Nuclear structure effects to atomic Lamb shift and hyperfine splitting

Ji Chen

doi:10.7498/aps.73.20241063

Abstract

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:

Authors and contacts

Ji Chen^1,2

1.
Key Laboratory of Quark and Lepton Physics, Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
2.
Southern Center for Nuclear-Science Theory, Institute of Modern Physics, Chinese Academy of Sciences, Huizhou 516000, China

Corresponding author: Ji Chen, jichen@ccnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12175083, 12335002, 11805078).

FullText HTML : translate this paragraph

References

[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

Cited By

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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)

DownLoad: CSV

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.

DownLoad: CSV

[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

[1]	Zhong Zhen-Xiang. Review of the hyperfine structure theory of hydrogen molecular ions. Acta Physica Sinica, 2024, 73(20): 203104. doi: 10.7498/aps.73.20241101
[2]	Chen Run, Shao Xu-Ping, Huang Yun-Xia, Yang Xiao-Hua. Simulation of hyperfine-rotational spectrum of electromagnetic dipole transition rotation of BrF molecules. Acta Physica Sinica, 2023, 72(4): 043301. doi: 10.7498/aps.72.20221957
[3]	Tang Jia-Dong, Liu Qian-Hao, Cheng Cun-Feng, Hu Shui-Ming. Hyperfine structure of ro-vibrational transition of HD in magnetic field. Acta Physica Sinica, 2021, 70(17): 170301. doi: 10.7498/aps.70.20210512
[4]	Peng Jun-Hui, Tikhonov Evgenii. First-principles study of vacancy ordered structures, mechanical properties and electronic properties of ternary Hf-C-N system. Acta Physica Sinica, 2021, 70(21): 216101. doi: 10.7498/aps.70.20210244
[5]	Li Jun, Liu Li-Sheng, Xu Shuang, Zhang Jin-Yong. Mechanical, electronic properties and deformation mechanisms of Ti₃B₄ under uniaxial compressions: a first-principles calculation. Acta Physica Sinica, 2020, 69(4): 043102. doi: 10.7498/aps.69.20191194
[6]	Huang Rui, Li Chun, Jin Wei, Georgios Lefkidis, Wolfgang Hübner. Ultrafast spin dynamics in double-magnetic-center endohedral fullerene Y₂C₂@C₈₂-C₂(1). Acta Physica Sinica, 2019, 68(2): 023101. doi: 10.7498/aps.68.20181887
[7]	Zhang Xiang, Lu Ben-Quan, Li Ji-Guang, Zou Hong-Xin. Theoretical investigation on hyperfine structure and isotope shift for 5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2 clock transition in Hg⁺. Acta Physica Sinica, 2019, 68(4): 043101. doi: 10.7498/aps.68.20182136
[8]	Pei Dong-Liang, He Jun, Wang Jie-Ying, Wang Jia-Chao, Wang Jun-Min. Measurement of the fine structure of cesium Rydberg state. Acta Physica Sinica, 2017, 66(19): 193701. doi: 10.7498/aps.66.193701
[9]	Ren Ya-Na, Yang Bao-Dong, Wang Jie, Yang Guang, Wang Jun-Min. Measurement of the magnetic dipole hyperfine constant Ahfs of cesium 7S1/2 state. Acta Physica Sinica, 2016, 65(7): 073103. doi: 10.7498/aps.65.073103
[10]	Wang Xin-Xin, Zhang Ying, Zhou Hong-Bo, Wang Jin-Long. Effects of niobium on helium behaviors in tungsten：a first-principles investigation. Acta Physica Sinica, 2014, 63(4): 046103. doi: 10.7498/aps.63.046103
[11]	Jin Shuo, Sun Lu. Stability of hydrogen in tungsten with carbon impurity: a first-principles study. Acta Physica Sinica, 2012, 61(4): 046104. doi: 10.7498/aps.61.046104
[12]	Yang Bao-Dong, Gao Jing, Wang Jie, Zhang Tian-Cai, Wang Jun-Min. Multiple electromagnetically-induced transparency of hyperfine levels in cesium 6S1/2 -6P3/2 -8S1/2 ladder-type system. Acta Physica Sinica, 2011, 60(11): 114207. doi: 10.7498/aps.60.114207
[13]	Yuan Peng-Fei, Zhu Wen-Jun, Xu Ji-An, Liu Shao-Jun, Jing Fu-Qian. High pressure phase transition and phonon-dispersion relations of BeO calculated by first-principles method. Acta Physica Sinica, 2010, 59(12): 8755-8761. doi: 10.7498/aps.59.8755
[14]	Li Jin, Gui Gui, Sun Li-Zhong, Zhong Jian-Xin. Structure transition of two-dimensional hexagonal BN under large uniaxial strain. Acta Physica Sinica, 2010, 59(12): 8820-8828. doi: 10.7498/aps.59.8820
[15]	Gu Juan, Wang Shan-Ying, Gou Bing-Cong. The geometrical structure, electronic structure and magnetism of bimetallic AunM2 （n=1,2; M=Sc, Ti, V, Cr, Mn, Fe, Co, Ni） clusters. Acta Physica Sinica, 2009, 58(5): 3338-3351. doi: 10.7498/aps.58.3338
[16]	Chen Sui-Yuan, Liu Chang-Sheng, Li Hui-Li, Cui Tong. Hyperfine stucture during nanocrystallization of amorphous Fe73.5Cu1Nb3Si13.5B9 alloy irradiated by laser. Acta Physica Sinica, 2005, 54(9): 4157-4163. doi: 10.7498/aps.54.4157
[17]	Wang Li－Jun, Yu Hui-Ying. The coherent excitation property of a two-level atom w itha hyperfine structure in narrow band laser field. Acta Physica Sinica, 2004, 53(12): 4151-4156. doi: 10.7498/aps.53.4151
[18]	Ma Hong-Liang, Lu Jiang, Wang Chun-Tao. Measurement of hyperfine structure spectrum in 56908 nm line of 141Pr+. Acta Physica Sinica, 2003, 52(3): 566-569. doi: 10.7498/aps.52.566
[19]	Zhao Lu-Ming, Wang Li-Jun. . Acta Physica Sinica, 2002, 51(6): 1227-1232. doi: 10.7498/aps.51.1227
[20]	LI GUANG-WU, MA HONG-LIANG, LI MAO-SHENG, CHEN ZHI-JUN, CHEN MIAO-HUA, LU FU-QUAN, PENG XIAN-JUE, YANG FU-JIA. HYPERFINE STRUCTURE MEASUREMENT IN LaⅡ5d2 1Ｇ4 →4f5d 1F3. Acta Physica Sinica, 2000, 49(7): 1256-1259. doi: 10.7498/aps.49.1256

Catalog

Vol. 73, Issue 20 - 2024-10-20

Metrics

Abstract views: 687
PDF Downloads: 46
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板