nazaryan V, Griffioen K 2011 Phys. Rev. A 83 042509
Google Scholar
[34] Kamada H, Nogga A, Glöckle W, et al. 2001 Phys. Rev. C 64 044001
Google Scholar
[35] Leidemann W, Orlandini G 2013 Prog. Part. Nucl. Phys. 68 158
Google Scholar
[36] Efros V D, Leidemann W, Orlandini G 1994 Phys. Lett. B 338 130
Google Scholar
[37] Efros V D, Leidemann W, Orlandini G, Barnea N 2007 J. Phys. G 34 R459
Google Scholar
[38] Nevo Dinur N, Barnea N, Ji C, Bacca S 2014 Phys. Rev. C 89 064317
Google Scholar
[39] Hernandez J O, Ji C, Bacca S, Nevo Dinur N, Barnea N 2014 Phys. Lett. B 736 344
Google Scholar
[40] Hernandez O, Ekström A, Dinur N N, Ji C, Bacca S, Barnea N 2018 Phys. Lett. B 778 377
Google Scholar
[41] Pachucki K 2011 Phys. Rev. Lett. 106 193007
Google Scholar
[42] Pachucki K, Wienczek A 2015 Phys. Rev. A 91 040503
Google Scholar
[43] Hernandez O J, Ji C, Bacca S, Barnea N 2019 Phys. Rev. C 100 064315
Google Scholar
[44] Friar J L 2013 Phys. Rev. C 88 034003
Google Scholar
[45] Emmons S B, Ji C, Platter L 2021 J. Phys. G 48 035101
Google Scholar
[46] Lensky V, Hagelstein F, Pascalutsa V 2022 Eur. Phys. J. A 58 224
Google Scholar
[47] Lensky V, Hagelstein F, Pascalutsa V 2022 Phys. Lett. B 835 137500
Google Scholar
[48] Carlson C E, Gorchtein M, Vanderhaeghen M 2014 Phys. Rev. A 89 022504
Google Scholar
[49] Nevo Dinur N, Ji C, Bacca S, Barnea N 2016 Phys. Lett. B 755 380
Google Scholar
[50] Ji C, Nevo Dinur N, Bacca S, Barnea N 2013 Phys. Rev. Lett. 111 143402
Google Scholar
[51] Ji C, Bacca S, Barnea N, Hernandez O J, Nevo-Dinur N 2018 J. Phys. G 45 093002
Google Scholar
[52] Wiringa R B, Stoks V G J, Schiavilla R 1995 Phys. Rev. C 51 38
Google Scholar
[53] Pudliner B S, Pandharipande V R, Carlson J, Wiringa R B 1995 Phys. Rev. Lett. 74 4396
Google Scholar
[54] Entem D R, Machleidt R 2003 Phys. Rev. C 68 041001
Google Scholar
[55] Navrátil P 2007 Few-Body Syst. 41 117
Google Scholar
[56] Pohl R, Nez F, Udem T, et al. 2017 Metrologia 54 L1
Google Scholar
[57] Parthey C G, Matveev A, Alnis J, Pohl R, Udem T, Jentschura U D, Kolachevsky N, Hänsch T W 2010 Phys. Rev. Lett. 104 233001
Google Scholar
[58] Shiner D, Dixson R, Vedantham V 1995 Phys. Rev. Lett. 74 3553
Google Scholar
[59] van Rooij R, Borbely J S, Simonet J, Hoogerland M D, Eikema K S E, Rozendaal R A, Vassen W 2011 Science 333 196
Google Scholar
[60] Cancio Pastor P, Consolino L, Giusfredi G, De Natale P, Inguscio M, Yerokhin V A, Pachucki K 2012 Phys. Rev. Lett. 108 143001
Google Scholar
[61] Zheng X, Sun Y R, Chen J J, Jiang W, Pachucki K, Hu S M 2017 Phys. Rev. Lett. 119 263002
Google Scholar
[62] Rengelink R J, Werf Y, Notermans R P M J W, Jannin R, Eikema K S E, Hoogerland M D, Vassen W 2018 Nature Phys. 14 1132
Google Scholar
[63] Huang Y J, Guan Y C, Peng J L, Shy J T, Wang L B 2020 Phys. Rev. A 101 062507
Google Scholar
[64] Khriplovich I B, Milshtein A I, Petrosian S S 1996 Phys. Lett. B 366 13
Google Scholar
[65] Khriplovich I B, Milstein A I 2004 J. Exp. Theor. Phys. 98 181
Google Scholar
[66] Faustov R N, Martynenko A P 2003 Phys. Rev. A 67 052506
Google Scholar
[67] Faustov R N, Martynenko A P, Martynenko G A, Sorokin V V 2014 Phys. Rev. A 90 012520
Google Scholar
[68] Krauth J J, Diepold M, Franke B, Antognini A, Kottmann F, Pohl R 2016 Ann. Phys. 366 168
Google Scholar
[69] Friar J L, Payne G L 2005 Phys. Lett. B 618 68
Google Scholar
[70] Kalinowski M, Pachucki K, Yerokhin V A 2018 Phys. Rev. A 98 062513
Google Scholar
[71] Antognini A, Hagelstein F, Pascalutsa V 2022 Ann. Rev. Nucl. Part. Sci. 72 389
Google Scholar
[72] Tomalak O 2019 Eur. Phys. J A 55 64
Google Scholar
[73] Antognini A, Lin Y H, Meißner U G 2022 Phys. Lett. B 835 137575
Google Scholar
[74] Tomalak O 2019 Phys. Rev. D 99 056018
Google Scholar
[75] Lin Y H, Hammer H W, Meißner U G 2021 Phys. Lett. B 816 136254
Google Scholar
[76] Lin Y H, Hammer H W, Meißner U G 2021 Eur. Phys. J. A 57 255
Google Scholar
[77] Lin Y H, Hammer H W, Meißner U G 2022 Phys. Rev. Lett. 128 052002
Google Scholar
[78] Kelly J J 2004 Phys. Rev. C 70 068202
Google Scholar
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